Final Report
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AN IMPULSIVE NOISE SOURCE POSITION LOCATOR
Final Report February 2002
P J Moore, I A Glover and C H Peck Department of Electronic and Electrical Engineering University of Bath
CONTENTS 1
SUMMARY
6
2
ACKNOWLEDGEMENTS
7
3
INTRODUCTION
8
4
TIME DELAY ESTIMATION
9
4.1 TECHNIQUES FOR ESTIMATING TIME DIFFERENCE OF ARRIVAL 4.2 OVERVIEW OF TIME DELAY ESTIMATION TECHNIQUES 4.2.1 General model for time delay estimation 4.2.2 Frequency domain weighting function 4.2.3 The smooth coherence transform (SCOT) 4.2.4 Hannan and Thomson processor 4.2.5 Spectral estimation 4.3 ADAPTIVE TIME DELAY ESTIMATION BASED ON CUMULANTS (ATDC) 4.4 SIMULATIONS AND RESULTS 5
9 9 10 12 13 14 15 16 18
DIRECTWAVE CROSS CORRELATION – A PROPOSED NEW TECHNIQUE22 5.1 SIGNAL MODELLING IN A MULTIPATH ENVIRONMENT 5.2 DIRECTWAVE CROSSCORRELATION (DWCC) 5.2.1 Time domain windowing 5.2.2 Signal truncation 5.2.3 Hanning window
22 25 25 25 27 ∧
5.2.4 5.2.5 5.2.6 5.2.7 5.2.8 5.2.9 6
Finding the optimum window delay parameter, Q Extension to multiple sensor inputs Limitations of the algorithm Algorithm flow chart Application of frequency weighting function Practical tests and results
SOURCE LOCATION 6.1 OVERVIEW OF DIFFERENT POSITION LOCATION TECHNIQUES 6.1.1 Direction Finding Position Location Systems 6.1.2 Rangebased Position Location System 6.1.3 Elliptical Position Location Systems 6.1.4 Hyperbolic Position Location System 6.2 COMPARISON OF POSITION LOCATION TECHNIQUES 6.3 HYPERBOLIC POSITION LOCATION SYSTEMS 6.4 SOLUTIONS FOR HYPERBOLIC POSITION FIXES 6.4.1 ThreeInput Position Location Systems 6.4.2 FourInput Position Location Systems 6.5 SIMULATION OF HYPERBOLIC POSITION LOCATION SYSTEM 6.6 DIFFICULTIES IN ESTIMATING POSITION LOCATION USING TDOA
7
HARDWARE 7.1
THE EFFECTS OF FINITE SAMPLING RATE
29 30 30 31 32 32 38 38 38 39 40 41 42 42 43 43 46 47 48 52 52
7.2 5.2 COMMON ARRAY GEOMETRIES 7.2.1 Uniformly spaced linear array 7.2.2 Square Array 7.2.3 YArray 7.3 GENERAL IMPLICATIONS OF A RESOLUTION MAP 7.4 EMPIRICAL DEMONSTRATION OF SPATIAL QUANTISATION EFFECTS 7.5 ARRAY CONSTRUCTION 7.6 ARRAY CALIBRATION 7.7 DATA ACQUISITION 7.8 MEASURES TO MINIMISE INTERFERENCE INDUCES ERRORS 7.8.1 Use of quickform cables 7.8.2 Precision cable lengths 7.8.3 Fibre optic links 8
EXPERIMENTAL RESULTS 8.1 TESTS CONDUCTED AT OATS, SEPTEMBER 2001 8.1.1 Impulsive interference noise source 8.1.2 Measurement setup 8.1.3 Results using small monopole antenna elements 8.2 TESTS CONDUCTED AT THE UNIVERSITY, DECEMBER 2001
9
ON SITE APPLICATION OF INTERFERENCE LOCATION 9.1 9.2 9.3 9.4 9.5
10 10.1 10.2
INTRODUCTION PROCEDURE RESULTS ANALYSIS OF RESULTS RELATIONSHIP OF IMPULSIVE NOISE WITH 50 HZ WAVEFORMS CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER WORK CONCLUSIONS RECOMMENDATIONS FOR FURTHER WORK
54 55 56 56 58 58 59 60 61 62 62 62 62 63 63 63 63 64 65 68 68 70 72 73 74 77 77 77
11
REFERENCES
79
12
APPENDICES
83
12.1 12.2 12.3 12.4
BICONICAL ANTENNA SPECIFICATIONS TESTS CONDUCTED IN UNIVERSITY SPORTS HALL, DECEMBER 2001 RESULTS FROM SITE CASE STUDY, BIRMINGHAM, OCTOBER 2001 SQUARE ARRAY LOCATED IN FRONT GARDEN
83 84 87 88
Page 2
1
L IST OF F IGURES
Figure 5.1 Overview of locator 8 Figure 6.1 Model of impulsive noise propagation and time delay estimation. 12 Figure 6.3 Configuration of the adaptive time delay estimation method based on cumulants (ATDC). 17 Figure 6.4 Simulated signals for time delay estimations. 18 Figure 6.5Time delay estimation by four different techniques: 1. Cross Correlation, 2. SCOT, 3. HT processor and 4. ATDC. 19 Figure 6.6 Plot of two signals received at a spatial separation of 0.46 m. 20 Figure 6.7 Performance of different processors under a practical test. 21 Figure 7.1 Impulsive noise reception via a plane reflecting surface. 22 Figure 7.2 Impulsive noise received at an antenna spacing of 0.79 m. 26 Figure 7.3 Recorded signal pair showing difference in arrival time and regions containing direct signals only and direct signals plus image signals (multipath). 26 Figure 7.4 Illustration of preprocessing for DWCC. 28 Figure 7.5. Flow chart for DWCC algorithm. 31 Figure 7.6 Array configuration and definition of delays. 32 Figure 7.7 Time delay D23 versus window width. 33 Figure 7.8 Time delay D24 versus window width. 33 Figure 7.9 Time delay D34 versus window width. 34 Figure 7.10 Variance of six time delays versus source angle for window width of 50 samples. 34 Figure 7.11 Variance of six time delays versus source angle for window width of 70 samples. 35 Figure 7.12 Variance of six time delays versus source angle for window width of 50 samples. 35 Figure 7.13 Time delay D23 versus source angle. 36 Figure 7.14 Time delay D24 versus source angle. 36 Figure 7.15 Time delay D34 versus source angle. 37 Figure 8.1 Direction Finding Based Position Location. 38 Figure 8.3 Antenna location coordinates for threesensor system. 44 Figure 8.4 Example 1: Source Location = (6, 2) m, sensor spacing = 0.79 m. 48 Figure 8.5 Example 2: Source Location (6,2) m, sensor spacing = 0.79 m. 48 Figure 8.6 Threesensor position location system using linear array geometry. 49 Figure 8.7 Location error versus source location and sensor spacing for βerror = 1 deg. 49 Figure 8.8 Graph of source location versus time delay. 51 Figure 8.9 Graph of source location versus time delay for two sensor spacings. 51 Figure 9.1 Signals received by (a) sensor 1 and (b) sensor 2 respectively and (c) the correlation of the two signals. 52 Figure 9.2 Plot to assess spatial resolution. 53 Figure 9.3 Sensor arrays of different geometries. 54 Figure 9.4 Resolution map for uniformly spaced linear array. 55 Figure 9.5 Resolution map for square array. 56 Figure 9.6 Resolution map for Yarray. 57 Figure 9.7 Resolution map of yarray using reduced (three) delay set. 57 Figure 9.8 Estimated location of sources at known positions. 59 Figure 9.10 Prototype square array, 2 m spacing 60 Figure 9.11 Calibration result. 61 Figure 9.12 Impulsive noise acquisition based on direct sampling. 61 Figure 10.1 OATS tests setup. 64 Figure 10.2 Monopole sensor used on array for OATS tests. 64 Figure 10.3 Results of Whyteleaves tests using small monopole antenna elements  in all cases the source was located 10 m from the locator. 65
Page 3
Figure 10.4 Y shaped array consisting of biconical elements being tested in the University Sports Hall 66 Figure 10.5 Results of University Sports Hall tests using biconical antennas in all cases the source was located at a bearing of 70° from the locator. 67 Figure 11.1 Plan view of house 68 Figure 11.3 Photographs showing details of the antennas and stand. 70 Figure 11.4 Rectangular array arrangement using antennas in both the front and back garden. 71 Figure 11.5 Signals obtained from antenna array depicted in figure 7.4 72 Figure 11.6 Diagrams representing the locating position of the interference source calculated from the measurements. 74 Figure 11.7 Graph showing distribution of 100 interference pulses recorded with respect to the point on wave of single phase mains voltage at domestic property (1 impulse recorded per half cycle). 75 Figure 11.8 Graph showing distribution of 500 interference pulses recorded from impulsive noise generator (see section 6.1.1) with respect to the point on wave of supply voltage (typically 510 impulses recorded per half cycle). 76 Fig. A2.1. Source at 30m 700 84 Fig. A2.2 Source at 20m 700 85 Fig. A2.3. Source at 15m 700 86 Figure A3.2 Waveforms recorded from antennas in figure A3.1. 87 Figure A3.3 Square array arrangement located in front garden 88 Figure A3.4 Waveforms recorded from antennas in figure A3.3. 89
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2
L IST OF TABLES
Table 6.1 Table of different processors that employ frequency domain weighting functions to improve correlation peak. 13 Table 7.1 Physical interpretation of terms in equation (3.8) for a single plane reflector. 24 Table 10.1 Summary of location results for Sports Hall tests (all results are the average of 5 separate waveforms). 66 Table 10.2 Signal and background noise magnitudes at varying distances 67 Table A2.1. Results of location estimation. 84 Table A2.2. Results of location estimation. 85 Table A2.3. Results of location estimation. 86
Page 5
3
S UMMARY
This report is the final deliverable of Radiocommunications Agency contract AY 3925, Design and production of a working prototype system to capture and store data on intermittent and wideband EMC disturbances which can subsequently be used to trace and identify the disturbance. The report describes the progress on the development of the interference locator during the period January to December 2001. The interference locator is based on the reception of a radiated impulsive interference signal on an array of antenna elements. The time delay apparent from the signal received at different array elements is calculated using a digital correlation approach; all signals from the elements are directly converted into digital form via the use of a 4 channel sampling oscilloscope operating at 2.5 or 25 Giga samples per second (GSps). The position of the noise source is subsequently calculated from the time delays using a hyperbolic location algorithm. The locator has been tested using a variety of experimental approaches and array constructions. In tests performed to measure the bearing of the source from the array, the locator worked to an accuracy of better than 3 degrees. For range measurements up to 30 m, the locator was accurate to within 3 m. Further testing is needed to confirm its ultimate limit, but it is estimated that it will operate for ranges up to 100 m. The locator has been successfully used on site, being able to locate partial discharges on a tv antenna situated below a 132 kV overhead line. Recommendations are given for further work including development of the algorithm to allow 3 dimensional positioning, improved time delay estimation, 50 Hz waveform point on wave analysis. Additionally, more testing of the locator is proposed; it is suggested that the locator is mounted in a vehicle to allow easier site testing.
4
A CKNOWLEDGEMENTS
This work was the result of the efforts of many people. The authors would particularly like to express their thanks to the following:
John Leadbetter
Radiocommunications Agency
Bill Martin
Radiocommunications Agency
Sean O'Connell
Radiocommunications Agency
Bob Taylor
Radiocommunications Agency
Mike Edwards
University of Bath
Dave Hatten
University of Bath
Iliana Portugués
University of Bath
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5
I NTRODUCTION
This report is the final deliverable of Radiocommunications Agency contract AY 3925 Design and production of a working prototype system to capture and store data on intermittent and wideband EMC disturbances which can subsequently be used to trace and identify the source. This work follows on initial studies made by the University of Surrey [Agi00]. The report describes the progress on the development of the interference locator during the period January to December 2001. An overview of the locator system is shown Figure 5.1. Radiated signals from an impulsive noise source are received by an array of antennas. The antenna signals are digitised, using a 4 channel sampling oscilloscope, and transferred to a laptop computer for analysis. The time delay apparent from the signal received at different array elements is calculated using a digital correlation approach. The position of the noise source is subsequently calculated from the time delays using a hyperbolic positioning algorithm. Since the system is designed to locate, in terms of bearing and range, the noise source from a position outside of the antenna array, the time delay between array elements has to be calculated to a very high degree of accuracy. Impulsive noise source Antenna array
PC
Digitiser
Figure 5.1 Overview of locator The following sections describe the work conducted into establishing (section 2) and optimising (section 3) the time delay estimation approach, the location algorithm (section 4), the hardware (section 5), testing (section 6) and conclusions (section 7).
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6
T IME DELAY ESTIMATION
To develop an interferencelocator based on closely spaced antenna elements requires accurate time delay estimation. This may be achieved by exploiting the impulsive character of the noise sources expected to be of interest in this project. By observing the signal’s characteristics closely, it is anticipated that a time delay estimation technique may be derived on the basis of the following features. The signals are typically large, wideband, transients with rapidly rising edges. A signal detection algorithm may not be necessary and a simple triggering algorithm base on amplitude may be adequate. Improved correlationbased location can be achieved by reducing the effects of multipath propagation and the effects of crosstalk between the receiving array elements. Performance may be further improved by minimising distortion that could result in the location receiver frontend via appropriate antenna design and strategic geometrical arrangement of the array elements. This section addresses some of the fundamental issues raised by these observations.
6.1
Techniques for estimating time difference of arrival
The Time Difference of Arrival (TDOA) of a signal can be estimated in two ways. These are: 1. Differencing of the absolute Time of Arrival (TOA) measurements made at each sensor 2. Crosscorrelating the signal received at one (or more) sensor(s) with the signal received at all other sensors While (1) is feasible, (2) dominates the field of TDOA estimation in practice due to its easier implementation. The discussion of TDOA estimation here is therefore restricted to that based on crosscorrelation. In the following section, a general model for TDOA estimation is developed and the techniques for TDOA estimation are presented.
6.2
Overview of time delay estimation techniques
The timedelay estimation problem occurs in various applications, e.g. the determination of range and bearing in radar and sonar problems [Nik88,Car81,Kna76,Ham74]. It also has some more esoteric applications, such as the measurement of the temperature of a molten alloy. Other applications include tracking and location of Radio Frequency (RF) sources [Tun00]. 6.2.1
General model for time delay estimation
A basic model for the estimation of time delay comprises records from two sensors of a signal in the presence of noise, one signal record being a delayed replica of the other, see Page 9
Figure 6.1. The signals, x1(t) and x2(t), received by a pair of sensors, spatially separated by a distance cD, (c = 3 x 108 m/s is the propagation velocity of e/m waves) are given by:
x1 (t ) = s (t ) + n1 (t )
(6.1)
x 2 (t ) = αs (t + D ) + n 2 (t )
(6.2)
where D is the delay (to be estimated), α is the relative amplitude of the second signal, n1(t) and n2(t) are widesense stationary, uncorrelated, Gaussian noise processes. The impulsive ‘noise’ signal of interest, s(t), is also uncorrelated with n1(t) and n2(t) and, being of finite duration, may be treated deterministically. This representation assumes no prior knowledge of the signal’s characteristics 6.2.2
Crosscorrelation
Estimation of time delay D is conventionally achieved using the crosscorrelation function Cx,x(τ). This is a measure of the similarity of two functions xi(t) and xj(t) as one is displaced through time by an amount τ relative to the other. Cx,x(τ).is given by:
[
C xi x j (τ ) = E xi (t ) x j (t + τ )
]
i, j = 1,2
(6.3)
Although calculation of the crosscorrelation function is essentially a time domain problem, many modifications of this approach have been made based on frequency domain techniques. It is therefore appropriate at this point to further develop the frequency domain analysis. The frequency spectrums of the signal and noise components are given by: X ( f ) = F{x i (t )}
(6.4)
S ( f ) = F{s (t )}
(6.5)
N ( f ) = F{ni (t )}
(6.6)
where F denotes the Fourier transform. section 6.6 describes how consistent frequency domain estimates of stationary signals can be obtained. The cross power spectral density can be calculated using the WienerKhinchine theorem, i.e.:
{
Pxi x j ( f ) = F C xi x j (τ )
}
(6.7)
or, more directly, using: ∗
Pxi x j ( f ) = X i ( f ) X j ( f )
(6.8)
Making substitutions from equations (6.1)and (6.2) via equations (6.4) and (6.5) (using the Fourier transform time delay theorem) into equation (6.8):
Page 10
Px1 x2 ( f ) = [ S ( f ) + N 1 ( f )][αS ( f )e − jωD + N 2 ( f )]∗
(6.9)
Since it is assumed that the signal and noise are uncorrelated the crossspectral density simplifies to: Px1 x2 ( f ) = αPss ( f )e − jωD + Pn1n2 ( f )
(6.10)
If the distance between sensors recording the two signals is greater than the spatial decorrelation distance of the noise process then n1(t) and n2(t) are uncorrelated. The result is that the second term of equation (6.10) is negligible and equation (6.10) reduces to: Px1 x2 ( f ) = αPss ( f )e − jωD
(6.11)
Equation (6.11) can be expressed in time domain as: C x1 x2 (τ ) = αC ss (τ ) *δ (τ − D ) , * denotes convolution
(6.12)
Equation (6.12) shows that the correlation peak of Css(τ) is displaced by (the time delay) D seconds which may therefore be readily estimated. Given the foregoing assumptions, Css(τ) is the autocorrelation of the target signal s(t). Cx1,x2(τ) can be estimated from a finite number of observations of the antenna signals x1(t) and x2(t).
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6.2.3
Frequency domain weighting function
Wave propagation
In practice, the nonideal signal propagation environment can make estimation of D problematic. Signals from an impulsive noise source
s(t)
s(t)
H1 (t)
H2 (t)
Nonideal transmission path
D
Delay caused by spatial difference
x 1 (t)
x 2 (t) F{}
Signal reception and processing
F{}
Transform to frequency domain
ψ(f)
Frequency domain weighting function
F1 (f)
Inverse transform to time domain
ˆ D
Peak detection
Time delay estimation
Figure 6.1 Model of impulsive noise propagation and time delay estimation. This can be modelled by modification of equation (6.12) in the frequency domain:
∫
C x1 x2 (τ ) = ψ ( f ) Px1x2 ( f ) exp( j 2πfτ )df
(6.13)
where ψ ( f ) is a frequency weighting function given by H 1 ( f ) H * 2 ( f ) . H 1 ( f ) and H 2 ( f ) are the frequency responses of the transmission paths between the impulsive noise source and the receiving antennas as shown in Figure 6.1. Note that in the direct crosscorrelation calculation there is no weighting function introduced to compensate for the effects of H 1 ( f ) and H 2 ( f ) i.e. ψ ( f ) =1. Consequently, the correlation will be poor when the signaltonoise Ratio (SNR) is low. To improve the situation, the weighting function can be estimated and many approaches have been developed including the Roth processor [Rot71], the Smoothed Coherence Transform (SCOT) [Car73b], the Eckart filter [Kna76] and the Hannan and Thomson (HT) processor [Han73]. Their main characteristics and differences are summarised in Table 6.1.
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Processor Name
Frequency Domain Weighting Function
Crosscorrelation
1
Roth
1 / Px1 x1 ( f )
SCOT
or
1 / Px2 x2 ( f )
1 Px1 x1 ( f ) ⋅ Px2 x2 ( f )
Eckart
Pss [ Pn1n1 ( f ) Pn2 n2 ( f )]
HT
γ x1x2 ( f )
2
2 Px1 x2 ( f ) ⋅ 1 − γ x1 x2 ( f )
Table 6.1 Table of different processors that employ frequency domain weighting functions to improve correlation peak. The SCOT [Car73b] and the HT [Han73] weighting functions have been applied to the case of impulsive noise source direction finding and location respectively [Pec01][Tun00] and are therefore of particular interest. 6.2.4
The smooth coherence transform (SCOT)
The SCOT is defined as a Fourier transform of the weighted coherence function. i.e.:
∫
C x1x2 (τ ) = W ( f )γ x1 x2 ( f )e jw τ df
(6.14)
where, γx1x2(f), the coherence function is given by: γ x1 x2 ( f ) =
Px1x2 ( f ) Px1 x1 ( f ) Px2 x2 ( f )
(6.15)
and W ( f ) is a smooth (e.g. Hanning) windowing function. The numerator of γ in equation (6.14) is the crossspectral power function being transformed and the denominator is the frequency domain weighting function that compensates at least in part for the effects of the different channel characteristics H1(f) and H2(f). The SCOT is designed to accentuate the peak of a cross correlation function by introducing a weighting function specifically to determine time delay under the influence of weak correlated noise. The problem is best described using Figure 6.2 below:
Page 13
x1(t)
s(t)
n1 (t) n 2(t)
D
x2(t)
Figure 6.2Model of noise addition process in delayed and nondelayed channels. Consider a case where the three sources s (t ) , n1 (t ) and n2 (t ) are uncorrelated. Both x1 (t ) and x 2 (t ) contain the signal components of s (t ) with the signal component of
x 2 (t ) being spatially delayed by time D. If the total power of the uncorrelated components, n1 (t ) and n2 (t ) is more than that of s (t ) , then the true correlation peak indicating the time delay may be obscured. The noise components however cannot be removed by filtering since s (t ) may contain both broadband and narrowband components. The (complex) coherence spectrum of x1 (t ) and x 2 (t ) may be written as:
γ x1x2
Pss ( f ) ⋅ e jωD = [ Pss ( f ) + Pn1n1 ( f )]1 / 2 [ Pss ( f ) + Pn2 n2 ( f )]1 / 2
(6.16)
If the spectrum of Pn1n1 ( f ) or Pn2 n2 ( f ) is much larger than Pss ( f ) at only a few frequencies, then γ x1 x2 ( f ) 2 since the higherorder cumulants of a nonGaussian signal can be recovered even in the presence of coloured (i.e. nonwhite) Gaussian noise [Nik93a][Nik93b][Men91][Swa91]. [Chi90][Nik88] saw the advantage of using higher order statistics and developed a technique for estimating the difference in arrival time between signals corrupted by spatially correlated Gaussian noise source of unknown correlation. The adaptive time delay estimation technique [Chi90] based on cumulants is described in Figure 6.3.
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C x1 x1 x1 (τ , ρ )
x1 (t )
T HIRD M OMENT COMP UTATION
C x3 x1 x1 (τ , ρ )
FIR FILTER
ADAPTIVE ALGORITHM
C x2 x1 x1 (τ , ρ )
CROSST HIRD MOMENT COMP UTATION
x2 (t )
Desired Out put

+ e(τ,σ)
Figure 6.3 Configuration of the adaptive time delay estimation method based on cumulants (ATDC). For the stationary case and assuming α = 1 , equations (6.1) and (6.2) may be rewritten as: s (t − D) = x1 (t − D) − n1 (t − D)
(6.25)
x 2 (t ) = x1 (t − D ) − n1 (t − D) + n 2 (t )
(6.26)
This may be rewritten in a more general form suitable for practical purposes as: x 2 (t ) =
P
∑ a x (t − i ) − n (t − D) + n i 1
1
2 (t )
i=− P
, P >> D
(6.27)
To form a thirdorder moment both sides of equation (6.26) are multiplied by x1 (t + τ )x1 (t + ρ ) (where ρ, like τ, is a time shift) and the expectation is then taken which results in: C x2 x1x1 (τ , ρ ) =
P
∑a C i
i=−P
x1x1x1 (τ
+ i, ρ + i ) − C n1 x1x1 (τ + D, ρ + D ) + C n2 x1x1 (τ , ρ )
(6.28)
where: C xi x j xk (τ , ρ ) = E[ x i (t ) x j (t + τ ) x k (t + ρ )]
, i, j, k = 1,2,3
(6.29)
Equation (6.28) may be further simplified since the last two terms of the equation are zero because the signal and noise are zero mean and the signal is independent of both noise waveforms (which are assumed to be Gaussian). Based on the parametric model described by (6.28), an adaptive version may be formed: C x2 x1x1 (n, τ , ρ ) =
P
∑ a (n)C i
i =− P
x1 x1x1 ( n, τ
+ i, ρ + i )
(6.30)
Page 17
The adjustment criteria, which determines the most suitable FIR filter coefficients {ai }, is given by: C x3 x1 x1 (τ , ρ ) =
6.4
P
∑a C i
i=P
x1 x1x1 (τ
+ i, ρ + i )
(6.31)
Simulations and results
Four different techniques have been tested using simulated waveforms generated by MatLab routines. The signaltonoise ratio (SNR) is defined as 20 log 10 (σ s σ n ) where σ s and σ n are the standard deviation of the signal and noise respectively. The signal consists of a sin(x)/x (sinc) function, whereas the noise is composed of part white noise (i.e. uncorrelated) and part coloured noise (i.e. correlated). The SNR in the simulation is set at 0 dB and a time delay of 16 samples is adopted between the two signals. The simulated signals are shown in Figure 6.4.
Figure 6.4 Simulated signals for time delay estimations. The simulated waveforms were applied to four different processors: (i) Crosscorrelation, (ii) SCOT, (iii) HT and (iv) ATDC. The results, Figure 6.5, show that all four processors were able to accurately determine the time delay. However, the presence of coloured noise is seen to produce multiple peaks in the time delay estimation for all processors except the ATDC. Particularly in the crosscorrelation and HT processors, the peak relating to the coloured noise component is ∼60% of the amplitude of the sinc function peak. The coloured noise peak can severely degrade the delay estimate if the time delay is small since a small delay separation will cause the true peak to be overlapped by the noise peak. Similarly a smaller signal to noise ratio will tend to equalise the size of the peaks making identification of the correct (signal) peak difficult.
Page 18
Figure 6.5Time delay estimation by four different techniques: 1. Cross Correlation, 2. SCOT, 3. HT processor and 4. ATDC. The four time delay processors were further investigated using a practical test, carried in a University classroom as described in section 7. The test consisted of two antennas separated spatially by 0.46 meters. The signals, Figure 6.6, were captured in a 1 GHz bandwidth channel using a sampling rate of 2.5 GSps. To improve the resolution of the estimates, the signals were interpolated by a factor of 10 making the effective pseudosampling rate of 25 GSps. In total 50 pairs of signals were taken with the interference source place on the line joining the antenna pair at a range of 8.0 meters from the nearest antenna. The captured signals were processed using the four algorithms already described; the maximum variance σ 2 of the estimated time delay was computed to be about 0.1 of a sample over the 50 sets of data. The output of the four techniques can be seen in Figure 6.7.
Page 19
Figure 6.6 Plot of two signals received at a spatial separation of 0.46 m. Since the source was located to yield a maximum time delay between the antenna pairs, the anticipated time delay (for a separation of 0.46 m) was 38.3 samples. The best processors were the HT and SCOT that gave an apparent error of 1.6 samples. This corresponds to an angular error of 2.39 degrees and is an improvement on earlier work [Pec01] (obtained principally by using a higher sampling rate). Given that the sampled signal data was interpolated by a factor of 10, these results were rather disappointing since none of the processors demonstrated errors of less than 1 sample. In view of the need for extreme accuracy of time delay estimation in order to able to locate sources outside of the antenna array boundary, none of these techniques can be used in the form shown. It is possible that the error observed is not inherent in the processing algorithms but is caused by one or more other factors. Candidate factors are: •
The effect of multipath
•
Mutual coupling between the antennas
•
Design and construction of the receiving frontend and array geometry
The latter two factors can be improved by hardware design, however, the problem of multipath propagation can only be resolved algorithmically. For this reason, the further development of the time delay estimation technique will take account of this effect.
Page 20
Figure 6.7 Performance of different processors under a practical test.
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7
D IRECT  WAVE CROSS CORRELATION – A PROPOSED NEW TECHNIQUE
Existing time delay estimation (see section 2) techniques have been shown to be inadequate in the context of impulsive noise sources for estimating very short time delays between the elements of receiving antenna array with small physical dimensions. DirectWave CrossCorrelation (DWCC) is a proposed new time delay estimation technique. In this section the principles of DWCC are explained and the algorithm presented in the context of manual signal inspection. Its engineering utility is underlined by observation of signal trends obtained from practical experiments. The performance of DWCC is realistic and well demonstrated with a resolution of better than 40×1012 s under practical conditions. It is especially formulated for the estimation of very short time delays using an impulsive noise process as the signal source.
7.1
Signal modelling in a multipath environment
The problem considered is that of measuring the delay between a pair of spatially separated antennas with spacing L. Consider the idealised reflective surface with a flat geometry depicted in Figure 7.1(diffuse multipath arising from surface irregularities is ignored.) The incident field at the receiving antennas comprises two components. These are: •
Freespace components that propagate from the source to the receiving antennas along direct paths
•
Multipath components that result from specular reflections
The freespace components are referred to as direct signals. The reflected components are referred to as image signals (since they reach the receiving antennas along paths that appear to originate from images of the source). True source (Point source assumption) a
b Finite duration True impulse
L c
Reflected impulse
Sensor 2 d
e
Reflective surface
Impulsive noise train
Sensor 1
Image source 1
Image source 2
Figure 7.1 Impulsive noise reception via a plane reflecting surface.
Page 22
A direct component propagates from the source to the receiving antenna via a direct transmission path and reaches Antenna 1 in the shortest possible time. A direct component also propagates via a direct transmission path to Antenna 2; the wavefront arriving at Antenna 2 after a time delay Dcb relative to reception at Antenna 1. The relative delay can expressed in terms of the absolute delays between source and Antennas 1 and 2 by: Dcb = D ab − Dac
(7.1)
where Dab and Dac are time delays from source to the respective antennas. Evaluating the delay is simple if the effects of multipath are negligible. If multipath is present, however, the problem of estimating time delay becomes more difficult. Unfortunately, the conditions under which the locator will be operated are likely to give rise to significant multipath propagation. In a case where a flat reflective surface is present, see Figure 7.1, a number of image sources, equal to the number of antennas employed must be considered. This confuses a conventional time delay algorithm and degrades its performance. The signal x1 (t ) received by the antenna closest to the source can be written as: x1 (t ) = s(t ) + n1 (t ) +
M
∑ρ
v
y v (t + J v (t ))
v =1
(7.2)
where s (t ) is the unknown direct signal (assumed to be a zeromean stationary random process), n1 (t ) is zeromean Gaussian noise statistically independent of s (t ) and the last term of the equation is a sum of M multipath components. On reflection, s(t) is modified by a transfer function h(t ) to give y (t ) = s (t ) * h(t ) . The reflected wave is shifted in time and altered in amplitude by a time delay J (t ) , that allows for nonzero relative velocity between at least two components in the system (selected from source, receiving antenna and reflecting plane(s)) and a gain factor ρ. The signal x 2 (t ) received by the second antenna comprises a delayed (and scaled) version of the direct signal received by the first antenna plus a set of image signals, i.e.: x 2 (t ) = α s(t + D (t )) + n 2 (t ) +
N
∑β w=1
w y w (t
+ K w (t ))
(7.3)
where α and β are gain factors and D (t ) and K (t ) are time delays for the directwave and reflected wave components respectively. n2 (t ) is zeromean Gaussian noise statistically independent of s (t ) . The last term of the equation represents the sum of N reflected waves where N may be different from M. The reflection process is assumed to be ideal i.e. h( f ) = 1 for the worstcase scenario. The source is assumed to be a stationary point source and the radiated signals are assumed to approach the antennas at a velocity c giving a respective time delay for each signal that is invariant with time. Under these conditions, the multipath model of Figure 7.1 is simplified and the equations above can be rewritten as: Page 23
x1 (t ) = s(t ) + n1 (t ) +
M
∑ ρ s(t + J v
v)
v =1
x 2 (t ) = α s (t + D ) + n 2 (t ) +
(7.4)
N
∑β
w s (t
+ Kw )
w=1
(7.5)
Estimation of D is conventionally achieved using the crosscorrelation function. This is a measure of the similarity of two functions x1 and x 2 as one is displaced through time τ relative to the other, and is defined by: C x1x2 (τ ) = E [x1 (t ) x 2 (t + τ )]
(7.6)
where E[ ] denotes the statistical expectation. Without considering the effects of multipath and assuming that n1 (t ) and n2 (t ) are zeromean, spatially uncorrelated, Gaussian processes, the crosscorrelation is: C x1 x2 (τ ) = αC ss (τ ) * δ (τ − D) , * denotes convolution
(7.7)
In the presence of multipath propagation, however, the complete description becomes: C x1 x2 (τ ) = α C ss (τ ) * δ (τ − D) + M
∑ρ αC v
ss (τ ) ∗ δ (τ
v =1
N
∑β
w C ss
(τ ) ∗ δ (τ − K w ) +
w =1
M
− ( D − J v )) +
N
∑∑ ρ
v β w C ss
(τ ) ∗ δ (τ − ( K w − J v ))
v =1 w =1
(7.8)
Assuming that there is only one flat reflective surface as depicted in Figure 3.1, i.e. N=M=1, then the righthand terms of equation (7.8) can be identified with physical wave components as summarised in Table 7.1. Function
Equivalent cross correlation (a, b)
α C ss (τ ) *δ (τ − D)
direct wave (ab) , direct wave (ac)
β C ss (τ ) ∗ δ (τ − K )
direct wave (ab) , reflected wave (adc)
ρα C ss (τ ) ∗ δ (τ − ( D − J ))
reflected wave (aeb) , direct wave (ac)
ρβ C ss (τ ) ∗ δ (τ − ( K − J ))
reflected wave (aeb) , reflected wave (adc)
Table 7.1 Physical interpretation of terms in equation (3.8) for a single plane reflector. Applying frequency weighting functions [Car73,Han73,Kna76] will not remove the multipath components that will smear the true correlation peak since most of them weight according to the coherence of the signals and multipath components are highly correlated. Implementation of an adaptive filter to minimise the effects of multipath components (as is carried out in a communication system channel equaliser) is not possible since the overall channel plus equaliser response will be subject to an additional Page 24
(and unknown) group delay. The proposed DirectWave CrossCorrelation represents a novel attempt to address these problems.
7.2
Directwave crosscorrelation (DWCC)
Previous research [Car73,Han73,Kna76] has been principally focused on frequencydomain signal processing algorithms that apply weighting functions formulated according to the coherence of the signals. These techniques were shown in section 2 to be unsuitable for the particular application of interest here. The new approach utilises timedomain windowing techniques and yields results that appear to be objectively superior. 7.2.1
Time domain windowing
The signals radiated by an impulsive noise source reach the receiving antennas in a welldefined sequential order. It can be observed from Figure 3.1 that the time taken, Dab , Dac , for the direct signal to reach the antennas is less than that for any of the reflected waves, i.e.: Dab < Dad + D dc
(7.9)
D ac < Dae + Deb
(7.10)
D ac < Dad + D dc
(7.11)
D ab < D ae + Deb
(7.12)
By fast sampling, and with a suitable truncation or windowing technique, the multipath components in the signals can be removed leaving only the direct signal components to be analysed. This removes the error introduced by multipath propagation when estimating the time delay. 7.2.2
Signal truncation
Figure 7.2 shows a pair of signals captured by two antennas spaced by 0.79 m (experimental details can be found in section 6). The waveforms exhibit an excursion of a typical transient with the characteristics of a damped sinusoid decaying exponentially in amplitude with time. At approximately 0.02 µs the waveform shapes start to diverge. This is due to the effects of multipath and is consistent with the position of the antennas within, and the dimensions of, the room used to take the measurements.
Page 25
Figure 7.2 Impulsive noise received at an antenna spacing of 0.79 m. Applying the waveforms directly to existing time delay algorithms proved to be inadequate (see section 6). Truncation of the timeseries prior to the presence of image signals ensures only direct signal components are analysed thus improving the estimation of the time delay. This implies a high sampling frequency in order to achieve good signal resolution for the short period of time when only the direct signal is present. Fast sampling can be easily achieved using a modern digital oscilloscope – a suitable instrument available for this work having a maximum equivalent sampling frequency, f s , of 25 GSps. Increasing the sampling frequency has the effect of zooming into the signal as shown in Figure 7.3.
Figure 7.3 Recorded signal pair showing difference in arrival time and regions containing direct signals only and direct signals plus image signals (multipath). Truncating the signal record is equivalent to rectangular windowing and results in a timeseries that contains only the direct signals.
Page 26
Signal truncation (or rectangular windowing) is expressed mathematically by: y1 (t ) = x1 (t )W1 (t ) = s (t ) + n1 (t ) +
M
∑ρ v =1
v s (t
+ J v ) W1 (t )
N β w s (t + K w ) W1 (t ) y 2 (t ) = x 2 (t )W1 (t ) = α s (t + D ) + n 2 (t ) + w=1
∑
(7.13)
(7.14)
where the window function W1 (t ) is given by: 0 t < t r , t ≥ t w W1 (t ) = î 1 tr ≤ t < t w
(7.15)
t r is the start time of the window function which (equal to the triggering time of the reference signal) and t w − t r is the window duration or width. The optimum width has been determined empirically by experiment. Results (presented later) show that simple signal truncation improves the accuracy of the time delay estimation significantly. This in turn gives good confidence in the initial hypothesis and suggests that an investigation into a more refined windowing method is worthwhile. 7.2.3
Hanning window
Rectangular windowing results in discontinuities in the signal timeseries that are problematic in the context of the subsequent crosscorrelation process. This can be addressed by adopting a window function that does not introduce such discontinuities such as a Hanning Window (HW) defined by:
0 t < t r , t > t w W2 (t ) = t − t r 0.51 + cos 2π (t − t ) t r ≤ t ≤ t w w r î
(7.16)
The role of the window is to extract only the initially occurring direct signal component of the waveform to be applied to the correlation algorithm, thus avoiding later components containing multipath signals (see Figure 3.3). This is illustrated in Figure 7.4.
Page 27
x1 (t ) x 2 (t ) W2 (t ) W2 (t + Qˆ ) x1 (t )W2 (t ) x 2 (t ) W2 (t + Qˆ )
Figure 7.4 Illustration of preprocessing for DWCC. The timedomain window suppresses the unwanted signal components in equations (7.4) and (7.5), i.e.: M ρ v s (t + J v ) W2 (t ) ≅ 0 v =1
(7.17)
N β w s(t + K w )W2 (t + Qˆ ) ≅ 0 w =1
(7.18)
∑ ∑ ∧
Q is an unknown timeshift that must be estimated. This leaves only the direct signal components of the recorded timeseries: y1 (t ) = x1 (t )W2 (t ) = s (t )W2 (t ) + n1 (t ) W2 (t )
(7.19)
y 2 (t ) = x 2 (t )W2 (t + Qˆ ) = α s (t + D)W2 (t + Qˆ ) + n 2 (t )W2 (t + Qˆ )
(7.20)
Equations (7.19) and (7.20) assume that the selection of the window time width t w − t r is small such that: tw < t + Jv
(7.21)
tw < t + K w
(7.22)
∧
When Q ≅ D and letting z (t ) = s (t )W2 (t ) equations (7.19) and (7.20) become: y1 (t ) = z (t ) + n1 (t ) W2 (t )
(7.23)
y 2 (t ) = αz (t − D) + n 2 (t )W2 (t − D)
(7.24)
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Since the noise components are uncorrelated, the crosscorrelation of equations (7.23) and (7.24) gives: C y1 y2 (τ ) = αC zz (τ ) * δ (τ − D)
(7.25)
This is effectively an autocorrelation function with its peak value shifted from 0 (the origin) to D where D indicates the time delay. ∧
7.2.4
Finding the optimum window delay parameter, Q
The Direct Wave CrossCorrelation (DWCC) algorithm requires the window parameter ∧
Q that is estimated by timeshifting the window one samplestep at a time. A confidence value is calculated which is used to establish the optimum window location. The function of the window is to select timeseries segments from the recorded channels that are most alike and prepare them for the crosscorrelation process. The confidence level, equivalent to the correlation coefficient, defined by: C y1 y 2 (τ ) c y1 , y 2 = max , c( y1 , y 2 ) < 1 î C y1 y1 (0)C y2 y2 (0)
(7.26)
describes a normalized crosscorrelation sequence. A search is performed by adjusting ∧
Q using a step size equal to the sampling period Ts = 1 f s , where f s is the sampling ∧
frequency. To reduce the number of iterations required, an initial condition for Q may be obtained from a simple crosscorrelation (described in section 7.2.2). The adjustment ∧
∧
of Q should be no more than the width of the window. It is assumed that Q ≅ D when the confidence level approaches its highest value. ∧
One may be tempted to use Q as the final estimate for the time delay D. However, in a ∧
digital system Q is quantised to the nearest timesample – the quantisation error ∧
depending on the system sampling frequency and since Q corresponds to only a single point result no further enhancement to the time delay resolution can be made. Therefore the correlation function Cy1 y2(τ) is preferred so that interpolation, polynomial and other curvefitting techniques may be applied to improve the overall resolution of the estimate.
Page 29
7.2.5
Extension to multiple sensor inputs
For multiple signals x1 , x 2 , x n , a similar methodology as in the case of a two input system described above may be implemented. A simultaneous measure of confidence level for n signals can be made using: ξ=
∏c
ij
y i (t ), y j (t ) ,
i =1,2, , n j = 1, 2, ,n , j ≠ i
(7.27)
where y = x(t )W (t ) . The number of delays, P, possible (calculated using all pairs of antennas) for an n element antenna array is a combination of 2 out of n, i.e.: P = n C2
(7.28)
In this case, a sequential timeshift adjustment of each window, one at a time, is executed and the confidence level calculated. The process is iterated until a highest possible confidence level (or a boundary condition) is met. This is useful in the application of source location where two or more time delays are required to compute an estimated source position. Equation (7.27) implies that the calculation of confidence level is strengthened as the number of antenna observations increases. 7.2.6
Limitations of the algorithm
Selection of the window timewidth is a compromise between the variance of the crosscorrelation estimation and the effects of multipath and mutual coupling. The windowing function has the effect of altering the phase of the signal. This effect is lessened with ∧
better approximation of the window time shift parameter Q . To make the algorithm ∧
insensitive to the input variable Q , the timewidth of the window used should be sufficiently wide. A useful empirical rule is to set the width of the window to at least one cycle of the centre as defined by the receiving system. As described, the DWCC algorithm is capable of estimating the delay apparent from antenna signals to the nearest sampling interval. In principle, an improvement in accuracy can be achieved by interpolating the input data prior to application of the DWCC algorithm.
Page 30
7.2.7
Algorithm flow chart
A flow chart of the DWCC algorithm is shown in Figure 7.5.
START Load input signals and interpolate
x1 , x 2 , … x n Qˆ i
Determine initial
j = 2,3,…, n i = j −1
E[ x1 (t ), x j (t + Qˆ i )] , Construct MHW
W1 (t ), W2 (t + Qˆ 1 ), … , Wn (t + Qˆ n −1 ) Process signals
y k = x k (t )Wk (t ) ,
k =1, 2,…, n
Compute confidence levels
ξ=
∏c
ij
y i (t ), y j (t ) ,
i =1, 2,…, n j = 1, 2,…, n , j ≠ i
Adjustment ↔ ˆ Q1 , Qˆ 2 , … , Qˆ n −1 ↔
↔
↔
Boundary ? Qˆ , Qˆ , … , Qˆ 1
2
False n −1
True Determine delays
E[ y i (t ), y j (t + Dij )] ,
i =1, 2,…,n j = 1, 2,…, n , j ≠ i
END
Figure 7.5. Flow chart for DWCC algorithm.
Page 31
7.2.8
Application of frequency weighting function
It may seem reasonable that a frequency weighting function should be applied to sharpen the peak of the correlation. Such an approach is often useful for sharpening and distinguishing adjacent correlation peaks that smear into the true delay peak. In this case, however, improved resolution is sensitive to the choice of window width. This is because in estimating time delays using fast impulsive noise transients (with typical pulse duration of 0.3 µs) the true spectrum cannot be estimated with any great degree of certainty. Since no adjacent correlation peak was observed when correlating the direct signal only components a simple crosscorrelation of the preprocessed data was thought to be more suitable for this particular application. 7.2.9
Practical tests and results
The DWCC algorithm was tested in a practical environment. The sampling frequency employed is 25 GSps. The duration of the signal records used is 500 samples (i.e. 20 ns, see Figure 7.3). A YShaped array, shown schematically in Figure 7.6, was used in the test.
90o
2
D12
D 23
1
D13
3
D 24
0o
D14 D34 4
Figure 7.6 Array configuration and definition of delays. Thirty measurements were recorded in a horizontal plane at angular increments of 30 degrees. Before performing the DWCC, the input signals were interpolated by a factor of 10 (i.e. effective sampling frequency of 250 GSps). Initially, the width of the Hanning Window must be set. By looking at the change of time delay with varying window size, near optimum window size may be selected. Figures 7.7, 7.8 and 7.9 show typical examples of computed time delays versus window width. (The delay values, Dij, referred to in the captions of these figures are defined in Figure 7.6). The measurements were made using an impulsive noise source (based on a faulty thermostat  see later) located 10 m from the array at a bearing of 90 degrees.
Page 32
At window widths equal to 120 samples or above the time delay estimation begins to deviate from the actual time delay significantly. This effect can be seen from all records, and in this case, the deviation has a peak of about 1 sample or 40 ps. Other records have shown a peak deviation of about 3 samples or 120 ps. Although this is small, it has a significant impact on the accuracy of a source locator (see section 8). If the window width is too small, the variance of the delay estimations increases. This is observed in the figures as sawtooth features for window widths in the region of 50 samples. The window width worth for this data is thus limited to the range 50  100 samples.
Figure 7.7 Time delay D23 versus window width.
Figure 7.8 Time delay D24 versus window width.
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Figure 7.9 Time delay D34 versus window width. The variance of time delay estimates for all six combinations of time delays defined in Figure 7.6 have been calculated using 30 signal records for each of 10 source bearings from 0 to 90 degrees inclusive at 10 degree intervals and for window widths of 50, 70 and 90 samples. The results are shown in Figure 7.10, 7.11 and 7.12 respectively.
Figure 7.10 Variance of six time delays versus source angle for window width of 50 samples.
Page 34
Figure 7.11 Variance of six time delays versus source angle for window width of 70 samples.
Figure 7.12 Variance of six time delays versus source angle for window width of 50 samples. The variance of the time delay estimation is largest when window width is 50 samples and smallest for 90 samples. The variances of the six delays seem to be fairly equal to each other. However, D12 , D13 and D14 will be discarded in the implementation of the source locator since the ratio of delay variance of maximum possible delay is significantly larger than D23 , D24 and D34 . This is because the latter has a larger antenna spacing of 0.79 m compared to 0.46 m for the former. Finally the performance of the DWCC technique can be summarised by a mean time delay plot over 30 estimates as shown in Figures 7.13, 7.14 and 7.15. These curves are compared over a single quadrant with the ideal case of a sinusoid.
Page 35
Figure 7.13 Time delay D23 versus source angle. The best results were obtained using a Hanning Window width of 70 samples (2.8 ns). This corresponds to time delay curves D23 , D24 and D34 . To build up a profile consisting of 30 different records takes only a small fraction of a second. The signal generated by the noise generator (based on a faulty thermostat) consists of a series of impulses each lasting, typically 0.3 µs. Using the fastframe feature of the oscilloscope, the average number of impulses was established to be about 2,000 pulse/s.
Figure 7.14 Time delay D24 versus source angle.
Page 36
Figure 7.15 Time delay D34 versus source angle.
Page 37
8
S OURCE L OCATION
Position Location (PL) is a complex process that comprises a hybrid of mathematical methods for its implementation. Each of these methods must be considered carefully to ensure none seriously degrades the overall performance of a locator. Impulsive noise location is accomplished in two stages. The first stage involves estimation of the time difference of arrival (TDOA) of the signal at the antennas (see section 7). The second stage utilises algorithms to produce an unambiguous solution to a set of nonlinear hyperbolic equations. In a search for the most effective and efficient algorithms, knowledge from other disciplines such as satellitebased navigation techniques have been investigated. Other problems, such as mathematical solutions that are inconsistent with the true (unambiguous) source location have also been considered and are discussed in detail in this section
8.1
Overview of different Position Location Techniques
PL systems can be classified by the number of measurements used (e.g. multilateration or trilateration) and by the type of measurement used such as phase, time or frequency. Multilateration PL systems are systems that utilize measurements from four or more sensors to estimate the threedimensional (3D) location of the user. Trilateration PL systems utilize measurements from three sensors to estimate the twodimensional (2D) location of the user. The following sections briefly describe several viable techniques for estimating position location of a noiselike source and also assess the limitations inherent in the physics of position location. 8.1.1
Direction Finding Position Location Systems
Direction finding (DF) systems estimate the PL of a source by measuring the direction of arrival, DOA (also referred to as angle of arrival, AOA), of energy from the source. The DOA measurement restricts the location of the source to a line. Multiple DOA measurements from multiple sensors are used in a triangulation configuration to estimate the location of the source that lies on the intersection of such lines. Consequently, DF PL systems are also known as DOA or AOA PL systems. Figure 8.1 illustrates a 2D PL solution of a DF system. Receiver 1
Receiver 2
θ2 θ1 Area of locat ion uncertainty
Figure 8.1 Direction Finding Based Position Location.
Page 38
While only two DOA estimates are required to estimate the PL of a source, multiple DOA estimates are commonly used to improve the estimation accuracy. DOA estimation is performed by signal parameter estimation algorithms that exploit the phase differences or other signal characteristics between closely spaced antenna elements of an antenna array and employ phasealignment methods such as beam/null steering. The spacing of elements within the antenna array is typically less than half a wavelength. This alignment is required to produce phase differences of the order of π radians or less, to avoid ambiguities in the DOA estimate. The resolution of DOA estimators improves as the baseline distances between the antennas increase. This improvement, however, is at the expense of ambiguities. As a result, DOA estimation methods are often used with short baselines to reduce or eliminate the ambiguities and long baselines to improve resolution. 8.1.2
Rangebased Position Location System
Rangebased PL systems can be categorized as ranging, range sum, or range difference PL system. The type of measurement used in each of these systems defines a unique geometry, or configuration, of the PL solution. Ranging PL systems locate a source by measuring the absolute distance between a source and sensor. Range measurements are determined by estimating the propagation time of the signal between the source and the sensor. This estimate defines a sphere of constant range around the sensor. The intersections of multiple spheres produced by multiple range measurements from multiple sensors provide the PL estimates of location. Consequently, ranging systems are also known as TOA or spherical PL systems. Range sum PL systems measure the relative sum of ranges between the source and sensors respectively. These systems measure the time sum of arrival (TSOA) of the propagating signal between two sensors to produce a range sum measurement. The range sum estimate defines an ellipsoid around the sensors, and when multiple range sum measurements are obtained, the PL estimate of the source is at the intersection of the ellipsoids. Consequently, range sum PL systems are also known as TSOA or elliptical PL systems. Range difference PL systems measure the relative difference in ranges between the source and sensors respectively. These systems measure the time difference of arrival (TDOA) of the propagating signal between two sensors to produce a range difference measurement. The range difference measurement defines a hyperboloid of constant range difference with a sensor at the foci. When multiple range difference measurements are obtained, producing multiple hyperboloids, the PL estimate of the user is at the intersection of the hyperboloids. Consequently, range difference PL systems are also known as TDOA or hyperbolic PL systems. Throughout this report, systems of this class will be referred to as hyperbolic PL systems. Ranging PL systems measure the absolute distance between a source and a set of sensors through the use of timeofarrival (TOA) measurements. The TOA measurements are related to range estimates that define a sphere around the sensor. When measurements are made from sensors with known locations, the spheres described by the range measurements intersect at a point indicating the PL estimate of the source. If the spheres described by the range measurements intersect at more than one point, an ambiguous solution to the PL estimate results. Redundant range measurements, resulting in a Page 39
multilateration ranging PL estimation, are commonly made to reduce or eliminate PL ambiguities. To illustrate the ranging PL concept, consider a 2D ranging PL system using N antennas. The time of arrival of a signal at each antenna is estimated and related to the range measurement Ri by the relationship: Ri = cDi
(8.1)
where c is the propagation speed (usually 3.0 × 10 8 m/s) and Di is the TOA estimate (or, more strictly, the time of flight estimate) at the ith antenna. The mathematical relationships between range measurements at N sensors, the coordinates of the known sensor locations, and the coordinates of the source are: Ri = ( x − x i ) + ( y − y i )
, i = 1,2,..., N
(8.2)
where (xi , y i ) is the coordinate of the ith sensor, Ri is the ith range estimate to the source with estimated coordinate at (x, y ). Equation (8.2) defines an N × 2 set of nonlinear equations whose solution is the location coordinates of the source. If the number of unknowns, or coordinates of the source to be solved, is equal to the number of range measurements, the set of equations are consistent and a unique solution exists. However, if redundant measurements produce more range measurements than the number of unknowns, then the system is inconsistent and a unique solution may or may not exist. This generally requires an error criterion to be selected and iterative techniques to be employed to converge onto a unique solution. A least squares fit is commonly used to simultaneously solve these equations for both the PL and error coefficients. Accurate time or phase measurements in ranging PL systems require strict clock synchronization between the source and sensors.
A disadvantage of the ranging PL technique is that accuracy is very dependent on system geometry. Highest accuracies are attained when the surfaces of all ranging spheres intersect at right angles. Degraded performance is experienced when the angles of surface intersection deviate from this. 8.1.3
Elliptical Position Location Systems
Elliptical PL systems locate a source by the intersection of ellipsoids describing the range sum measurements between multiple sensors. The range sum is determined from the sum of signal TOA estimates at multiple sensors. The relationship between range sum R s ji , and the TOA (strictly, time of flight) between sensors is given by: Rijs = cS ij = Ri + R j
(8.3)
where c is propagation speed and S ij is the sum of the TOAs at sensor i and j. The range sum measurement restricts the possible location of the source to lie on the surface of an ellipsoid. The ellipsoids that describe the range sum between sensors is given by:
Page 40
Rijs = ( x − x i ) 2 + ( y − y i ) 2 + ( x − x j ) 2 + ( y − y i ) 2
(
(8.4)
)
where (xi , y i ) and x j , y j denote the locations of sensors i and j, and (x, y ) is the PL estimate of the source. A source location can be uniquely determined by the intersection of three or more ellipsoids. Redundant range sum measurements can be made to improve location accuracy. While there exist some systems that use this method, it appears that it offers no performance advantage over the spherical or hyperbolic configurations. 8.1.4
Hyperbolic Position Location System
Hyperbolic PL systems estimate the location of a source by the intersection of hyperboloids describing range difference measurements between three or more sensors. The range difference between two sensors is determined by measuring the difference in TOA of a signal between them. The relationship between range difference Rij and the time difference of arrival (TDOA) between sensors is given by: Rij = cDij = Ri − R j
(8.5)
where c is propagating speed and Dij is the TDOA between sensor i and j. The TDOA estimate, in the absence of noise and interference, restricts the possible source locations to the surface of the hyperboloid of revolution having the sensors at its foci. In a 2D system, the hyperbolas that describe the range difference Rij , between sensors are given by: Rij = ( x − x i ) + ( y − y i ) − ( x − x j ) + ( y − y j )
(
(8.6)
)
where (xi , y i ) and x j , y j denote the locations of sensors i and j respectively, Rij is
the range difference measurement between sensors i and j, and (x, y ) is the unknown coordinate of the source. If the number of unknowns, or coordinate of the source to be determined, is equal to the number of equations or range difference measurements, the system is consistent and a unique solution exists. If redundant range difference measurements are made, the system may be inconsistent and a unique solution may or may not exist. In this situation, some error criteria must be selected for determining the optimum solution to the system of equations. If the source and sensors are coplanar, 2D source location can be estimated from the intersection of two or more hyperboloids produced from three or more TDOA measurements, resulting in a hyperbolic trilateration solution. 3D source location estimation is produced by the intersection of three or more independently hyperboloids generated from four or more TDOA measurements, resulting in a hyperbolic multilateration solution. If the hyperbola determined from multiple sensors intersects at more than one point, then ambiguity in the estimated position exists. This location ambiguity may be resolved by using a priori information about the source location, bearing measurements at one or more of the stations, or redundant range difference measurements at additional sensors to generate additional hyperboloids. A major
Page 41
advantage of this TDOA method is that it does not require knowledge of the transmit time from the source, as do TOA methods. Consequently, strict clock synchronization between the source and sensor is not required making PL of an arbitrary impulsive noise source possible. Furthermore, the hyperbolic PL method is able to reduce or eliminate errors common to different channels. Precise clock synchronization is, however, required for all sensors used for the PL estimate.
8.2
Comparison of Position Location Techniques
The two PL techniques that have been considered for the location of impulsive noise sources are the DF and hyperbolic methods. While DF systems exploit the relative phase differences between closely spaced sensor elements and employ phasealignment methods for beam/null steering to estimate the direction of arrival (DOA) of the signal of interest, hyperbolic methods exploit the relative time differences of a signal arriving at different sensors. The need for high resolution arises primarily when closely spaced sources give rise to multiple received signals that cannot be separated by preprocessing methods before the PL estimate is made. For example, when crosscorrelating TDOAs of multiple signals that are not separated by more than the widths of their crosscorrelation peaks, the peak crosscorrelation of the signal of interest cannot usually be resolved with conventional TDOAbased methods. To minimize this problem, the distance between platforms is typically made as large as possible to decrease the overlap of adjacent peaks. This represents a fundamental resolution limit for TDOA estimation of two closely spaced sources. The best performing arraybased DF methods attempt to resolve the resolution problem in locating multiple signal sources by simultaneously estimating multiple DOAs rather than estimating the DOA of each signal as is commonly done by conventional beamforming and TDOAbased techniques. Although DF methods offer greater spatial resolution and the ability to simultaneously locate a number of signals, their complexity is typically much higher than that of TDOA methods.
8.3
Hyperbolic Position Location Systems
An interference source can be located using an array of sensors utilizing Time Delay Estimation (TDE). Figure 8.2 shows the locus of the possible source location for a twosensor system given a time delay estimate D12 where: cD12 = R1 − R2
(8.7)
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Figure 8.2 Locus of source location for a twosensor system. The locus satisfies the general hyperbolic relationship described by: x2 y 2 − =1 a b
(8.8)
where: a = (2 g − ( R1 − R 2 )) / 2 = (2 g − cD12 ) / 2
(8.9)
and: b = g 2 − a2
(8.10)
The constants in equations (8.8) – (8.10) are defined in Figure 8.2.
8.4
Solutions for Hyperbolic Position Fixes
A fast solution to a set of simultaneous hyperbolic equations is often important in navigation applications where effectively instantaneous results are required on request. To achieve this the use of iterative algorithms (typically used for solving simultaneous hyperbolic equations) is avoided since such algorithms can be slow and/or expensive in terms of processing requirements. For nonreal time applications, where the speed/processing constraints are less critical indirect iterative methods such as NewtonRaphson are typically employed. 8.4.1
ThreeInput Position Location Systems
Page 43
For three arbitrarily placed sensors and a consistent system of equations in which the number of equations equals the number of unknown source coordinates to be solved, there exists a direct solution. Fang [Fan90] has derived an exact solution for solving the unknown source coordinates directly. He establishes a coordinate system with the first sensor located at (0,0,0 ), the second at (x2 , y2 = 0, z 2 = 0) and the third at
(x3 , y3 , z 3 = 0 ) . Setting
y 2 = 0, z 2 = 0 for the second sensor position and z 3 = 0 for
the third (without loss of generality) greatly simplifies the relationships between the equations. y ( x 2 , y 2 = 0, z 2 = 0)
R12
(0,0,0) x
Sensor 2
Sensor 1
R13
( x 3 , y 3 , z 3 = 0) Sensor 3
Figure 8.3 Antenna location coordinates for threesensor system. Figure 8.3 shows a coordinate system for three antennas. A righthanded Cartesian coordinate system is chosen as shown. The origin is located at antenna 1, the xaxis is lies along the line connecting the origin and antenna 2, and the yaxis is orthogonal to the xaxis and lies in the plane defined by the three antennas. D12 = D1 − D2 and
D13 = D1 − D3 are the differences in the times of signal arrival, cD12 = R1 − R2 and cD13 = R1 − R3 are the distances between antennas 1 and 2, and 1 and 3, respectively. From the geometry of Figure 8.3: x 2 + y 2 + z 2 − ( x − x 2 ) 2 + y 2 + z 2 = cD12 = R12
(8.11)
x 2 + y 2 + z 2 − ( x − x 3 ) 2 + ( y − y 3 ) 2 + z 2 = cD13 = R13
(8.12)
where x , y and z are the coordinates of the source. R12 and R13 are the range differences from the source location to the antennas – a function of the measured time difference of arrival. Rearranging the first term on the right hand side of both equations followed by squaring and simplifying gives: 2 R12 − x 22 + 2 x 2 = 2 R12 x 2 + y 2 + z 2
2 R13 − L23 + 2 x 3 x + 2 y 3 y = 2 R13 x 2 + y 2 + z 2
where L3 =
(8.13) (8.14)
x32 + y 32 is the length of the antenna pair baselines. These two equations,
when squared, represent two hyperboloids of revolution with foci at antennas 1, 2 and 1, 3 respectively.
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Note that for measurements consisting of sums instead of differences of times of arrival, a set of equations similar to (8.11) and (8.12) with positive signs between the radicals will result. This is interpreted as range sums instead of range differences. Squaring these new equations will give an identical result to that of equations (8.13) and (8.14), although they now represent ellipsoids of revolution rather than hyperboloids. The derivations are therefore applicable to range sum measurements in addition to range difference measurements. y is obtained by equating (8.13) and (8.14) to produce: y = ux + v
(8.15)
where: u=
R13 ( x 2 / R12 ) − x 3 y3
L23
−
2 R13
v=
(8.16)
x + R13 R12 1 − 2 R 12 2 y3
2
(8.17)
Substituting (8.15) into (8.13) gives z , i.e.: z = ± dx 2 + ex + f
(8.18)
or: z 2 = dx 2 + ex + f
(8.19)
where:
{
d = − 1 − ( x 2 / R12 ) 2 + u 2
{
}
(8.20)
}
e = x 2 ⋅ 1 − ( x 2 / R12 ) 2 − 2u ⋅ v
{
2 f = ( R12 / 4) ⋅ 1 − ( x 2 / R12 ) 2
} −v 2
(8.21) 2
(8.22)
The curve produced by these equations is either an ellipse or a hyperbola depending on whether x2 < 0 or x2 > 0 . Finally, the source location can be written as a vector depending on a single unknown parameter x: →
→
→
→
R = x ⋅ i + (u ⋅ x + v ) j ± (d ⋅ x 2 + e ⋅ x + f ) ⋅ k
(8.23)
To fix the source position on the ellipse or hyperbola, additional information is required. By restricting the problem to be coplanar so that z = 0 , x is now obtainable as a solution of (8.19), i.e.,
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d ⋅ x2 + e⋅ x + f = 0
(8.24)
Solving this quadratic equation produces two admissible solutions corresponding to its two roots. This twofold ambiguity can be resolved by some knowledge of the general location of the source. 8.4.2
FourInput Position Location Systems
An exact solution for a fourantenna system can be derived in a similar way to that described for the threeantenna system in section 8.4.1. Details can be found in [Buc00] but the following abstracts the essential mathematics required for an implementation. cD1 = R1 = ( x − x1 ) 2 + ( y − y1 ) 2 + ( z − z1 ) 2
(8.25)
cD2 = R 2 = ( x − x 2 ) 2 + ( y − y 2 ) 2 + ( z − z 2 ) 2
(8.26)
cD3 = R3 = ( x − x 3 ) 2 + ( y − y 3 ) 2 + ( z − z 3 ) 2
(8.27)
cD4 = R 4 = ( x − x 4 ) 2 + ( y − y 4 ) 2 + ( z − z 4 ) 2
(8.28)
Rij = Ri − R j and xij = xi − x j where i, j = 1,2,3 simplifies the equations. Solving the above four equations for the three unknowns results in: x = Gz + H
(8.29)
y = Iz + J
(8.30) 2
z=
N O N ± − 2M 2 M M
(8.31)
where
(
)
2 M = 4 R13 G 2 + I 2 + 1 − L2
(8.32)
2 (G( x1 − H ) + I ( y1 − J ) + z1 ) + 2 LK N = 8 R13
(8.33)
[
]
2 (x1 − H )2 + ( y1 − J ) 2 + z12 − K 2 O = 4 R13
(8.34)
G=
E−B A−D
(8.35)
H=
F −C A−D
(8.36)
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I = AG + B
(8.37)
J = AH + C
(8.38)
2 + x12 − x 32 + y12 − y 32 + z12 − z 32 + 2 x 31 H + 2 y 31 J K = R13
(8.39)
L = 2(x 31G + y 31 I + 2 z 31 )
(8.40)
R x − R12 x 31 A = 13 21 R12 y 31 − R13 y 21
(8.41)
R z − R12 z 31 B = 13 21 R12 y 31 − R13 y 21
(8.42)
2 + x12 − x 22 + y12 − y 22 + z12 − z 22 ] − {R13 [ R12 2 + x12 − x 32 + y12 − y 32 + z12 − z 32 ]} R12 [ R13 2( R12 y 31 − R13 y 21 )
C=
(8.43)
R x − R32 x 43 D = 34 23 R32 y 43 − R34 y 23
(8.44)
R z − R32 z 43 E = 34 23 R 32 y 43 − R34 y 23
(8.45)
2 + x 32 − x 22 + y 32 − y 22 + z 32 − z 22 ] − {R34 [ R 32
F=
2 + x 32 − x 42 + y 32 − y 42 + z 32 − z 42 ]} R32 [ R 34 2( R32 y 43 − R34 y 23 )
(8.46)
Only two references, [Fan90][Buc00], have been found pertaining to this area of work, i.e. an exact solution for hyperbolic and related position fixes.
8.5
Simulation of Hyperbolic Position Location System
A simulation of the Hyperbolic Position Location System has been made in order to assess its ability to locate the source at any position without ambiguity given the required delay estimates. Only two pairs of these curves are required to produce an intersection that indicates the position of the source. The redundant curves are for diagnostic purposes e.g. to detect anomalies such as a faulty channel and to give a qualitative measure of the closedloop delay performance of the position location system. The closedloop delay performance is best when the intersections converge together at a single point. Figures 8.4 and 8.5 show simulation examples.
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Figure 8.4 Example 1: Source Location = (6, 2) m, sensor spacing = 0.79 m.
Figure 8.5 Example 2: Source Location (6,2) m, sensor spacing = 0.79 m.
8.6 Difficulties in estimating Position Location using TDOA The PL algorithm using TDOA is closely related to DF algorithm. An accurate TDOA location algorithm is constructed using two or more bearing intersections to locate the noise source. The performance of such a location system depends on the performance of the DF technique it employs. For a system to locate a source that is distant from its antenna array (compared with the dimensions of the array), the tolerance of the bearing error must small (if this is not the case the error in the computed location may be so large as to make it worthless). A threepoint linear array, Figure 8.6, has been used to develop insight in to this problem.
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Interference Source
S
θ
β
L1 Sensor 1
δ
L2 Sensor 2
Sensor 3
Figure 8.6 Threesensor position location system using linear array geometry. By setting δ = 0 degrees in Figure 8.6, location error can be plotted versus source location and sensor spacing, Figure 8.7.
Figure 8.7 Location error versus source location and sensor spacing for βerror = 1 deg. For a sensor element spacing of 2 m, a source range of 100 m will produce an error of 600 m if the direction, β, has an error of 1 degree. It can be observed from Figure 4.7, that in order to reduce location error the sensor spacing must be sufficiently large or the direction error must be very small. Signal processing becomes a vital part of the whole process to achieve an accurate and unambiguous result. The AOA is calculated from the inverse sine of the estimated normalised time delay. Normalisation is with respect to the maximum possible time delay between the two sensors, i.e.: cD β ≅ sin −1 21 deg L2
(8.47)
cD β ≅ sin −1 32 deg L1
(8.48)
The relative time delay between the sensors is:
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Dij = Di − D j
, i , j = 1,2,3
(8.49)
The range, R, from the midpoint of the array to the source location can be expressed exactly in terms of Dij and Li as:
R=
cD 2 cD 21 + L2 1 − 32 L1 1 − L1 L2 î
2
cD cD 2 32 − 21 L1 L2
(8.50)
Similarly the bearing, θ, can be expressed as:
[
L2 − 2RcD32 − (cD32 ) 2 θ = cos −1 2 [2 RL2 ]
]
(8.51)
where Li are the distances between the sensor pairs as shown in the Figure 7.6. For large R the middle term in the arccosine expression becomes dominant. If the spacings between the sensor pairs are set equally, i.e. L = L1 = L2 , equation (4.50) reduces to: R=
2 L2 − (cD) 221 − (cD) 232 2(cD32 − cD21 )
(8.52)
In the special case where the source location lies on a line that bisects the array, i.e. D = D32 = − D21 , then: R=
L2 − (cD) 2 2(cD)
(8.53)
Substituting R into equation (3.51) gives θ = cos −1 (0) = 90 0 . The bearing stands for all values of 0 < cD ≤ L2 . Differentiating equation (3.52) with respect to delay gives the sensitivity of source location to time delay: −
dR L2 1 = + 2 dD 2(cD) 2
(8.54)
For large R, D becomes small, implying a steep gradient, making the range sensitive to delay error. Using equation (8.53) a family of curves can be plotted, Figure 8.8 and 8.9, to show the effect of variation in time delay estimation on source location with different sensor spacing L.
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Figure 8.8 Graph of source location versus time delay. The curve in Figure 8.8 is plotted as a set of discrete points reflecting the spatial quantisation due to a finite sampling rate (which in this case is 10 GSps). As the time delay approaches zero, the gradient of the source location rises rapidly causing the points to become more widely separated along the location axis corresponding to degraded spatial resolution. This figure shows, for example, that a time delay of one sample corresponds to a source distance of ~12 m, whereas a 2 sample time delay is equivalent to a distance of ~7 m; no resolution of location between 7 and 12 m is possible using a sampling frequency of 10 GSps and sensor element spacing of 1 m. Improvements to the resolution can only be made by increasing the sampling frequency and spacing. Figure 8.9 shows the effect of 20 GSps sampling frequency and spacings of both 1 m and 2 m from which it can be seen that the spatial resolution is improved.
Figure 8.9 Graph of source location versus time delay for two sensor spacings. These results yield insight into the difficulties of estimating source location. Specifically, it can be easily observed that inherent in the source location problem is the need for large antenna array dimensions, accurate time delay estimates or close absolute range from the receiving array. Tradeoffs between these interlinked parameters are possible.
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9
H ARDWARE
This section discusses the limiting effect of digital quantisation on source location resolution and strategies for minimising this effect. A discussion of performance assessment techniques to inform the choice of array geometry is included. All discussions are focused on a fourantenna array and assume the employment of a hyperbolic based location algorithm. Experimental evidence is given to establish the effects of spatial quantisation.
9.1
The effects of finite sampling rate
In the digital interference location system, received signals are converted into digital format for processing. The sampling frequency f s imposes a spatial limitation to the resolution of the location system even if the signals received are ideal, i.e. not corrupted by noise or modified by any transfer function. The peak crosscorrelation of two signals x1 (t ) and x 2 (t ) received via a pair of spatially separated antennas at spacing L m, see Figure 9.1, will give a corresponding time delay of τ seconds. The range of τ is therefore between − L / c and L / c depending on the location of the source where c = 3.0 ×10 8 m / s . A resolution limit arises due to the finite sampling frequency of a practical system of which the estimated τ is quantised. This causes τ to change in time steps of Ts .
(a)
x1 ( t )
(b)
x 2 (t ) τ
Cx x (τ ) = E[x1(t)x2 (t +τ )]
(c)
1 2
Ts
Figure 9.1 Signals received by (a) sensor 1 and (b) sensor 2 respectively and (c) the correlation of the two signals. The number of time steps, N s for the given range of τ is therefore:
Ns =
2L 2 f s L = cTs c
(9.1)
Page 52
N s is directly proportional to the sampling frequency f s and the spacing between the
sensors L . This implies that by increasing f s or L or both, N s will increase accordingly. With more time steps to describe a fixed range of time delay τ , the time resolution of the system is improved. It is not possible to locate a source using only two sensors unless the source is restricted to lie between the sensors and on the line joining them, see Figure 9.2 (this line is sometimes referred to as the sensor baseline). Under such restricted conditions the system can resolve the source location in space but only to within spatially quantised steps given by:
∆S =
L c = meters Ns 2 fs
(9.2)
For a timedelay τ , there is a hyperbolic curve representing the locus of all possible source locations corresponding to the delay (see section 4). An assessment of the spatial resolution of different array geometries can therefore be obtained by plotting the time delay hyperbolic curves in steps of ∆S over L m as shown in Figure 9.2.
Figure 9.2 Plot to assess spatial resolution. Suitable adjustment and rotation of these results can be used to produce resolution maps that provide a visual display of the resolution versus location for different array geometries. The term resolution as used here refers to the degree to which a source can be discriminated. The lines on a map reflect the possible locations of a source. A higher line density represents better resolution. In contrast, a large unintersected region will produce a larger location estimation error. It is shown later that the choice of array geometry significantly affects the system’s ability to locate a noise source due to the effects of digital quantisation.
Page 53
9.2
Common Array Geometries
The choice of array geometry is influenced by a number of factors, i.e.: •
Number of input channels
•
Processing algorithms
•
Constraints on physical dimensions
•
Quantifiable improvement contributed to the overall performance of the system
The most obvious geometries are the uniformly spaced linear array, square array and Yshaped array. These configurations are investigated here. Figure 9.3 shows the different types of array geometries. Ls
Ll
Ly 2Ll
3
Ly
Ls 2
3Ll a) Uniformly spaced linear array
b) Square array
c) Yshaped array
Figure 9.3 Sensor arrays of different geometries. The arrays have sensor spacing of Ll , Ls and Ly for linear, square and Yshaped array respectively as shown in Figure 9.3. There are six pairs of delays for each configuration. Assuming that all the delays are utilised, the total baseline length is defined as the sum of the baselines between all the combinations of array elements. For the linear array the total baseline length is: Bl = 10Ll meters
(9.3)
Similarly, the respective square and Yshaped array total baseline lengths are: B s = L s (4 + 2 2 ) meters B y = 3L y (1 +
1
) meters
(9.4) (9.5)
3
An equal baseline length B = 10 m is set to assess the performance of different array geometries for a fourinput system. The performances of the three array geometries are investigated below.
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9.2.1
Uniformly spaced linear array
The simplest antenna array for a source locator is linear consisting of antenna elements positioned in a straight line and equally separated a distance L (see Figure 9.3(a)). This configuration has been used, for example, to locate electric arcs generated in a substation [Sid97]. It has been found that this array performs best when the source is located directly in front of the array. Reasons for employing such an array geometry are to minimise the complexity of DSP algorithms and to take advantage of wellestablished superresolution algorithms [Sch86,Tsa96] typically used for DF systems. Figure 9.4 shows that regions adjacent to a linear array have poor location resolution. For a finite sampling rate blind regions on either side of the array are created.
Figure 9.4 Resolution map for uniformly spaced linear array.
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9.2.2
Square Array
An array geometry with 90 degree rotational symmetry such as a square array avoids blind spots. Figure 9.5 shows the resolution map for a square array.
Figure 9.5 Resolution map for square array. This array geometry has been used for radio frequency location systems [Tsa96]. 9.2.3
YArray
The Yshaped array positions the antennas in such a way that two no elementpair baselines are parallel. This is important in improving the overall location capabilities of the system. As demonstrated experimentally and reported later, the timedelay variance is smallest when the source lies on the centre axis perpendicular to the baseline. Having baselines with the maximum variety of different orientations maximises the probability that this desirable condition will be met or approximated.
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Figure 9.6 Resolution map for Yarray. It can be seen from Figure 9.6 that the resolution map for Yconfigured array is superior to that of both linear and square arrays due to the greater incidence of hyperbolae intersections. If only three delays with the smallest variance are used, as recommended in section 7, the resolution map is as shown in Figure 9.7 below. Deterioration in the mesh is small, but the total baseline length is decreased significantly to 6.34 m. An advantage of using only three delays is the availability of fast and accurate processing algorithms as introduced in section 8. It is concluded that this configuration represents the best overall choice from the array geometries discussed here.
Figure 9.7 Resolution map of yarray using reduced (three) delay set.
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9.3
General Implications of a Resolution Map
In all the array geometries investigated, resolution within the areas bounded by the sensors is finer than resolution outside this area. This implies that the best performance of a system may be achieved if the source is positioned within the array. Furthermore, it can also be seen from the maps that the mesh size around the maps is nonuniform and changes with bearing angle. The location accuracy of sources will therefore be a function of bearing. The resolution map concept has focused exclusively on digital quantisation effects and the exploitation of different array geometries to minimise these effects. It is based on the assumption that the received signals are not corrupted by noise and that distortion, if present, is common to all channels. It is therefore important to know if the performance of a source location system is significantly influenced by other factors such as: •
The performance of the sensors
•
The variance of the Time Delay Estimation (TDE) algorithm due to noise corruption and/or distortion
9.4 Empirical demonstration of spatial quantisation effects An experiment was devised to reveal the practical effects of spatial quantisation by estimating the bearing and range to a source at a known location. The sensor spacing was 0.32 m and the source was moved along the arc of a circle at fixed ranges of 1 m, 3 m and 5 m, as shown in Figure 5.8. The dashed lines in Figure 5.8 are the source locus at time delay equals to 0, 6, 12 and 15 samples ( 6, 12 and 15 samples for the negative quadrant). Details of the time delay estimation technique can be found in section 7. Ten records, each consisting of 500 samples (sampling rate = 25 GSps), were taken at each position and the estimated location plotted on the figure with a cross. The results obtained were influenced only by the time delay estimate and the effects of quantised time delay estimation are therefore apparent. As the source moves further away the location estimates become scattered over a larger area. If no compensating technique such as interpolation is introduced to improve the location resolution, the estimated location error will be large. There is a limit to the improvement in spatial resolution that interpolation can realise, however, since in practice the signals are subject to additive noise.
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Figure 9.8 Estimated location of sources at known positions. As the source is moved to positions where the absolute time delay is large, the variance of the time delay estimates increases. A similar effect can be observed when the source moves away from the sensor pair in range. The latter is mainly due to the deterioration of the SNR as the source moves further away from the sensors. This confirms experimentally the general advantage of an array geometry possessing baselines having as uniform a distribution of orientations as possible.
9.5
Array construction
An important factor in the array design is practicality. Since the system must locate an impulsive noise source in an urban or suburban environment (possibly mounted on a vehicle of modest size) or operate inside domestic dwellings, the physical dimensions of the array must be kept as small as possible. A physically small array dimension, however, reduces the instrument’s capability to locate distant noise sources. A prototype array has been constructed using the largest element spacing thought practical. The configuration and dimensions of the array are shown in Figure 9.9. 1.25m
0.28m
Aluminium baseplate
Ly 3
L y = 0.79m
1.25m
Yshaped array
Figure 9.9 Prototype array configuration and dimensions. A baseplate acts as an earth plane for the operation of monopole antenna elements. Page 59
During the course of the project many different arrays have been tested. Initially, a square array having a 2 m spacing was constructed, Figure 9.10.
Figure 9.10 Prototype square array, 2 m spacing This array proved to be impractical, requiring a van for transportation and two people for assembly. Early results taken from the array were poor in terms of location accuracy. As a result of this, greater attention was placed on the positioning of the antenna elements within the array. Experiments with smaller square arrays showed that the accuracy could be improved by mounting the antennas at least half a wavelength (at their resonant frequency) from the edge of the earth plane. Both helical and monopole antennas were used as array elements. However, the location accuracy remained poor which lead to the theoretical study of array geometries described earlier in this section, and the eventual adoption of the Y configuration. Irrespective of geometry, however, arrays constructed with a single earth plane common to all elements still suffer the problem that waves incident to the array, before reaching an antenna, must propagate over a varying length of earth plane dependent on bearing. Due to the extreme timing accuracy required from the array, this degrades location accuracy. To eliminate this effect, arrays were constructed from antenna elements without the use of a common earth plane. Some investigations using arrays constructed from biconical antenna elements are reported in section 10 (although the majority of the testing was performed with the Y shaped array described in Figure 9.9).
9.6
Array calibration
The array was calibrated using a handheld spark generator. The spark generator was used because of its convenient size and ability to emulate the effect of an impulsive point source. It was built based on a simple capacitor discharge principle and was capable of providing a constant stream of spark discharges. The spark generator can produce discharge lengths of up to 5 mm accompanied by a momentary flash of visible light accompanied by audible clicking.
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15 readings were taken with the generator mounted over the centre of the array and the mean result was calculated. Figure 9.11 shows an example of an array calibration. The dark cross shows the actual position of the source. The intersection of the three loci is approximately 5 mm from the cross. This result proves that the integrity of the design of the array, coaxial connections, sampling system and processing algorithms. No adjustments were made as a result of this calibration result.
Figure 9.11 Calibration result.
9.7
Data acquisition
The wideband signal was acquired by direct sampling of the received RF waveform as available at the array element terminals using a highspeed digitiser with flash ADC. A modern digital oscilloscope was used for this purpose allowing an effective sampling rate of up to 25 GSps. Figure 9.12 shows the entire system. The bandwidth of the oscilloscope was 1 GHz. Since impulsive noise is, by its very nature, wideband, capture of such data could be easily made using the amplitude triggering facility of the oscilloscope. BNC adaptors
Aerial type sensors
Aluminium plane sensor array Laptop computer with Ethernet capabilities Quickform cables
RJ45 RJ45
LAN to optic converter
Tektronix 4channel digital scope
All matched to 50Ω input impedance
Fibre optic links
Figure 9.12 Impulsive noise acquisition based on direct sampling.
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It should be noted that the oscilloscope's highest continuous sampling rate was 2.5 GSps; operation at 25 GSps was only possible for repetitive waveforms in which case offset triggering at the lower sampling frequency allows the waveform to be constructed at the higher sampling frequency. Results from the oscilloscope were transferred to a laptop computer for further analysis.
9.8
Measures to minimise interference
The following measures were taken to guard against interferenceinduced errors. 9.8.1
Use of quickform cables
Mutual coupling between antenna elements will have a significant effect on the accuracy of the locator. Experiments with conventional 50Ω laboratory coaxial cable revealed that coupling occurred between the array and the oscilloscope. This problem was solved by the use "Quickform" coaxial cable, manufactured by Alcatel. Quickform consists of a silver plated copper inner conductor, a tin soaked copper outer braid, and a PTFE dielectric. Electrically, Quickform performance is similar to semirigid coax, but mechanically has the advantage of being easily formed. All results have been taken using Quickform cables. 9.8.2
Precision cable lengths
Uniform electrical lengths for the Quickform cables connecting array elements to the oscilloscope inputs were achieved using the time domain reflectometry facility of an HP network analyser. 9.8.3
Fibre optic links
A fibre optic link was used to connect the oscilloscope to a laptop computer running the instrument control, data logging and data analysis software. This minimised long cable runs carrying digital signals that could potentially be a source of interference.
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10 E XPERIMENTAL R ESULTS During the development of the locator, many sets of results were acquired through tests conducted at the University and at the Open Air Testing (OATS) facility at Whyteleave Laboratory, Croydon. The results of some of these tests have already been described in previous sections. Since the progress made during these tests was incremental only the most significant results, in terms of describing the locator accuracy, are described here. These are: •
Tests conducted at OATS during September 2001.
•
Tests conducted at the University during December 2001.
Additionally, the interference locator has been tested on site to trace a source of tv interference. This investigation is described in section 11.
10.1 Tests conducted at OATS, September 2001 In these tests, the Y shaped, 4sensor array described in Figure 5.9 was tested. 10.1.1
Impulsive interference noise source
An impulsive noise source for use in field trials was provided by the radio communications agency. It was based on a faulty thermostat  extracted from a domestic central heating boiler system  that had lost its hysteresis effect. When operating, the unit periodically switched the thermostat between the opening and closing state and, in the process, generated wideband interference. Typical waveforms received by the locating system from this source are shown in Figures 3.2 and 3.3. The waveforms produced by the source were very repetitive, allowing the oscilloscope to sample at 25 GSps as described in section 9.7. 10.1.2
Measurement setup
Figure 10.1 shows the setup used for the tests. The array, which was connected to the oscilloscope using matched sections of quickform coaxial cable, was placed on the rotatable turntable in OATS. The array was fitted with four monopole sensors, as shown in Figure 10.2. The scope was controlled by a laptop computer connected via a GPIB interface. These tests allowed the performance of the locator to be assessed for bearing accuracy, by rotating the turntable. The interference noise source was placed at the same height as the array, and separated from it by a distance of 10 m.
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Figure 10.1 OATS tests setup. 48 mm
BNC fitting
Figure 10.2 Monopole sensor used on array for OATS tests. The impulsive waveforms were captured by the scope at a sampling frequency of 25 GSps. This sampling frequency is only supported by the scope due to the repetitive nature of the waveform, which allowed a 500 sample buffer to be filled at 25 GSps by 'building up' the waveform through repetitive sampling of the impulse. The signals thus recorded, were processed using MATLAB programs, firstly to calculate the time delays, as described in section 7, and then for the source location, as described in section 4. Ten sets of results were recorded at each position of the turntable. The array was rotated through 90° at 10° increments. 10.1.3
Results using small monopole antenna elements
The calculated position of the source was made for each group of results and are displayed in Figure 10.3. Due to the symmetry of the array, only a 60° sector is required to characterise its performance. The results show that the locator displays bearing accuracy to within several degrees, and a range accuracy to within 2 m. It can be seen from Figure 10.3 that the locator was unable to locate at either 0° or 60°  due to the array symmetry, these angles represent the same effect. This is due to the signal propagating from a direction that lies on a line drawn between two of the outer array sensor elements. In this condition, the time delay from the sensors on the source line contributes no information about the range of the source. Despite the lack of range, the locator is, however, able to predict the bearing for source locations corresponding to 0°, 60°, 120°, 180°, 240° and 300° bearings.
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90 120
60
15
150
30 10
5
180
0
210
330
0.79 m 240
300 270
Figure 10.3 Results of Whyteleaves tests using small monopole antenna elements  in all cases the source was located 10 m from the locator.
10.2 Tests conducted at the University, December 2001 In these tests, a Yshaped, 4sensor array having a distance of 7 m between the outer sensor elements was tested in the University Sports Hall. Biconical antennas supplied by the Radiocommunications Agency were used as the array elements, further details are given in appendix 14.1. The significant feature of these antennas was that they did not require a common earth plane. Figure 10.4 shows a photograph of the testing arrangements.
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Figure 10.4 Y shaped array consisting of biconical elements being tested in the University Sports Hall The connections between the antennas and oscilloscope were made with Quickform coax. The oscilloscope sampled the data at 2.5 GSps. The aim of these tests was to study the effect of range between the source and the locator. The interference generator was located at several positions along a straight line making an angle of 70° the array. Measurements were taken at distances of 15 m, 20 m and 30 m – the maximum range for these tests was limited by the physical size of the Hall. The location determination was made as outlined in previous sections, although changes to the software were required due to the lower sampling rate of 2.5 GSps. A full analysis of the results is given in appendix 14.2, a summary is given here: Range to source (m)
Estimated range (m)
Range error (m)
Estimated bearing (degrees)
Bearing error (degrees)
30
31.92
1.92
71.6°
1.6°
20
22.63
2.63
71.7°
1.7°
15
16.33
1.33
72.8°
2.8°
Table 10.1 Summary of location results for Sports Hall tests (all results are the average of 5 separate waveforms).
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120
90
40
60
30 150
30
20
10 o Estimated source + Actual source 180 location location
0
210
330 7m
240
300 270
Figure 10.5 Results of University Sports Hall tests using biconical antennas (in all cases the source was located at a bearing of 70° with respect to the locator). It should be noted that the electromagnetic environment of the Sports Hall is less favourable than the OATS facility at Whyteleaves. The building is steel framed and situated close to campus radio and mobile phone transmitters. Since the building size restricted the maximum distance that the source can be placed from the array, an estimate has been made of the limiting range of location. Using results taken at a bearing of 90°, the impulsive and background noise signal magnitudes are as follows: Distance from Impulse signal magnitude Background noise array, D (peak to peak), S (peak to peak) S×D 12 m
60 mV
6.2 mV
0.72 Vm
20 m
38 mV
6.5 mV
0.76 Vm
28 m
23 mV
2.8 mV
0.64 Vm
Table 10.2 Signal and background noise magnitudes at varying distances It should be noted the background noise levels vary considerably as indicated above. Assuming that the locator will be unable to function when the impulsive signal magnitude equals the largest prospective noise signal magnitude, this distance can be found by dividing the average of the S×D vallues by 6.5 mV. This gives an answer of nearly 109 m.
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11 O N SITE APPLICATION OF INTERFERENCE LOCATION 11.1 Introduction The method of radio interference location using a fourantenna array was put into practise in a domestic property during October 2001. The householder, whose property was built under a 132 kV transmission line in the Sedgeley district of Birmingham, suffered from interference problems that affected both UHF analogue TV and VHF FM radio reception. The interference  typically snow on the television screen  was aggravated under dry weather conditions, and often disappeared during rain. A plan of the area is shown in Figure 11.1; the positioning of the house with respect to the overhead line is depicted in Figure 11.2. This type of complaint is consistent with partial discharge activity occurring from the overhead line. The conductors of the line are typically constructed from stranded aluminium wire and are energised to 76 kV (i.e. 132/√3 kV) with respect to the earth. A common defect is caused by a broken strand on the one of the phases protruding from the surface of the conductor into a highly stressed region, this will cause the air to breakdown locally in the region of the protruding strand  a partial discharge (PD). PDs are a well documented source of broadband, localised radio interference [e.g. Bro99]. Conversely, however, it was also possible that the line was inducing a PD effect on the receiving antennas or fixtures. It will be evident from the photographs that the antenna pole, due to its proximity to the line, would experience a high electric field strength. If part of the antenna or fixtures were corroded  sufficient to cause an electrically 'floating' section  then PD activity can result. In both hypotheses  PD from the line, or PD from the antenna pole  the disturbances may reduce under rainfall, since the electrical conducting properties of water would be sufficient to relieve the electrical stress around a broken conductor strand, or to effectively ground part of a floating section.
Figure 11.1 Plan view of house
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(b)
(a) (c)
(e)
(f)
(e)
Figure 11.2 (a)  (d) photographs showing views of antenna and overhead line, (e) and (f) show location of line with respect to the house.
= earth wire
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Figure 11.3 Photographs showing details of the antennas and stand.
11.2 Procedure Since previous studies had shown the accuracy of the location array to be related to the distance between antennas, and that the use of a common ground plane to be problematic (and in this case not particularly practical), each antenna was placed on a separate stand. This enabled greater separation between antennas and also allowed positioning of the antennas in a direct line of sight with the overhead line. Figure 11.3 shows photographs of the stands and monopole sensors (see Figure 10.2) used in the tests. To gain insight into the correct positioning of the array, three different antenna configurations and locations were used: square array located in rear garden; square array located in front garden; rectangular array located in both front and back garden. The positions of the antennas, with respect to the house, were estimated using a measuring tape. As described in section 9, the antenna signals, connected via Quickform coax, were sampled using a Tektronix scope sampling at 2.5 GSps. The most successful arrangement in terms of locating the partial discharge was with the antennas positioned in the front and back garden, this arrangement is shown in Figure 11.4.
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Figure 11.4 Rectangular array arrangement using antennas in both the front and back garden.
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11.3 Results CH1
CH3
(a)
(b)
CH2
CH4
(c)
(d)
Figure 11.5 Signals obtained from antenna array depicted in Figure 11.4 Figure 11.5 shows typical signals of the partial discharge recorded using the array described in Figure 11.4. It is clear from these signals that the source is closer to antennas 1 and 2  located in the rear garden  than antennas 3 and 4  located in the front garden  by comparing the signal magnitudes alone. In previous experimental tests, signals received at the array sensors demonstrated a period at the beginning of the impulse (the direct wave  see Figure 7.3) where the detailed nature of the four waveforms are very similar, followed by a period where multipath effects cause the waveforms to differ. This is also apparent in Figure 11.5, although the direct wave component is not identical in all cases. For the other array arrangements, the signals demonstrated significant differences, particularly in situations where the antenna was located close to the building. It is likely Page 72
that the direct wave is being attenuated in these cases. Further details of these results can be found in appendix 14.3.
11.4 Analysis of results Due to the relative large antenna spacing afforded by the array arrangement of Figure 11.4, the time delay estimates were made by simply finding the position of the initial rising edge of the direct wave component to the nearest sampling interval. Under the conditions described, the source of the interference was clearly coming from above ground level and, hence, the use of the twodimensional location algorithm described in section 4 would not be suitable. A three dimensional approach was therefore needed, and is solved as follows: Assuming the source is located at unknown position (u, v, w) and the receiver antennas are located at known positions: R1 (x1, y1, z1), R2 (x2, y2, z2), R3 (x3, y3, z3), R4 (x4, y4, z5), the system of equations to solve becomes, ( x1 − u ) 2 + ( y1 − v) 2 + ( z1 − w) 2 = d 2
(11.1)
( x2 − u )2 + ( y2 − v) 2 + ( z3 − w) 2 = (d + c∆T12 ) 2
(11.2)
( x3 − u ) 2 + ( y3 − v) 2 + ( z3 − w) 2 = (d + c∆T13 )2
(11.3)
( x4 − u ) 2 + ( y4 − v) 2 + ( z4 − w) 2 = (d + c∆T14 )2
(11.4)
providing four equations with four unknowns, where d is the distance between the source and antenna 1, c is the speed of light and ∆T12 is the time delay between antenna 1 and 2, etc.. This can be solved iteratively by guessing the position of the source, calculating the theoretical time delays between the antennas, and then comparing these with the measured values to form an error function. By searching in 3 dimensional space, the position of minimum error can be found which indicates the partial discharge source location. This approach is not particularly efficient and requires human intervention, but does allow calculation of the source location. Using this method, several waveforms from the array arrangement of Figure 11.4 were analysed and revealed the source to be located at x = 3.04 m, y = 2.73 m and z = 5.41 m . With reference to the plan view of Figure 11.1, and the rear photograph of the house, Figure 11.2(d), the source of the partial discharge can be seen to be located on the tv antenna on top of the pole, see Figure 11.6. This result was confirmed at a later date using a directional ultrasound gun.
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Figure 11.6 Diagrams representing the locating position of the interference source calculated from the measurements.
11.5 Relationship of impulsive noise with 50 Hz waveforms The impulsive noise measured in this work, both experimentally and on site, has arisen due to unwanted effects in an electrical power system  i.e. has been concerned with 50 Hz. This is selfevident in the case of the overhead line partial discharge, but in the case of the noise generator used for the experimental results, the noise arises due to a prolonged switching operation of a single phase load. Power system effects are thus significant generators of impulsive wideband noise. It is therefore important to be able to recognise when impulsive wideband noise is occurring due to power system effects. A further point of interest regarding the occurrence of partial discharges is their relationship with a particular point on the waveform of the local electricity supply. During the recordings made in Birmingham, a separate measurement was made of 100 partial discharge impulses and the local supply voltage simultaneously. Figure 11.7 shows the distribution of the impulses with respect to the voltage angle from which it is clear that impulse generation is related to the electricity supply. It should be pointed out that the phase of the local supply is not necessarily  in fact very unlikely to be  the same as the phase angle on any of the overhead conductors on the line. In Figure 11.7, the impulses are more likely to be occurring at the peaks of the waveform since partial discharge is a voltage related phenomena. Further to this, only one partial discharge impulse was recorded during any voltage halfcycle; on a few halfcycles no impulse was recorded.
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No. of pulses
degrees Figure 11.7 Graph showing distribution of 100 interference pulses recorded with respect to the point on wave of single phase mains voltage at domestic property (one impulse recorded per halfcycle). A similar measurement was made for the impulsive noise generator described in section 10.1.1. In this case the voltage angle was measured from the same voltage used to supply the generator. Figure 11.8 shows the results in the same format as Figure 11.7. In this case a total of 500 impulses were recorded; typically, each halfcycle contained 1025 impulses.
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No. of pulses degrees Figure 11.8 Graph showing distribution of 500 interference pulses recorded from impulsive noise generator (see section 6.1.1) with respect to the supply voltage phase angle (typically 510 impulses recorded per half cycle). The characteristics displayed in Figures 11.7 and 11.8 show power system related wideband impulsive noise can be readily identified by recording the time and rate of arrival of the impulses and noting any repetitions that occur in multiples of 10 ms.
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12 C ONCLUSIONS AND R ECOMMENDATIONS FOR F URTHER W ORK 12.1 Conclusions •
A device capable of locating the source of wideband impulsive interference has been developed based on a 4 element antenna array, a 2.5/25 GSps digital sampling oscilloscope and a laptop computer.
•
The locator has been tested using a variety of experimental approaches and array constructions. In terms of locating sources a significant distance away from the array, the following factors promote the best operation: Y shaped array, large element spacing within the array and high sampling frequency
•
In tests performed to measure the bearing of the source from the array, the locator worked to an accuracy of better than 3 degrees. For range measurements up to 30 m, the locator was accurate to within 3 m. Further testing is needed to confirm its ultimate limit, but it is estimated that the locator will operate up to 100 m.
•
The locator has been successfully used on site, being able to locate partial discharges on a TV antenna situated below a 132 kV overhead line.
12.2 Recommendations for further work Further development of the algorithm is needed as follows: •
A sampling rate of 25GSps was used for the majority of the tests. As explained in section 5.4, the oscilloscope can only work in realtime at sampling rates up to 2.5 GSps. The 25 GSps sampling rate was possible because the interference generator used in the experiments produced a waveform consisting of repetitive impulses of similar waveshapes. This may not be the case in the majority of interference incidents  there may be situations where the impulses exhibit random waveshapes additionally  in which case the lower sampling will be restricted to the lower rate of 2.5 GSps. It would be preferable to use the 2.5 GSps sampling rate for all digitisation and average the located source positions.
•
The search method used to find the optimum window size in the time delay estimation is time consuming. Further development is needed improve this aspect of the algorithm.
•
The locating algorithm was based on a 2dimensional model. It was clear from the site tests in Birmingham that a 3dimensional model is required.
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•
Analysis of the impulses with respect to the point on wave of a 50 Hz sinewave should be made to confirm the nature (i.e. power system related or not) of the impulsive source.
Further practical testing of the locator is needed as follows: •
Further range tests should be performed to confirm the estimated figure of 100 m maximum range capability
•
The biconical antenna described in Appendix 9.1 was the most successful antenna used in the array. Further testing is needed to discover how this antenna performs when the array has a small spacing.
•
The tests made on site in Birmingham were the most relevant in terms of proving the worth of the locator. More site experience of this kind is required.
•
The site tests were disadvantaged by the long lead time needed to set up the equipment and measure the array spacings, etc. In order to facilitate more site work, the locator should be mounted in a vehicle such that it can be operated independently.
12.3 Suggested programme for further work Development of 3dimensional model:
1 month
Changes to time delay algorithm:
2 weeks
Development of 50 Hz point on wave analysis:
2 weeks
Testing at Whyteleave using variable sized arrays based on biconical elements:
1 week
Development of vehicle mounted location capability:
1 month
Vehicle testing at Whyteleave:
1 week
Site testing:
1 month
Analysis of results:
1 month
Estimated manpower:
120 days
Estimated costs of travel, vehicle mounting etc.:
£15,000.
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13 R EFERENCES References – section 5 [Agi00] Agius A. A. and Saunders S. R., "Design and development of a methodology for efficiently tracing the source if intermittent wideband EMC disturbances to Radio Reception", report written for the Radiocommunications Agency, May 2000.
References – section 6 [All77] Allen J. B., “Shorttime spectral analysis, synthesis and modification by discrete Fourier transform,” IEEE Trans. Acoust., Speech, Signal Processing, Vol. 25, pp. 23538, June 1977. [Bril81] Brillinger D. R., Time Series: Data Analysis and Theory, McGraw Hill, 1981. [Bril83] Brillinger D. R., Krishnaiah P. R., “Handbook of statistics 3 – Time series in the frequency Domain,” Elsevier Science Publishers B. V., pp. 111123, 1983. [Car73a] Carter G. C., Knapp C. H. and Nuttall A. H., “Estimation of the magnitudesquared coherence function via overlapped fast Fourier transform processing,” IEEE Trans. Audio Electroacoustics, Vol. AU21, no. 4, pp. 337344, Aug. 1973. [Car73b] G. C. Carter, Nuttall A. H. and Cable P. G., “The smoothed coherence transform,” Proc. IEEE (Letter), Vol. 61m, pp. 14971498, Oct. 1973. [Car81] Carter G. C., “Time delay estimation for passive sonar signal processing,” IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP29, no. 3, Jun. 1981. [Chi90] Chiang H. H. and Nikias C. L., “A New Method for Adaptive Time Delay Estimation for NonGaussian Signals,” IEEE Trans. Acoust., Speech, Signal Processing, Vol. 38, No. 2, Feb. 1990. [Eck52] Eckart C. “Optimal rectifier systems for the detection of steady signals,” Univ. California, Scripps Inst. Oceanography, Marine Physical Lab., Rep SIO 12692, SIO Ref 5111, 1952. [Gab46] Gabor D., “Theory of communication,” J.i.e. E., Vol. 93, pp. 42959, 1946. [Ham74] Hamon B. V. and Hannan E. J., “Spectral estimation of time delay for dispersive and nondispersive systems,” Appl. Statist., Vol. 23, no. 2, pp. 134142, 1974. [Han73] Hannan E. J. and Thomson P. J., “Estimating group delay,” Biometrika, Vol. 60, pp. 241253, Feb. 1973.
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[Has79] Hassab J. C. and Boucher R. E., “Optimum Estimation of Time Delay by a Generalized Corrrelator,” IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP27, pp.373380, Aug. 1979. [Joh82] Johnson D. H., “The application of spectrum estimation methods to bearing estimation problems,” Proc. IEEE, Vol. 70, pp. 97589, 1982. [Kna76] Knapp C. H. and Carter G. C., “The generalized correlation method for estimation of time delay,” IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP24, pp. 320327, Aug. 1976. [Men91] Mendel J. M., “Tutorial on higherorder statistics (spectra) in signal processing and system theory: Theoretical results and some applications,” Proc. IEEE, Vol. 79, pp. 278305, 1991. [Nik87] Nikias C. L. and Raghuveer M. R., “Bispectrum estimation: A digital signal processing framework,” Proc. IEEE, Vol. 75, pp. 86991, July 1987. [Nik88] Nikias C. L. and Pan R., “Time delay estimation in unknown Gaussian spatially correlated noise,” IEEE Trans. Acoust., Speech, Signal Processing, Vol. 36, pp. 170614, Nov. 1988. [Nik93a] Nikias C. L. and Mendel J. M., “Signal processing with higherorder spectra,” IEEE Signal Processing Magazine, Vol. 10, No 3, pp. 1037, July 1993. [Nik93b] Nikias C. L. and Petropulu A., HigherOrder Spectra Analysis: A Nonlinear Signal Processing Framework, New Jersey: PrenticeHall, 1993. [Pec01] Peck C. H. and Moore P. J. “A DirectionFinding Technique for WideBand Impulsive Noise Source,” IEEE Trans. Electromag. Compat. Vol. 43, No. 2, May 2001. [Rag85] Raghuveer M. R. and Nikias C. L., “Bispectrum Estimation: A Parametric Approach,” IEEE Trans. Acoust., Speech, Signal Processing, Vol. 33, pp. 121330, 1985. [Ran91] Rangoussi M. and Giannakis G. B., “FIR modeling using logbispectra: Weighted leastsquares algorithms and performance analysis,” IEEE Trans. Cir. Sys., Vol. 38, pp. 28196, 1991. [Rio91] Rioul O. and Vetterli M., “Wavelets and signal processing,” IEEE Signal Processing Magazine, pp. 1438, Oct 1991. [Rot71] Roth P. R., “Effective measurements using digital signal analysis,” IEEE Spectrum, Vol. 8, pp. 6270, Apr. 1971. [Her85] Hero A. O. and Schwartz S. C., “A New Generalized Cross Correlator,” IEEE Trans. Acoust., Speech, Signal Processing,” Vol. ASSP33, No. 1, Feb. 1985. [Sub84] Subba Rao, T. and Gabr M., An Introduction to Bispectral Analysis and Bilinear TimeSeries Models, pp. 4243, New York: SpringerVerlag, 1984.
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[Swa91] Swami A. and Mendel J. M., “Cumulantbased approach to the harmonic retrieval and related problems,” IEEE Trans. Acoust., Speech, Signal Processing, Vol. 39, pp. 10991109, May 1991. [Tun00] Tungkanawanich A., Abe J., Kawasaki Z. I. and Matsuura K., “Location of partial discharge source on distribution line by measuring emitted pulsetrain electromagnetic waves”, Proceedings of IEEE Power Engineering Society Winter Meeting 2000, IEEE catalog 00CH37077C, CDROM 0780359380.
References – section 7 [Car73b] G. C. Carter, Nuttall A. H. and Cable P. G., “The smoothed coherence transform,” Proc. IEEE (Letter), Vol. 61m, pp. 14971498, Oct. 1973. [Chi90] Chiang H. H. and Nikias C. L., “A New Method for Adaptive Time Delay Estimation for NonGaussian Signals,” IEEE Trans. Acoust., Speech, Signal Processing, Vol. 38, No. 2, Feb. 1990. [Han73] Hannan E. J. and Thomson P. J., “Estimating group delay,” Biometrika, Vol. 60, pp. 241253, Feb. 1973. [Kna76] Knapp C. H. and Carter G. C., “The generalized correlation method for estimation of time delay,” IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP24, pp. 320327, Aug. 1976. [Pec01] Peck C. H. and Moore P. J. “A DirectionFinding Technique for WideBand Impulsive Noise Source,” IEEE Trans. Electromag. Compat. Vol. 43, No. 2, May 2001.
References – section 8 [Fan90] Fang B. T., "Simple Solutions for hyperbolic and Related Position Fixes," IEEE Trans. On Aerospace and Electronic Systems, vol.26, no.5, pp. 748753, Sept.1990 [Buc00] Bucher R. and Misra D. "A Synthesizable Low Power VHDL Model of the exact Solution of Three Dimensional Hyperbolic Positioning System," New Jersey Center for Wireless and Telecommunication, 2000.
References – section 9 [Ell01] Ellingson S. W., “Design and Evaluation of a Novel Antenna for Azimuthal AngleofArrival Measurement,” IEEE Trans. Antenna and Propagation, Vol. 49, No. 6, pp. 971979, Jun 2001. [Hua91] Hua Y., Sarkar T. and Weiner D., “An Lshaped array for estimating 2D directions of arrival,” IEEE Trans. Antenna and Propagation, Vol. 39, pp. 143146, Feb 1991. Page 81
[Sch86] Schmidt R. O. and Franks R. E., “Multiple Source DF Signal Processin: An Experimental System,” IEEE Trans. Antenna and Propagation, Vol. AP34, No. 3, pp. 281, Mar 1986. [Sid97] Sidhu T. S., Singh G. and Sachdev M. S. “Microprocessor Based Instrument for Detecting and Locating Electric Arcs,” IEEE Trans. Power Delivery, PE331PWRD0111997, Nov. 1997. [Tsa96] Tsakalides P. and Nikias C. L., “The Robust CovariationBased MUSIC (ROCMUSIC) Algorithm for Bearing Estimation in Impulsive Noise Environments,” IEEE Trans. Signal Processing, Vol.44. No. 7, pp. 16231633, July 1996.
References  section 11 [Bro99] Brosche T., Hilken W., Fauser E. and Pfeiffer W., "Novel characterisation of PD signals by realtime measurement of pulse parameters", IEEE Trans on Dielectrics & Electrical Insulation, Vol 6, No. 1, pp 5159, February 1999.
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14 A PPENDICES 14.1 Biconical antenna specifications 13.35 cm dia.
110 deg 7.83 cm 4.09 cm 55 deg
3 3
35 deg. 43 deg.
9.43 cm
6.675 cm 47 deg 5.35 cm 8.55 cm
94 deg. 43 deg . 17.1 cm
N connector
ground plane
N / SMA adaptor
antenna
plan view
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14.2 Tests conducted in University Sports Hall, December 2001
Fig. A2.1. Source at 30m 700
Data file
Location
Location
(Folder 2.5GSs at 30m 700)
Xaxis (m)
Yaxis (m)
Data01
9.73082
29.5375
Data02
10.1604
30.8619
Data03
9.87238
29.3431
Data04
10.2556
30.5795
Data05
10.3090
31.1241
Estimated Average
10.0656
30.2892
Actual Location
10.2606
28.1907
Absolute Error (m)
0.19500
2.09850
Table A2.1. Results of location estimation.
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Fig. A2.2 Source at 20m 700
Data file
Location
Location
(Folder 2.5GSs at 20m 700)
Xaxis (m)
Yaxis (m)
Data01
7.19896
21.8263
Data02
7.25334
21.9948
Data03
7.22583
21.7956
Data04
6.94014
20.9036
Data05
6.94014
20.9036
Estimated Average
7.11168
21.4847
Actual Location
6.84040
18.7938
Absolute Error (m)
0.27128
2.6909
Table A2.2. Results of location estimation.
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Fig. A2.3. Source at 15m 700
Data file
Location
Location
(Folder 2.5GSs at 15m 700)
Xaxis (m)
Yaxis (m)
Data01
4.48201
14.1324
Data02
4.93278
15.9767
Data03
4.88128
15.7401
Data04
5.02000
16.4013
Data05
4.87109
15.7183
Estimated Average
4.83743
15.5937
Actual Location
5.13030
14.0953
Absolute Error (m)
0.29287
1.49840
Table A2.3. Results of location estimation.
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14.3 Results from site case study, Birmingham, October 2001
Figure A3.1 Square array arrangement located in rear garden
3
6
3
CH1
x 10
4
CH2
x 10
3 4 2 1 Voltage / V
Voltage / V
2
0
2
0 1 2 3
4
4 6 5 8
0
0.2
0.4
0.6
0.8
3
6
1 Time / s
1.2
1.4
1.6
1.8
6
2
0.2
0.4
0.6
0.8
x 10
3
CH4
x 10
0
7
8
5
1 1.2 Tiime / s
1.4
1.6
1.8
2 7
x 10
CH3
x 10
6
4 4 2
2
Voltage / V
Voltage / V
3
1 0
0 2
1 4 2 6
3 4
0
0.2
0.4
0.6
0.8
1 Time / s
1.2
1.4
1.6
1.8
2
8
7
x 10
0
0.2
0.4
0.6
0.8
1 Time / s
1.2
1.4
1.6
1.8
2 7
x 10
Figure A3.2 Waveforms recorded from antennas in figure A3.1. Location: x = 2.13 m, y = 2.31 m, z = 3.22 m.
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14.4 Square array located in front garden
Figure A3.3 Square array arrangement located in front garden
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3
3
CH1
x 10
8
6
6
4
4
2
2 Voltage / V
Voltage / V
8
0
0
2
2
4
4
6
6
8
0
0.2
0.4
0.6
0.8
3
3
1 1.2 Time / s
1.4
1.6
1.8
8
2
0
0.2
0.4
0.6
0.8
7
x 10
3
CH2
x 10
CH4
x 10
5
1 1.2 Time / s
1.4
1.6
1.8
2 7
x 10
CH3
x 10
4
2
3 1
0
Voltage / V
Voltage / V
2
1
1 0 1
2 2 3
4
3
0
0.2
0.4
0.6
0.8
1 1.2 Time / s
1.4
1.6
1.8
2 7
x 10
4
0
0.2
0.4
0.6
0.8
1 1.2 Time / s
1.4
1.6
1.8
2 7
x 10
Figure A3.4 Waveforms recorded from antennas in figure A3.3.
Location: x = 3.02 m, y = 2.93 m, z = 4.08 m.
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