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CA-CFAR Detection against K-Distributed Clutter in GPR Yıldırım Bahadırlar*a and Mehmet Sezgina a The Scientific and Technological Research Council of Turkey Marmara Research Center, Information Technologies Institute P.O. Box 21, 41470 Gebze-Kocaeli/Turkey ABSTRACT In this study buried object detection on the GPR data is examined using CA-CFAR detector. In the first part of the study the background signals of B-scan frames from a pulse GPR are statistically inspected. The results revealed that the background signals residual from a removing process of the dominant GPR signals due to air-to-ground interface have shown K-Distributed statistics. The form and scale parameters of K-Distribution are estimated using the fractional moments. The background or the clutter signals from three different soils have resulted in distinctive shape parameters. The shape parameter of the distribution could generally discriminate three soils. In the second part of the study the receiver loss of CA-CFAR detector is estimated using a numerical method and the Monte-Carlo simulation. The receiver loss is also associated to the K-Distribution and CA-CFAR detector parameters in the simulation. Time series with statistical properties similar to those of the real measurements are obtained using SIRV and employed in the Monte-Carlo simulation. In the third part of the study effectiveness of CA-CFAR detector on B-scan frames is analyzed by measuring the ROC of the detector. High detection probabilities of buried objects at relatively low SNR data are obtained by CA-CFAR detector. Keywords: Adaptive filtering, Buried Object Detection, CA-CFAR, GPR B-scan, K-Distribution, Receiver Operating Characteristics, Spherically Invariant Random Vectors.
1. INTRODUCTION This study aims to detect buried objects on GPR (Ground Penetrating Radar) B-scan data using the CA-CFAR (Cell Averaging-Constant False Alarm Rate) detector. A B-scan frame is formed from the A-scan data at a certain pulse repeating frequency of the radar while GPR antenna is moving along a line on the soil. Each A-scan is due to a short pulse of the antenna focused on the ground. Thus a B-scan frame characterizes the backscattering electromagnetic waves from a vertical cross-section of the ground. In the ideal case the radiation from the antenna should be as large as possible and clutter should be minimized, so that the backscattering from the buried object is not obscured. In practice, however there are inevitable sources of clutter due to the antenna, the soil and the interactions of both. The sources of clutter particularly includes multiple reflections between the rough surface of the soil and antenna, reflections internal to antenna and reflections from the soil due to radiation from the open ends of the antenna. Fortunately, the frequency components and magnitude distributions of most clutter can be assumed as wide-sense stationary processes and they have slowly varying values along a B-scan frame. The clutter resulting from the interactions mentioned may be defined as slowly varying strong background signals included in a raw GPR data. Before an application of the detection process, these heavy reflections should be removed from a B-scan to enhance the signal-to-clutter ratio (SCR). In this study a transform-domain adaptive filter scheme is implemented for this background elimination process. 1 The residual signal after the adaptive filtering may be mostly composed of the radar system noise and the impulse response of an effective system which is generally formed by the soil itself, inhomogeneous structures (distinct scatterers) of the soil and buried object in the soil. The statistical properties of the remaining clutter in this composite signal have to be determined while designing a CA-CFAR detector. The B-scan data in the study is acquired using a pulse GPR with modified bow-tie antenna and operating in the frequency band below 1GHz. *
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If the radar signals backscattered from rough surfaces and from a small number of scatterers in a target volume are also influenced by a slowly varying and modulating factor, the time series quantized from these signals have mainly KDistributed statistics. Similar statistics can also be observed on the backscattered signals of active laser and ultrasound sensors. 2-4 With the motivation of these findings the statistical properties of GPR data from three different test pools filled with different soil types are inspected after the data is processed by the adaptive filtering. The most segments of the data prove K-Distributed statistics and this is verified by Kolmogorov-Smirnov tests. The scale and shape parameters of the K-Distribution are estimated using the fractional higher order moments. 5 In general it is observed that the soil types can be differentiated using the shape parameter of the K-Distribution. It is probable to obtain a desired PFA (Probability of False Alarm) at the output of a receiver by calculating CDF (Cumulative Density Function) of an underlying distribution and by using a constant threshold detector when the parameters of the distribution are known ideally and the time series does not locally show any non-stationary characteristics. Otherwise, CA-CFAR (Cell Averaging-Constant False Alarm Rate) detector can be used to get constant PFA rate over a non-stationary data set. The mean value of the clutter is locally estimated in the CA-CFAR detector and dependent on the number of averaging cells and the number of guard cells of the detector. Thus, a CA-CFAR loss should be defined and the gain factor α of the detector has to be modified by this loss factor which can be also defined depending on the CA-CFAR parameters and the properties of the underlying distribution. 6-7 Because of the difficulties to derive the close form solution to the loss factor the Monte-Carlo Simulations are fulfilled to get the gain factor α. The time series of K-Distribution having similar statistical parameters to the measured data are produced using SIRV (Spherically Invariant Random Vector) and used in the Monte-Carlo Simulations. The CA-CFAR loss represented by the changes in α is obtained for each corresponding PFA value. The CA-CFAR detector is realized using the results of these simulations and promising results are achieved in buried object detection on GPR data.
2. TRANSFORM-DOMAIN ADAPTIVE FILTER FOR BACKGROUND ELIMINATION The reflections resulting from the interactions mentioned above may be defined as slowly varying strong background signals included in a raw GPR data. Before an application of the detection process, this dominant background should be eliminated from a B-scan to enhance the signal-to-clutter ratio. In this study a transform-domain adaptive filter scheme represented in Fig. 1. is implemented for this background removing process.
Reference signal Averaging
Wk(m) Xk N-Point FFT
Ek(m)
-
Σ
N-Point FFT-1
+ s(m)
N-Point FFT
Dk(m)
B-scan without background
Raw B-scan Fig. 1. Transform-domain adaptive filter with a raw B-scan, a reference signal and an output without heavy background.
The adaptive filter utilizes first five A-scans to get an average of the background and keeps this average vector as the reference signal throughout the adaptive process of a B-scan frame. The filter seeks to decrease the energy of the signal or the error at the output. 1
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3. DATA ANALYSIS AND DETECTION 3.1. Parameter Estimation of the K-Distribution The K-Distribution as a general class includes Rayleigh and Rician Distributions and can be given as in the equation (1) with the shape and the scale parameters:
f X ( x) =
2 ⎛ x ⎞ ⎜ ⎟ aΓ (v + 1) ⎝ 2a ⎠
v +1
⎛ x⎞ K v ⎜ ⎟, x > 0, v > −1 ⎝a⎠
(1)
Where, Γ(.) is Gamma function, Kv(.) is modified Bessel function, v and a are the shape and the scale parameters, respectively. If a measured signal can be statistically characterized by (1) the Probability of False Alarm PFA corresponding to a particular threshold value XT is written as the following: 5, 8
PFA =
2 ⎛ XT ⎞ ⎜ ⎟ Γ(v + 1) ⎝ 2a ⎠
v +1
⎛X ⎞ K v +1 ⎜ T ⎟ ⎝ a ⎠
(2)
The shape and the scale parameters should be also estimated from the time series to obtain a particular rate of the false alarm. Although these parameters are conventionally approximated using the second and the fourth order moments, the fractional moments can be utilized to achieve better parameter estimation with lower standard deviations. The equation (3) can be written to estimate the shape parameter and the equation (4) is used to calculate the scale parameter using the first order moment µˆ1 . 5 The particular sample moment µˆ k can be estimated using measured data as given by (5). 2
⎛⎜ p + 2 ⎞⎟ − β p µ p+2 2⎠ v=⎝ , βp = , p>0 µ pµ2 β p − ⎛⎜ p + 2 2 ⎞⎟ ⎠ ⎝
µk =
(3)
Γ(0.5k + 1)Γ(v + 1 + 0.5k ) ( 2a ) k Γ(v + 1)
(4)
1 N k ∑ xi , k ≥ 0 N i =1
(5)
µˆ k =
Where, N presents the number of samples used in the sample moment estimations. Fig. 2 shows the Probability Density Functions (PDFs) of K-Distribution while the scale parameter a is kept constant and the shape parameters v is changed in between v=2 to v=9. While the PDF with the biggest shape parameter approximates to Rayleigh PDF, the other with smaller shape value approximates to the Exponential PDF at the limit case and represents more spiky clutter signals. In the study the shape parameter v is estimated by selecting p=0.5 and using the fractional moments; k=0.5, 2.0 and 2.5. One hundred segments with N=768 samples corresponding to three soil types are analyzed. Table 1. shows the mean and the median values of the shape and the scale parameters as the results of this clutter analysis.
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Fig. 2. The PDFs of the K-Distribution with respect to varying shape parameter.
Kolmogorov-Smirnov tests are applied using estimated parameters in Table 1. to confirm that the segments have KDistributed statistics. 81% of them have demonstrated K-Distributed statistics in 95% confidence interval. 9 Fig. 3. shows three K-Distributions plotted using the median values of the shape and the scale parameters of the soils. Table 1. The shape and the scale parameter estimations particular to the test pools. Pool P-1 P-2 P-3
Soil Type
Mean a
v
normal w/ coarse grains w/ fine grains
0.55 0.53 0.58
2.34 2.52 1.92
Mean
0.55
Median a v 0.56 0.54 0.58
1.71 2.06 1.51
0.56
Fig. 3. The PDFs of the K-Distribution corresponding to estimated shape and the scale parameters specified in Table 1.
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3.2. CA-CFAR Detector and the Loss Estimation using Monte-Carlo Simulation
A typical CA-CFAR detector is shown in Fig. 4. with the guard cells G, averaging cells M and the gain factor α. If ideal parameters of the PDF are known the threshold value XT of a detector can be calculated for a particular PFA using the equation (2) and in principle the gain factor α of the CA-CAFAR detector then equals to XT/µ1, assuming that the input signal x does not have local statistical variations. However, for the case of non-stationary input signal the CACFAR detector uses local estimates of the mean ( µˆ1 ) and thus the factor α may be higher than its ideal value and changes with time. In addition an autocorrelation feature of the input signal may also change the factor α (see Fig. 8-9.). The difference defined in between the ideal value of α and the value estimated by the numerical analysis can be called CA-CFAR loss. 6, 7
y x
M/2
G
G
Σ
M/2
t
Σ 1/M
Σ
µˆ
α
Fig. 4. The CA-CFAR detector with gain factor α.
In the study the K-Distributed time series were generated in accordance with the shape and the scale values given in Table 1. and using SIRVs. 10 Each gain factor α corresponding to a particular PFA, a number of guard cells and averaging cells was estimated using Monte-Carlo simulations in which the time series with 106 samples were composed and used as simulated clutter signal for the CA-CFAR detector. The equation (2) was solved by a numerical technique for each XT particular to a PFA and the factor α is calculated using the first order sample moment. The differences in between the estimated and analytic values of α were shown as the loss of the CA-CFAR detector. The α values from the Monte-Carlo simulations were utilized in buried object detection and as extracting the Receiver Operating Characteristics (ROC) of the CA-CFAR detector. Fig. 5. shows the gain factor α versus PFA in dB scale and indicates the CA-CFAR loss in particular to the number of averaging cells M=64 and the number of guard cells G=40.
Fig. 5. The CA-CFAR loss corresponding to different shape parameters; v = 1.5, v = 2.0 and a = 0.55.
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4. RESULTS AND DISCUSSIONS In the analysis the B-scan frames are initially passed through the adaptive filter as depicted in Fig. 1. and then a linear range gain is applied to compensate the systematic loss of the electromagnetic waves penetrating into the soil. Each Ascan of the frame is considered to come one after the other, so that “a long range” data is virtually obtained. While the CA-CFAR detector is applied to this data the slices of a buried object signature passed periodically through the detector. In the analysis a qualified operator accepted a buried object as detected if significant slices of the signature could appear at the output of the detector. Fig. 6. presents the ROC of the CA-CFAR detector, for which 20 B-scan frames from the soil with the lowest shape parameter (v=1.51) are averaged in the analysis. In the case, the probability of detection (PD) is equal to 80% for PFA=10-3 at the SCR achieved after the adaptive filtering. The PD is about 95% for PFA=10-2. However some impulsive detections are observed on the B-scans. An excessive local variation of the shape parameter and/or a strong background scattering may cause these weak detections. A 3x3 median filter can easily suppress these impulsive noises on the processed B-scans. The PD reduces to 85% for PFA=10-2 as the median filter is used. Fig. 7. shows examples of the detections from four different buried objects. The figure also presents three phases of the detection process proposed in the study; namely, the adaptive filtering, the CA-CFAR detection and the median filtering. It can be also inferred from Fig. 7. by inspection that the SNR of the GPR data is relatively low. In conclusion the residual clutter signals from three different soil types have generally K-distributed statistics with distinctive shape parameters that can be successfully estimated using the fractional moments in the study. The proposed study has promising results both in discrimination of the soils using the GPR data and in detection of buried objects using the CA-CFAR detector. The CA-CFAR detection and similar analysis will be realized on higher resolution and on higher SNR comprehensive GPR data.
Fig. 6. The ROC of the CA-CFAR detector with median filtering.
REFERENCES 1. 2.
Y. Bahadırlar and G.B. Kaplan, “Frequency-domain preprocessing and directional correlation-based feature extraction for classification of the buried objects using GPR B-scan data,” SPIE Defence & Security Symp., Orlando, 5415-112, April 2004 E. Jakeman and P.N. Pusey, “A Model for Non-Rayleigh Sea Echo,” IEEE Trans. on AP, 24(6), pp. 806-814, 1976.
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(a)
(b)
(c)
Fig. 7. Some examples of the CA-CFAR detections and the median filtering; the output of (a) the adaptive filter, (b) the CA-CFAR detector, (c) the median filter.
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3.
K.D. Ward, C.J. Baker and S. Watts, “Maritime surveillance radar Part 1: Radar scattering from the ocean surface,” IEE Proc., 137(2), Pt. F, pp. 51-61, 1990. 4. R.C. Molthen and et. al., “Comparison of the Rayleigh and K-Distributed Models using in vivo Breast and Liver Tissue,” Ultrasound in Med. & Biol., Elsevier, 24(1), pp. 93-100, 1998. 5. D.R. Iskander and A.M. Zoubir, “Estimation of the Parameters of the K-Distribution using Higher Order and Fractional Moments,” Trans. on AES, 35(4), pp. 1453-1457, 1999. 6. S. Watts, “Cell-averaging CFAR gain in spatially correlated K-distributed clutter,” IEE Proc. Radar, Sonar Navig., 143(5), pp. 321-327, 1996. 7. S. Watts, “The Performance of Cell-Averageing CFAR Systems in Sea Clutter,” IEEE Intl. Radar Conference, Alexandria VA, pp.398-403, May 2000. 8. R.S. Raghavan, “A Method for Estimating Parameters of K-Distributed Clutter,” Trans. on AES, 27(2), pp. 238246, 1991. 9. E.W. Weisstein, “Kolmogorov-Smirnov Test,” from MathWorld - A Wolfram Web Resource, http://mathworld.wolfram.com/Kolmogorov-SmirnovTest.html. 10. M. Rangaswamy, D.D. Weiner and A. Öztürk, “Computer generation of correlated non-Gaussian radar clutter,” IEEE Trans. on AES, 31(1), pp. 106-116, 1995.
Fig. 8. The CA-CFAR loss drops as the data has an autocorrelation property as given in Fig. 9.
Fig. 9. Typical autocorrelation curves of a B-scan frame in the data and its curve fitted counterparts.
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