Adaptive matched filter spatial detection performance

Transcription

1 Adaptive matched filter spatial detection performance on standard imagery from a wideband VHF/UHF SAR Mark R. Allen Seth A. Phillips Dm0 J. Sofianos Science Applications International Corporation Campus Point Drive, San Diego, CA ABSTRACT The adaptive matched filter was Implemented as a spataj detector for amplitude-only or complex images, and applied to an image formed by standard narrowband means from a wide angle, wideband radar. Direct performance comparisons were made between different implementations and various matched and mismatched cases by using a novel approach to generate ROC curves parametrically. For perfectly matched cases, performance using imaged targets was found to be significantly lower than potential performance of artificial targets whose features differed from the background. Incremental gain due to whitening the background was also found to be small, indicating little background spatial correlation. It is conjectured that the relatively featureless behavior in both targets and background is due to the image formation process, since this technique averages together all wide angle, wideband information. For mismatched cases where the signature was unknown, the amplitude detector losses were approximately equal to whatever gain over noncoherent integration that matching provided. However, the complex detector was generally very sensitive to unknown information, especially phase, and produced much larger losses. Whitening under these mismatched conditions produced further losses. Detector choice thus depends primarily on how reproducible target signatures are, especially if phase is used, and the subsequent number of stored signatures necessary to account for various imaging aspect angles. 1. INTRODUCTION A CFAR adaptive matched filter (AMF) detector was previously introduced [1] for an array antenna radar, under the assumption of zero-mean complex Gaussian interference with estimated covariance. This detector was shown to be CFAR and, when the signal is matched, to have theoretical detection performance similar to that of a generalized likelihood-ratio test (GLRT). The AMF detector has the computational advantage of a simplified test statistic that is the limiting case of the GLRT detector when a large number of reference samples is used to estimate the background covariance matrix. In addition, the AMF detector was shown to be less sensitive to mismatch between the true and hypothesized signal vectors. In this paper, the AMF detector is applied as a spatial matched filter, on imagery obtained from a wideband VHF/UHF SAR. The radar uses a wideband impulse waveform and a wide angle linear dipole array with horizontal polarization [2]. Data under study were collected during a foliage penetration (FOPEN) 188 ISPIE Vol /94/$6.OO

2 experiment in August 1992 at Portage, Maine. Returns from the MHz receiver were digitized by two eight-bit AID converters operating at 500 MHz to form I/O samples - apparently without saturation. Image formation consisted of a standard narrowband integration operating over about 40 azimuth angles [3]. The AMF spatial detector is implemented in two ways, one for amplitude images and one for complex images, as described in Section Il. Detection results for certain important matched and mismatched cases are presented in sections Ill and IV for amplitude and complex implementations, respectively. Section V summarizes tentative conclusions and recommendations. The objective is to quantify bounds on AMF detection performance and robustness for targets obscured by trees, using this SAR experimental data and standard image formation. This serves for comparison with other radars and other detection or image formation algorithms, as part of the War Breaker program FOPEN detection study sponsored by the Advanced Research Projects Agency (AR PA). 2. AMF DETECTOR IMPLEMENTATION Using lexicographic ordering, an MxN rectangular image patch can be written as a vector of length MN. Following the notation in [1], the target signal is modeled as vector bs, where S is a hypothesized signature vector and b is an unknown complex scalar (amplitude and initial phase). The measurements consist of a primary measurement vector z, and a set of secondary reference vectors, z(k), k=1,..,k from which the covariance matrix M is estimated using the maximum likelihood formula (superscript "+" denotes conjugate transposition), = z(k) z(k) (1) The adaptive matched filter (AMF) test form is then, Hi S+ f1_1 z2 >a (2 S+11S < H0 where the product s forms an estimated weight vector *. Although neither the AMF detector above nor the GLRT detector mentioned previously is optimum in the Neyman-Pearson sense of maximizing d for fixed Pf, both detectors approach optimum detector performance (i.e., covariance matrix M is known) if the background is stationary Gaussian and the number of reference vectors z(k) is large. The SAR data under study does not satisfy this stationary Gaussian hypothesis. Using estimates of its first four moments, the image background intensity (squared magnitude) pdf appears to closely follow a gamma pdf where number of duo-degrees of freedom is less than the unity result obtained for Gaussian data. This however is consistent with the well known K-density compound clutter model [4] for the case where narrowband speckle contribution is small. SPIE Vol. 2217/ 189

3 The SAR image signature vector S may not be fully known or even stable enough to fully quantify, especially its phase information. Thus the test is implemented either for fully complex or for amplitude-only image data. The only difference is that, since the amplitude data has nonzero mean, the mean is estimated and subtracted from each pixel before processing. The signature vector S is matched when, under target-present conditions, the measurement vector consists of the sum z=s+n, where n is the mean-zero noise vector; any other signature vector is mismatched. It is assumed for simplicity that the target signal is contained in a rectangular patch whose size is known; signatures of other shapes can be accounted for by zero padding. Since the image data contains only a few targets, direct construction of a receiver operating characteristic (ROC) curve has limited meaning. Morevover, some target vehicles in the image are different, exacerbating the situation. Thus instead of the common approach, we have used the following novel method to obtain ROC curves. Start with the largest single rectangular cut from the image that, from ground surveys, is known to contain only background interference from trees (1024x256 pixels). Since this image background cut is a fairly homogeneous sample of dense forest returns, the covariance matrix M is estimated once using the entire cut. As the detector scans the background cut, a signal patch is scaled according to desired SIR and added to the background patch being operated on by the detector to obtain the detector measurement vector z. In this way, many independent opportunities are created for detecting the same target signature, and furthermore the SIR is under control by scaling. A ROC curve is generated by first forming a histogram of the detector output when signal is absent and integrating this histogram to obtain false alarm probability Pf versus threshold. Using the same histogram bin values, the detector output when signal is present (at specified SIR) is then placed into a second histogram and integrated to obtain detection probability d versus threshold. The resulting two functions are plotted against each other and numerically smoothed to obtain a single-valued d versus Pf ROC curve. A family of curves can be generated by repeating this procedure for several SIR values. By specifying an operating point (fixed Pd and Pf values) the family of ROC curves can be used to find required single pixel SIR values which, when compared for various cases, yield direct estimates of detector gains or losses. The signature vector s can be chosen to either match or mismatch the vector used for the measurement z. In addition, the detector can be simplified to a nonwhitening form by forcing the covariance matrix M to be the identity matrix, in order to find the incremental gain due to whitening the background. Results for certain important matched and mismatched cases, using both whitening and nonwhitening detector forms, are summarized below. 3. AMPLITUDE-AMF DETECTOR RESULTS Three signal patches were used; two were cuts from known concealed targets in the image, designated as "target a" and "target b", and the third was a "uniform" (constant amplitude) patch of the same size. The two targets were chosen among a group of eight because they had a relatively bright and well defined signature of similar size, and their orientation in the 190/SPIE Vol. 2217

4 image was vertical, making them easy to cut using a rectangular patch (8 range by 16 cross-range pixels). Note that 500 MHz digitization yielded approximately two and one half times oversampling in range whereas the combination of PRF and aircraft velocity resulted in approximately two times oversampling in cross-range. Thus the number of pixels used in the detection patch (128) is about five times the number of nearly independent pixels. Each independent pixel represents about one meter by one meter on the ground. Five cases were computed for both whitening and nonwhitening detector forms; the first three are the matched cases for the three signal patches. For each matched case the signature vector S is scaled and added to the background to form the measurement vector z. The last two cases are mismatched cases that use the uniform signature S to detect one of the two targets in the measurement vector z. From the family of ROC curves computed for each case, the required single pixel db SIR was extracted for an operating point of interest. For the amount of background data at hand, this operating point was chosen to be d=o9, Pf=1 and results are given in Table 1. Signal Model Detector Form Signature (s) Measurement (z) Whitening Nonwhitening Target a Target a Targetb Targetb Uniform Uniform Uniform Target a Uniform Targetb Table 1. Required Single Pixel db-sir for Pd=0.9, Pf=1 0 Amplitude-AMF Detector in Dense Tree Background (8x16 Pixels). To interpret these results, note that a square-law noncoherent integrator (simple energy detector) was also used for both targets in this data, and the resulting required single pixel db-sir was the same, as it should be, at db. With this in mind, the first two cases show that, for realistic targets cut from the image, if the signature is known exactly but the background covariance is not estimated (nonwhitening), the detector gain is only about 2-3 db over energy detection. For these perfectly matched cases the whitening gain due to background covariance estimation is an additional 1-4 db. Thus the total gain possible for realistic targets is about 3-7 db, compared with energy detection. The third case was also perfectly matched, but used a uniform signature. Interestingly, both the nonwhitening and whitening detector gains are consistent with those obtained for the two targets. The uniform signature can be thought of as a perfectly correlated "blob" whose only feature is that its overall response does not decay in space in exactly the same way as the system impulse response; apparently, the targets are about as featureless. SPIE Vol. 2217/ 191

5 The last two cases are mismatched to represent when the target signature is completely unknown and hence a uniform model is assumed. For the nonwhitening detector, the loss for this mismatch (compared with itself) is only about a db or less, whereas for the whitening detector the loss was so large that the resulting performance was about the same as or worse than energy detection. Thus although the whitening detector gave some additional gain in matched cases, it is not as robust to signature modelling errors as the nonwhitening detector. 4. COMPLEX-AMF DETECTOR RESULTS For the complex implementation, the same two targets were used in both matched and mismatched cases. In addition, two artificial signatures were used to illustrate potential gains if more features were present. A total of eight cases were computed, with the first four matched and the last four mismatched. Results in the form of required single pixel db-sir for the same operating point are summarized in Table 2. Signal Model Detector Form Signature (s) Measurement (z) Whitening Nonwhitening Targeta Targeta Targetb Targetb Uniform (A and ) Uniform (A and i) A=Unif, =lndex A=Unif, =Index A=Unif, =Target a Target a A=Target a, =Unif Target a A=Unif,=Targetb Targetb A=Targetb,=Unif Targetb Table 2. Required Single Pixel db-sir for d=o.9, Pf=104. Complex-AMF Detector in Dense Tree Background (8x16 Pixels). The first two cases in Table 2 are matched using the same target cuts from the image as before. Since the phase information provides another degree of freedom, performance is better than the corresponding result for the amplitude detector. However, considering the number of independent pixels involved in the detection patch, about one-fifth of the number of pixels present, gains over amplitude detection should be much larger than the 3-5 db exhibited. The third and fourth cases in Table 2 show this to be true. For the third case a signature with uniform amplitude and phase is used. Since the image contains an average phase progression in range due to range delay, this signature has a phase progression very different from the average background in the range dimension. The gain due to this is large; about 20 db over the two realistic target cases. The fourth case showns that an additional 20 db or so is gained if the signature phase is very different from the average background in both dimensions. Thus although potentially the complex AMF detector can 192/SPIEVoI. 2217

6 gain 50 db in sensitivity over noncoherent integration (for the patch size used), gains for targets in the image were only about 9-10 db. The last four cases are mismatched to represent when either the target signature amplitude or its phase is unknown and therefore assumed to be uniform. For the whitening detector all such cases are disastrous, whereas for the nonwhitening detector, if only the amplitude is unknown, little loss is incurred. However, even the nonwhitening detector is very sensitive to phase information, exhibiting losses of more than 10 db over simple energy detection. 5. CONCLUSIONS For both the amplitude and complex AMF detector implementations, upper bounds on performance for targets cut from the image were significantly below potential bounds. The incremental effect of whitening for perfectly matched cases was small, indicating that the image background contained little spatial correlation. We believe that the relatively featureless properties of both target and background exhibited are mainly due to the standard narrowband technique used to form the images, since this technique averages together all the wide angle, wideband information present, washing it out. Since the various implementations exhibit differing degrees of sensitivity to signature, detector choice depends primarily on how reproducible the target signatures are and the subsequent number of stored signatures necessary to account for various imaging aspect angles. Detector performance is particularly sensitive to phase information, whose reproducibility is highly questionable for images formed synthetically from wideband sensors. 6. ACKNOWLEDGEMENTS The authors greatly thank Dr. Lawrence F. Hoff of NCCOSC and Dr. Larry B. Stotts of ARPA for their productive discussions and support. 7. REFERENCES [1] Robey, F.C., et al., "A OFAR adaptive matched filter detector", IEEE Trans. on Aerospace and Electronic Systems, vol. AES-28, pp , January [2] Vickers, R.S., et al., "Results from a VHF impulse synthetic aperture radar", SPIE vol (Conference:Ultrawideband Radar), pp , January [3] Toups, M.F., and Gosselin, D.R., "The Maine 1992 foliage penetration experiment - part 1: experiment and FOPEN phenomenology", 39th Tn-Service Radar Symposium, Monterey, CA, June [4] Jao, J.K., et al., "K-distribution and polarimetric radar clutter", Journal of Electromagnetic Waves and Applications, vol. 3, pp , August SPIE Vol. 2217/ 193