US H2222 H1 Abstract This invention addresses the problem of radar target detection in severely heterogeneous clutter environments. Specifically, we present the performance of the normalized matched filter test in a background of disturbance consisting of clutter having a covariance matrix with known structure and unknown scaling plus background white Gaussian noise. It is shown that when the clutter covariance matrix is low rank, the (LRNMF) test retains invariance with respect to the unknown scaling as well as the background noise level and has an approximately constant false alarm rate (CFAR). Therefore, a technique known as self-censoring reiterative fast maximum likelihood/adaptive power residue (SCRFML/APR) is developed to treat this problem and its performance is discussed. The SCRFML/AP method is used to estimate the unknown covariance matrix in the presence of outliers. This covariance matrix estimate can then be used in the LRNAMF or any other eigen-based adaptive processing technique.
Claims(5) 1. A radar target detection process for producing a target detection signal from a radar data stream received from a heterogeneous clutter environment with clutter and interference using a signal vector with radar target detection process producing a detection signal for hypothesis H
_{0}, when the signal of interest is not present in the observed data signal and H_{1 }when the signal of interest is present in the observed data signal, said radar target detection process comprising the steps of:
forming an estimate of a covariance matrix of the clutter and interference in the heterogeneous clutter environment;
a first subtracting step that comprises subtracting the signal vector from the observed data signal from the host system to produce thereby a first subtraction signal;
estimating the signal of interest from the observed data signal to produce an estimate signal;
a first step which uses a first linear prediction error filter which processes the first subtraction signal and the estimate signal to produce thereby an output signal;
a second step which uses a second linear prediction error filter which processes the observed data signal from the host system with the estimate signal to produce an output signal;
a transforming step that comprises transforming the output signal of the first linear prediction error filter using a first ZMNL tansformation unit;
a second transforming step that comprises transforming the output of the second linear prediction error filter using a second ZMNL transformation unit
a second subtracting step that comprises subtracting the second ZMNL transformed signal from the first ZMNL transformed signal to produce thereby a second subtraction signal; and
generating threshold signals from the second subtraction signal to produce thereby said detection signal for said host system.
2. A radar target detection process as described in
where
is a steering vector of the host system and {circumflex over (Σ)}
^{−1 }is an inverse of an estimated data covariance matrix, and X is the observed data signal received by said host system.3. A radar target detection process as described in
4. A radar target detection process, as described in
5. A radar target detection process, as described in
where H
_{0 }denotes the condition where no signal of interest is present in the observed data signal and H_{1 }denotes that the signal of interest is present in the observed data signals received by the host system and wherein G.sub.j.sup.2 (k) is the associated estimated variances of the error signals.Description The invention described herein may be manufactured and used by or for the Government for governmental purposes without the payment of any royalty thereon. The invention relates generally to radar receivers, and more specifically, it relates to a low rank approximation to interference covariance for target detection in non-Gaussian clutter. This invention addresses the problem of signal detection in interference composed of clutter (and possibly jamming), having a covariance matrix with known structure but unknown level and background white noise. The technique developed in this paper ensures invariance with respect to the unknown level and the background noise power. The research is motivated by the problem of space-time adaptive processing (STAP) for airborne phased-array radar applications. Typically, a radar receiver front end consists of an array of J antenna elements processing N pulses in a coherent processing interval. We are interested in the problem of target detection given the JN×1 spatio-temporal data vector. Patented art of interest includes the following U.S. Patents, the disclosures of which are incorporated herein by reference: U.S. Pat. No. 6,771,723 entitled Normalized parametric adaptive matched filter receiver issued to Davis U.S. Pat. No. 5,640,429 issued to Michels and Rangaswamy; U.S. Pat. No. 5,272,698 issued to Champion; U.S. Pat. No. 5,168,215 issued to Puzzo; U.S. Pat. No. 4,855,932 issued to Cangiani; and U.S. Pat. No. 6,266,321 issued to Michels, et al. The Davis patent describes an apparatus and method for improving the detection of signals obscured by either correlated Gaussian or non-Gaussian noise plus additive white noise. Estimates from multichannel data of model parameters that described the noise disturbance correlation are obtained from data that contain signal-free data vectors, referred to as “secondary” or “reference” cell data. These parameters form the coefficients of a multichannel whitening filter. A data vector to be tested for the presence of a signal passes through the multichannel whitening filter. The filter output is then processed to form a test statistic. Cangiani et al. disclose a three dimensional electro-optical tracker with a Kalman filter in which the target is modeled in space as the superposition of two Guassian ellipsoids projected onto an image plane. Puzzo offers a similar disclosure. Champion discloses a digital communication system. Michels et al., U.S. Pat. No. 6,226,321, hereby incorporated by reference, discloses implementations, for a signal that has unknown amplitude. For the signal of unknown amplitude, Michels et al. teaches us how to incorporate the estimated signal amplitude directly into the parametric detection procedure. Furthermore, Michels teaches two separate methods, namely, (1) how to detect the signal in the presence of partially correlated non-Gaussian clutter disturbance and (2) how to detect the signal in the presence of partially correlated Gaussian clutter disturbance. Furthermore, the method to detect the signal in the presence of partially correlated non-Gaussian clutter involves processing the received radar data and requires the use of functional forms that depend upon the probability density function (pdf) of the disturbance. Thus, the latter method requires knowledge of the pdf statistics of the non-Gaussian disturbance. The method does not teach how to process the data in such a manner that would not require knowledge of the disturbance processes. Furthermore, it does not teach how to process the data with one method that would detect the signal in either Gaussian or non-Gaussian disturbance. Thus there exists a need for apparatus and method of processing the data with a detection method that does not require knowledge of the clutter statistics. Furthermore, there exists a need for a method that detects the signal in either Gaussian or non-Gaussian disturbance. The performance improvements of the presently disclosed invention relative to prior art are detailed in J. H. Michels, M. Rangaswamy, and B. Himed, “Evaluation of the Normalized Parametric Adaptive Matched Filter STAP Test in Airborne Radar Clutter,” IEEE Internationals Radar 2000 Conference, May 7-11, 2000 Washington, D.C. and J. H. Michels, M. Rangaswamy, and B. Himed, “Performance of STAP Tests in Compound-Gaussian Clutter,” First IEEE Sensor Array and Multichannel Signal. Previous efforts derived the normalized matched filter (NMF) test for the problem of detecting a rank one signal in additive clutter modeled as a spherically invariant random process. The NMF test is given by
We developed a technique known as the low rank normalized matched filter (LRNMF) for radar target detection in disturbance composed of clutter and background white noise, having unknown but differing power levels. We show that the LRNMF test exhibits invariance with respect to the unknown clutter and noise power levels, when the clutter covariance matrix is low rank. Performance of the test is shown to be a function of the number of antenna array elements, number of pulses processed in a coherent processing interval (CPI) and the rank of the clutter covariance matrix, which can be determined from system parameters such as platform speed, inter-element spacing, and pulse repetition interval (PRI). Consequently, the technique offers a constant false alarm rate (CFAR) for the case where the clutter and noise covariance matrices have known structure and unknown scaling. An adaptive version of the test known as the low rank normalized adaptive matched filter (LRNAMF) is developed to address the problem of target detection when both the covariance structure and level for the clutter and noise are unknown. The LRNAMF performance is benchmarked in terms of the sample support needed for attaining detection performance to within 3 dB of the LRNMF. Issues of CFAR and clutter rank determination are also addressed. Performance analysis is carried out using data from the knowledge aided sensor signal processing and expert reasoning (KASSPER) Program. The present invention includes a technique known as the low rank normalized matched filter (LRNMF) for radar target detection in disturbance composed of clutter and background white noise, having unknown but differing power levels. This invention seeks to extend previous work by including the effect of additive white Gaussian noise. Specifically, we consider the binary hypothesis testing problem given by
In order to understand the advantages of the present invention, the reader's attention is now directed towards The output of the 56 Kalman filter The prior art invariable properties fail for the problem where the clutter power and noise variance are unknown and different from each other. This is due to the fact that invariance condition of requires a common unknown scaling on the clutter and background white noise—a condition that is seldom satisfied in practice. A uniformly most powerful invariant (UMPI) test for this problem becomes mathematically intractable in general. However, in many practical airborne radar applications Rc has rank r which is much less than the spatio-temporal product M=JN. For example, the clutter rank in the airborne linear phased array radar problem under ideal conditions (no mutual coupling between array elements), is given by the Brennan rule
Additionally, the low rank approximation enables reduction of training data support compared to full dimension STAP processing. An adaptive version of the test is also developed and its performance is studied. Target contamination of training data has a deleterious impact on the performance of the test. Therefore, a technique known as self-censoring reiterative fast maximum likelihood/adaptive power residue (SCRFML/APR) is developed to treat this problem and its performance is discussed. The SCRFML/APR method is used to estimate the unknown covariance matrix in the presence of outliers. This covariance matrix estimate can then be used in the low rank normalized adaptive matched filter (LRNAMF) or any other eigen-based adaptive processing technique. Now, we introduce the low-rank normalized matched filter (LRNM). Tiie performance of the LRNMF in terms of analytical calculation of false alarm probability (P The disturbance covariance matrix can be expressed as R We now use the form of R Observe that the false alarm probability is independent of the nuisance parameters s and σ We then proceed to calculate the probability of detection for the test of (6). Under H As the clutter rank increases, performance of the LRNMF degrades. The performance degradation (approximately 4 dB loss) with increasing rank (from r=4 to 55) can be accounted for due to the fact that the threshold incurs an increase with increasing clutter rank. Furthermore, A This is expected since the full rank NMF test for r=0 is invariant to the unknown white noise level. However, addition of clutter results in the loss of gain invariance in general. Nevertheless, imposing a low rank structure approximation of the clutter covariance matrix restores the gain invariance for small values of clutter rank. When the clutter rank follows the Brennan's rule (r=33), we note that there is a slight detection loss of the LRNMF compared to the full rank NMF test with r=0. However, the LRNMF test still retains the advantage of not requiring knowledge of s and σ In this discussion, we present the performance analysis of an adaptive version of the LRNMF test of (6). The disturbance covariance matrix is seldom known in practice and thus must be estimated using representative training data. Specifically, we consider the LRNMF test of (6) with P replaced by its estimate ^P formed from a singular value decomposition (SVD) of a data matrix Z whose columns z Typically r is unknown in practice. Consequently, a key issue in this context is the determination of r from the training data. Several techniques for determining r are available in the literature. The method of is best suited for our analysis since it does not require explicit knowledge of σ
Data from the L-band data set of the KASSPER program is used for carrying out performance analysis of the LRNAMF. The L-band data set consists of a datacube of 1000 range bins corresponding to the returns from a single coherent processing interval (CPI) from 11 channels and 32 pulses resulting in a spatio-temporal product of 352. Relevant system parameters for the L-band data sets from the KASSPER and RLSTAP programs are provided in Tables 1 and 2, respectively. Since analytical expressions for P In This invention presents an analysis of the NMF test for the case of clutter plus white noise. Imposing a low rank structure on the known clutter covariance matrix enables approximate CFAR behavior yielding robustness with respect to unknown clutter scaling and unknown background noise level. Analytical expressions for the detection and false alarm probabilities are presented and illustrated with numerical examples in the form of plots P Performance of the LRNAMF, an adaptive version of the LRNMF is studied using the KASSPER radar data. We observe a 4 dB degradation in performance due to the finite sample support used in estimating the clutter subspace. Furthermore, we note a loss of CFAR for the LRNAMF due to the threshold dependence on the Doppler beam position. An important feature of the LRNAMF is the ability to reduce the training support for subspace estimation. Finally, we note that accurate determination of the rank of the clutter subspace significantly impacts detection performance. Critical to the performance of the LRNAMF is the ability to obtain representative training data. However, in dense target environments, significant performance penalty is incurred due to target contamination of the training data. This results in signal cancellation causing a degradation in the SNR. Consequently, the SCRFML/APR method presented here is useful for rejecting outliers in the training data and obtaining good estimates of the projection matrix. Further performance analysis using this technique with the LRNAMF will be investigated in the future. An important issue in this context is the development of a suitable stopping criterion for the SCRFML/APR method. Additionally, finite sample support used in clutter subspace estimation causes subspace perturbation and subspace swapping. The impact of these effects on LRNAMF performance is currently under investigation. These issues will be reported on in the future. While the invention has been described in its presently preferred embodiment it is understood that the words which have been used are words of description rather than words of limitation and that changes within the purview of the appended claims may be made without departing from the scope and spirit of the invention in its broader aspects. Patent Citations
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