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Two detection schemes for the detection of a spatially distributed, Doppler-shifted target in non-Gaussian clutter are developed. The non-Gaussian clutter is modeled as a spherically invariant random vector (SIRV) distribution. For the first detector, called the non-scatterer density dependent generalized likelihood ratio test (NSDD-GLRT), the detector takes the form of a sum of logarithms of identical functions of data from each individual range cell. It is shown under the clutter only hypothesis, that the detection statistic has the chi-square distribution so that the detector threshold is easily calculated for a given probability of false alarm P F. The detection probability P D is shown to be only a function of the signal-to-clutter power ratio (S=C) opt of the matched filter, the number of pulses N, the number of target range resolution cells J, the spikiness of the clutter determined by a parameter of an assumed underlying mixing distribution, and P F. For representative examples, it is shown that as N, J, or the clutter spikiness increases, detection performance improves. A second detector is developed which incorporates a priori knowledge of the spatial scatterer density. This detector is called the scatterer density dependent GLRT (SDD-GLRT) and is shown for a representative case to improve significantly the detection performance of a sparsely distributed target relative to the performance of the NSDD-GLRT and to be robust for a moderate mismatch of the expected number of scatterers. For both the NSDD-GLRT and SDD-GLRT, the detectors have the constant false-alarm rate (CFAR) property that P F is independent of the underlying mixing distribution of the clutter, the clutter covariance matrix, and the steering vector of the desired signal.

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This paper addresses the problem of radar target detection in severely heterogeneous clutter environments. Speciÿcally, we present the performance of the normalized matched ÿlter 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). Performance of the test depends only upon the number of elements, the number of pulses processed in a coherent processing interval, and the rank of the clutter covariance matrix. Analytical expressions for calculating the false alarm and detection probabilities are presented. Performance of the method is shown to degrade with increasing clutter rank especially for low false alarm rates. An adaptive version of the test (LRNAMF) is developed and its performance is studied with simulated data from the KASSPER program. Results pertaining to sample support for subspace estimation, CFAR, and detection performance are presented. 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 LRNAMF or any other eigen-based adaptive processing technique. ?