Kevin J. Sangston

Coherent detection of radar targets in a non-gaussian background

The problem of detecting radar targets against a background of coherent, correlated, non-Gaussian clutter is studied with a two-step procedure. In the first step, the structure of the amplitude and the multivariate probability density functions (pdfs) describing the statistical properties of the clutter is derived. The starting point for this derivation is the basic scattering problem, and the statistics are obtained from an extension of the central limit theorem (CLT). This extension leads to modeling the clutter amplitude statistics by a mixture of Rayleigh distributions. The end product of the first step is a multidimensional pdf in the form of a Gaussian mixture, which is then used in step 2. The aim of step 2 is to derive both the optimal and a suboptimal detection structure for detecting radar targets in this type of clutter. Some performance results for the new detection processor are also given. >

Coherent Radar Target Detection in Heavy-Tailed Compound-Gaussian Clutter

This paper deals with the problem of detecting a radar target signal against correlated non-Gaussian clutter, which is modeled by the compound-Gaussian distribution. We prove that if the texture of compound-Gaussian clutter is modeled by an inverse-gamma distribution, the optimum detector is the optimum Gaussian matched filter detector compared to a data-dependent threshold that varies linearly with a quadratic statistic of the data. We call this optimum detector a linear-threshold detector (LTD). Then, we show that the compound-Gaussian model presented here varies parametrically from the Gaussian clutter model to a clutter model whose tails are evidently heavier than any K-distribution model. Moreover, we show that the generalized likelihood ratio test (GLRT), which is a popular suboptimum detector because of its constant false-alarm rate (CFAR) property, is an optimum detector for our clutter model in the limit as the tails get extremely heavy. The GLRT-LTD is tested against simulated high-resolution sea clutter data to investigate the dependence of its performance on the various clutter parameters.

Optimum and sub-optimum coherent radar detection in compound Gaussian clutter: a data-dependent threshold interpretation

We propose a possible approach to the problem of optimum and sub-optimum detection of radar targets against a background of coherent, correlated, K-distributed clutter. It is well-known that the optimum strategy to detect a perfectly known signal embedded in correlated Gaussian clutter is given by comparing the whitening-matched filter output to a given threshold, which is predetermined according to the desired probability of false alarm. When the clutter is non-Gaussian the performance of the matched filter degrades, and the optimum detector in such a disturbance may be non-linear. For the non-Gaussian clutter model considered, the optimum detector is a function of two statistics: a linear statistic (the matched filter output) and a quadratic statistic. We show that the optimum detection strategy can be seen as the classical matched filter output compared to an adaptive threshold that depends on the data through the quadratic statistic. This interpretation has given us an insight into the structure of the optimum detector and has suggested an approach to obtain, analyze and compare suboptimum detectors that are easily implementable with a performance close to optimal.

New results on coherent radar target detection in heavy-tailed compound-Gaussian clutter

In this work we prove that if the texture of compound-Gaussian clutter is modeled by an Inverse-Gamma distribution, the optimum detector is the optimum Gaussian matched filter detector compared to a data-dependent threshold that varies linearly with a quadratic statistic of the data. The compound-Gaussian model presented here varies parametrically from the Gaussian clutter model to a clutter model whose tails are evidently heavier than any K-distribution model. Moreover, we also show that the GLRT, which is a popular suboptimum detector due to its CFAR property, is in fact an optimum detector for our clutter model in the limit as the tails get extremely heavy.

Robust locally optimum detection of signals in dependent noise

A robust locally optimum detector of a signal embedded in additive dependent nonGaussian noise is presented. The performance criterion is Bayes risk, the sample size is finite, and the uncertainty class of multivariate inputs is the in -contamination model. The locally optimum detector is shown to be a censored version of the nominal likelihood ratio. >

New Results on Coherent Radar Target Detection in Heavy-Tailed Compound-Gaussian Clutter

In this work we prove that if the texture of compound-Gaussian clutter is modeled by an Inverse-Gamma distribution, the optimum detector is the optimum Gaussian matched filter detector compared to a data-dependent threshold that varies linearly with a quadratic statistic of the data. The compound-Gaussian model presented here varies parametrically from the Gaussian clutter model to a clutter model whose tails are evidently heavier than any K-distribution model. Moreover, we also show that the GLRT, which is a popular suboptimum detector due to its CFAR property, is in fact an optimum detector for our clutter model in the limit as the tails get extremely heavy.

A sharp false alarm upper-bound for a matched filter bank detector

A sharp upper bound on the probability of false alarm, P/sub F/, of a matched filter bank detector over the class of input variates that are zero mean and have a specified covariance matrix, R/sub xx/, is derived. This bound is a function of the detector threshold, T, and R/sub xx/. It is shown that the bound is inversely proportional to T/sup 2/. Hence there may be a wide variation of P/sub F/ over the class since the P/sub F/ for Gaussian inputs varies as exp(-T/sup 2/). >