Optimal Predictive Inference and Noncoherent CFAR Detectors

Abstract

A Bayesian predictive inference approach, for the development of classical sliding window detection processes, is the focus of this article. It will be demonstrated that this methodology can produce such detectors with the constant false alarm rate (CFAR) property for clutter modeled by statistics, which are invariant with respect to a group of scale and power transformations. For such a clutter model, it will be shown that the derived detector achieves optimality in the sense of strong consistency. This implies that the Bayesian CFAR detector will have the best performance, in the class of CFAR detectors, for this specific clutter distribution. Although these Bayesian detectors are produced under the assumption of homogeneous clutter, they nonetheless provide the practical engineer with a benchmark on potential CFAR performance. To illustrate the results, the optimal CFAR detector for the Weibull-distributed clutter is derived. Although the Pareto Type I clutter model fits into the class of scale- and power-invariant distributions, there is complexity in the derivation of the Bayesian decision rule. Hence, this special case is also examined, and it will be shown that the Bayesian CFAR corresponds to a well-known detector for this clutter environment.