An Invariant Sliding Window Detection Process

Recent advances in the development of sliding window detection processes have shown that a transformation approach is a very effective means of producing decision rules. This approach begins with the classical detectors, designed for operation in exponentially distributed intensity clutter, and adapts them for operation in any desired clutter environment. The approach preserves the original probability of false alarm and threshold multiplier relationship. A consequence of this approach is that the resultant detector often inherits clutter parameter dependence. As an example, in the Pareto clutter case, the modified decision rule is dependent on the Pareto scale parameter, while providing a constant false alarm rate (CFAR) detector with respect to the Pareto shape parameter. Recently, it has been shown that this dependence on the Pareto scale parameter can be eliminated by replacing it with a complete sufficient statistic, resulting in a new detector that achieves the full CFAR property. It will be shown that this result is due to the fact that the decision rule is based upon an invariant statistic. In particular, a general class of clutter models is identified, and it is shown that a generic transformed decision rule can be proposed, which is invariant with respect to a group of transformations, thus allowing the determination of sliding window CFAR detectors. This provides one with an effective means of producing such detectors for operation in many of the clutter environments of interest in radar signal processing.