Enhanced convergence adaptive detection
Abstract
We addressed the problem of detecting targets using an array of active sensors. We have been concerned with devising means of obtaining reliable detection with a small number of samples (small relative to the number of unknown parameters). This problem arises with large arrays, and/or low cross section targets. Past techniques for addressing this problem incorporated prior structure into likelihood procedures. Such approaches are as follows: (1) intractable, requiring iterative solution, (2) not CFAR, and (3) not optimal. We have approached this problem using group symmetries. Specifically, we introduce a framework for exploring array detection problems in a reduced dimensional space by exploiting the theory of invariance in hypothesis testing. This involves calculating a low dimensional basis set of functions called the maximal invariant, the statistics of which are often tractable to obtain, thereby making analysis feasible and facilitating the search for tests with some optimality property. Using this approach, we obtain a locally most powerful test for the unstructured covariance case and show that the Kelly and AMF detectors form an algebraic span for any invariant detector. Applying the same framework to structured covariance matrices, we gain some insights and propose several new detectors which are shown to outperform existing detectors.
 Publication:

Final Report
 Pub Date:
 February 1993
 Bibcode:
 1993corn.reptT....S
 Keywords:

 Adaptation;
 Adaptive Filters;
 Convergence;
 Invariance;
 Matched Filters;
 Radar Detection;
 Random Noise;
 Signal Processing;
 Target Acquisition;
 Algebra;
 Covariance;
 Hypotheses;
 Iterative Solution;
 Matrices (Mathematics);
 Optimization;
 Radar Targets;
 Communications and Radar