Adaptive Detection in Partially Homogeneous Environment with Limited Samples Based on Geometric Barycenters

To solve the problem of adaptive detection in partially homogeneous environment with outliers and limited samples, a class of two-step detectors are designed based on geometric barycenters. The first step is to construct a data selector based on generalized inner product and eliminate sample data containing outliers. The second step is to construct detection statistics of the adaptive coherence estimator using covariance matrix estimators, which are based on geometric barycenters. The detectors utilize geometric barycenters of the positive definite matrix space without any knowledge of prior probability distribution of sample data. The performance of the proposed two-step detectors is evaluated in terms of the probabilities of correct outliers excision, false alarm, and detection. Experiment results, based on simulated and real data, show that the proposed approach has better detection performance than the existing ones based on traditional covariance estimator.