Adaptive detection using both the test and training data for disturbance correlation estimation

This paper examines a target detection problem in colored Gaussian disturbance with an unknown covariance matrix. In many classic adaptive detectors, the covariance estimator is formed by using only the training data. This necessitates calculating a new covariance estimator for each cell under test (CUT) during the cell-by-cell target search process. We consider herein an alternative approach that forms the covariance matrix estimate by using both test and training data for detection in homogeneous environments. This approach is computationally much more efficient since the covariance matrix estimator is computed only once and can be applied for target detection at each CUT. Using this estimator, we propose a new detector with two tunable parameters, which includes several existing detectors as special cases. Closed-form expressions for the probabilities of false alarm and detection are derived in the matched and mismatched cases for both non-fluctuating and fluctuating target models. Simulation results reveal that the rejection capability of mismatched signals of the proposed detector can be flexibly controlled by adjusting its tunable parameters. In particular, the proposed detector can achieve the same detection performance as the generalized likelihood ratio test (GLRT) detector derived by Kelly, but has a much lower computational burden.