Bayesian Distributed Target Detection for Mismatched Signals in Sample-Starved Environment

In the case of distributed target detection in unknown Gaussian noise, training data are often limited, and signal mismatch is a common issue. To tackle these problems, we utilize the Bayesian theory by taking the noise covariance matrix as an inverse Wishart distribution. Our approach involves incorporating a fictitious determinist jamming signal in the signal-absence hypothesis to create a selective detector. Although this detector provides enhanced capability to reject mismatched signals, it comes at the cost of lower detection performance in the absence of signal mismatch. We propose a flexible Bayesian detector to tackle this limitation, wherein a customizable parameter can regulate the performance of mismatched signals. The tunable Bayesian detector is particularly robust to signal mismatch. In addition, it can achieve a higher probability of detection (PD) compared with existing methods when the tunable parameter is appropriately adjusted for matched signals. All the proposed Bayesian detectors can work with limited training data or even with no training data. The effectiveness of the proposed detectors is demonstrated through both simulated and actual data.