Statistical normalization of spherically invariant non-Gaussian clutter

Conventional detection in active sonar involves comparing the normalized matched filter output power to a fixed preset threshold. Threshold crossings from contacts of interest are labeled as detections and those from undesired clutter echoes as false alarms. To maintain a constant false-alarm rate (CFAR) in the presence of strong transient clutter, the system can either increase the threshold or apply some function that suppresses this background down to an acceptable level. The latter approach leads to a more consistent background on the display, which enables operator-assisted detection. Background clutter suppression should not come at the expense of contact detection; to maximize the probability of detection (PD) for a given probability of false alarm (PFA), the likelihood ratio test (LRT) is used. However, the LRT does not address display issues, since the threshold that achieves a desired PFA varies with the input distribution. Ideally, the LRT output is monotonically transformed using a "statistical normalizer" (SN) that returns a consistent CFAR background without degrading the optimized PD. Within the radar community, clutter suppression is proposed using a LRT tuned to a K-distributed spherically invariant random vector (SIRV) model. However, this model does not lend itself to SN, as a closed-form expression for the LRT output density does not exist. In contrast, the proposed SIRV clutter model, with Pareto distributed power, leads to a closed-form density from which the SN function is readily derived. This combined Pareto-LRT/SN detector nearly matches the optimized PD performance of the K-distributed LRT and maintains a consistent CFAR background for display purposes.