Modeling sonar performance using J-divergence

Abstract

This presentation demonstrates the use of J-divergence as a performance measure for detection in a sonar system. The inherent inaccuracies between system-level performance and the cell-level (PD,PF) detector operating point used in traditional analysis open the door to using approximate performance measures such as J-divergence. The properties of J-divergence making it an appealing choice are covered: summing to accrue J-divergence across multiple independent measurements (e.g., from multiple source signals, waveforms, or arrays), a data-processing inequality dictating that processing cannot improve J-divergence, and an asymptotic relationship to the traditional (PD,PF) operating point. Simple forward models of J-divergence are presented for matched filters and energy detectors when applied to the standard signal models in Gaussian noise. A “design” J-divergence, which is chosen by the desired qualitative performance level, is used in simple equations to obtain the “design” SNR require to achieve it. This provides a direct replacement for the detection threshold (DT) term in the sonar equation that is easier to apply and evaluate. Example applications of J-divergence are presented illustrating its utility in the modeling and adaptation of current systems as well as the design and analysis of new ones.