Bayesian Processors for Physics‐Based Applications

This chapter develops a sequential Bayesian solution to the broadband modal function tracking and pressure‐field enhancement problem using a particle filter then coupled it to a sequential source detection scheme. It demonstrates the application of the Kullback‐Leibler divergence statistic as a reliable metric to evaluate the particle filter performance for this nonstationary problem. The chapter motivates each application, succinctly develop the process and measurement models, develop the Bayesian processor (BSP), and analyze its performance. The main objective is to demonstrate the applicability of the Bayesian approach to a variety of interesting applications and analyze their performance. Next, the chapter develops a sequential detector that was capable of detecting the broadband source in noisy pressure‐field measurements and evaluated its performance from the associated receiver operating characteristic (ROC) curve. It shows the results of the design demonstrating the capability of such an approach.