Change detection using non-linear filtering and likelihood ratio testing

This article presents a framework for general change detection problems. A two-model approach is used, wherein signals and parameters subject to change are modeled by Brownian motion for the faulty case and by constant values in the nominal case. A detection algorithm using likelihood ratio testing is implemented through the use of recursive dynamic filtering. In the case of change in mean of a Gaussian sequence, a detailed analysis of the detection scheme reveals that for fixed error rates, there exist optimal filtering parameters which optimize the detection rate. For non-linear and non-Gaussian change detection, approximate filtering algorithms based on Bayes' law can be employed in the present framework. A computational filtering algorithm based on Bayes' law, probability grid filtering, is reviewed. The proposed framework combined with probability grid filtering is compared to the local asymptotic approach through a non-linear dynamical example. The proposed method's performance is vastly superior to the latter's.