Change detection with unknown post-change parameter using Kiefer-Wolfowitz method

摘要

We consider a change detection problem with an unknown post-change parameter. The optimal algorithm in minimizing worst case detection delay subject to a constraint on average run length, referred as parallel CUSUM, is computationally expensive. We propose a low complexity algorithm based on parameter estimation using Kiefer-Wolfowitz (KW) method with CUSUM based change detection. We also consider a variant of KW method where the tuning sequences of KW method are reset periodically. We study the performance under the Gaussian mean change model. Our results show that reset KW-CUSUM performs close to the parallel CUSUM in terms of worst case delay versus average run length. Non-reset KW-CUSUM algorithm has smaller probability of false alarm compared to the existing algorithms, when run over a finite duration.