Sequential multi-sensor change-point detection

TL;DR

This paper introduces a mixture procedure for detecting change-points in multiple data streams, especially when only a subset is affected, without relying on spatial structure, and provides analytical and simulation results for its performance.

Contribution

It develops a new mixture likelihood ratio-based method for multi-sensor change-point detection that handles unknown affected subset size and post-change means, with analytical performance approximations.

Findings

Accurate ARL expression when no change occurs.

Approximate expected detection delay post-change.

Numerical comparisons show advantages over existing methods.

Abstract

We develop a mixture procedure to monitor parallel streams of data for a change-point that affects only a subset of them, without assuming a spatial structure relating the data streams to one another. Observations are assumed initially to be independent standard normal random variables. After a change-point the observations in a subset of the streams of data have nonzero mean values. The subset and the post-change means are unknown. The procedure we study uses stream specific generalized likelihood ratio statistics, which are combined to form an overall detection statistic in a mixture model that hypothesizes an assumed fraction $p_0$ of affected data streams. An analytic expression is obtained for the average run length (ARL) when there is no change and is shown by simulations to be very accurate. Similarly, an approximation for the expected detection delay (EDD) after a change-point is also obtained. Numerical examples are given to compare the suggested procedure to other procedures for unstructured problems and in one case where the problem is assumed to have a well-defined geometric structure. Finally we discuss sensitivity of the procedure to the assumed value of $p_0$ and suggest a generalization.