Multi-Sensor Slope Change Detection

TL;DR

This paper introduces a mixture-based method for detecting gradual slope changes in multi-sensor data streams, providing analytic performance metrics and demonstrating asymptotic optimality and adaptability.

Contribution

It extends previous abrupt change detection methods to handle non-stationary slope changes, with new analytic expressions and an adaptive empirical Bayes approach.

Findings

Accurate ARL and EDD expressions for the proposed method

Demonstrated asymptotic optimality of the mixture procedure

Good performance shown through numerical examples

Abstract

We develop a mixture procedure for multi-sensor systems to monitor data streams for a change-point that causes a gradual degradation to a subset of the streams. Observations are assumed to be initially normal random variables with known constant means and variances. After the change-point, observations in the subset will have increasing or decreasing means. The subset and the rate-of-changes are unknown. Our procedure uses a mixture statistics, which assumes that each sensor is affected by the change-point with probability $p_0$. Analytic expressions are obtained for the average run length (ARL) and the expected detection delay (EDD) of the mixture procedure, which are demonstrated to be quite accurate numerically. We establish the asymptotic optimality of the mixture procedure. Numerical examples demonstrate the good performance of the proposed procedure. We also discuss an adaptive mixture procedure using empirical Bayes. This paper extends our earlier work on detecting an abrupt change-point that causes a mean-shift, by tackling the challenges posed by the non-stationarity of the slope-change problem.