Misspecified and Asymptotically Minimax Robust Quickest Change Detection

摘要

We investigate the quickest detection of an unknown change in the distribution of a stochastic process generating independent and identically distributed observations. We develop new bounds on the performance of misspecified cumulative sum (CUSUM) rules, and pose minimax robust versions of the popular Lorden and Pollak criteria with polynomial (or higher order moment) detection delay penalties. By exploiting our results for misspecified CUSUM rules, we identify solutions to our robust quickest change detection problems in the asymptotic regime of few false alarms. In contrast to previous robust quickest change detection treatments, our asymptotic results hold under relaxed conditions on the uncertainty sets of possible prechange and postchange distributions. We illustrate our results in simulations and apply them to the problem of detecting target manoeuvres in low signal-to-noise ratio settings (i.e., dim-target manoeuvre detection).