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The problem of sequentially detecting an abrupt change in a sequence ofindependent and identically distributed (IID) random variables is addressed.Whereas previous approaches assume a known probability density function (PDF)at the start of the sequence, the problem addressed is the detection of asingle change in distribution among a finite number of known 'equal-energy'PDFs, but where the initial and final distributions are not known a priori. ABayesian multiple hypothesis approach is proposed where (i) unlike previousthreshold policies, the minimum cost hypothesis is tracked through time, (ii)under an exponential delay-cost function that satisfies an upper bounddetermined by the distances between hypotheses, the probability of detecting achange from an incorrect initial distribution asymptotically vanishes withtime, (iii) computation is recursive and constant per unit time, and (iv) theunknown initial state gives rise to unavoidable incorrect detections that bemade to vanish with a constant test threshold with negligibly small effect oncorrect detection delay for change times beyond a lower bound. Simulationsillustrate the analysis and reveal that average delay approaches that of theoptimal CUSUM test after an initial transient period determined by an incorrectdetection probability constraint.

Sequential Detection of an Abrupt Change in a Random Sequence with Unknown Initial State