Evaluating the state probabilities of M out of N sliding window detectors

The term M out of N sliding window detectors refers to processes that determine whether there have been M successes in a sequence of N binary trials, where the window (of N trials under examination) slides along a possibly M t e sequence stopping when the criterion (of M successes in N successive trials) is met. They are frequently used to model the operators of naval surveillance systems such as radar and sonar. When an M out of N sliding window detector is exama sequence of trials it may be in one of several states. The state of most interest is the accepting state into which it enters (and remains) when it encounters a sequence of N successive trials containing M successes. This paper describes a generalised method for estimating the probability that an M out of N sliding window detector is in its accepting state given a sequence of probabilities representing the likelihood of success on each of a sequence of binary trials. APPROVED FOR PUBLIC RELEASE D E P A R T M E N T O F D E F E N C E v DEFENCE SCIENCE AND TECHNOLOGY ORGANISATION