Evaluating the State Probabilities of M out of N Sliding Window Detectors

摘要

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 infinite 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 examining a 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 trials containing M successes. This paper describes a generalized 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.