Detection of hidden Markov model transient signals

摘要

Addressed here is the quickest detection of transient signals which can be represented as hidden Markov models (HMMs), with the application of detection of transient signals. Relying on the fact that Page's test is equivalent to a repeated sequential probability ratio test (SPRT), we are able to devise a procedure analogous to Page's test for dependent observations. By using the so-called forward variable of an HMM, such a procedure is applied to the detection of a change in hidden Markov modeled observations, i.e., a switch from one HMM to another. Performance indices of Page's test, the average run length (ARL) under both hypotheses, are approximated and confirmed via simulation. Several important examples are investigated in depth to illustrate the advantages of the proposed scheme.