The Bhattacharyya distance and detection between Markov chains

Abstract

When the statistical structure under each of two hypotheses is time varying, the collection of infinitely many observations does not guarantee an error probability that approaches zero. A recursive formula for the Bhattacharyya distance between two Markov chains is derived, and it is used to derive necessary and sufficient conditions for asymptotically perfect detection (APD). It is shown that the use of incorrect prior probabilities in the Bayes detection rulee does not affect AID. The results are also extended to time-continuons finite-state Markov observations. An application is analyzed, in which the behavior of a message buffer is monitored for the purpose of detecting malfunctions in a computer communication network.