Adaptation of Transition Probability Matrix for Multiple Model Estimators

This work addresses the problem of state estimation for Markovian switching systems with unknown transition probability matrix (TPM) of the embedded Markov chain governing the switching. Under the assumption of constant but random TPM, an approximate recursion of the TPM’s posterior probability density function (PDF) within the Bayesian framework is obtained. This general PDF recursion is then utilized to derive several recursive algorithms for minimum mean-square error (MMSE) estimation of the TPM. Various approximation approaches are used. The proposed TPM estimation is naturally incorporable into a typical Bayesian multiple model (MM) estimation scheme (such as IMM or GPB). Thus adaptive versions of MM state estimators with unknown TPM are provided. Simulation results of TMP-adaptive IMM algorithms for a system with failures and maneuvering target tracking are presented.