Estimation of Markovian Jump Systems with Unknown Transition Probabilities through Bayesian Sampling
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
Brief paper: Risk-sensitive filtering for jump Markov linear systems
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Multiple model target tracking with variable rate particle filters
Digital Signal Processing
Visual tracking via adaptive tracker selection with multiple features
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part IV
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part II
| Hi-index | 35.69 |
Markovian jump systems (MJSs) evolve in a jump-wise manner by switching among simpler models, according to a finite Markov chain, whose parameters are commonly assumed known. This paper addresses the problem of state estimation of MJS with unknown transition probability matrix (TPM) of the embedded Markov chain governing the jumps. Under the assumption of a time-invariant but random TPM, an approximate recursion for the TPMs posterior probability density function (PDF) within the Bayesian framework is obtained. Based on this recursion, four algorithms for online minimum mean-square error (MMSE) estimation of the TPM are derived. The first algorithm (for the case of a two-state Markov chain) computes the MMSE estimate exactly, if the likelihood of the TPM is linear in the transition probabilities. Its computational load is, however, increasing with the data length. To limit the computational cost, three alternative algorithms are further developed based on different approximation techniques-truncation of high order moments, quasi-Bayesian approximation, and numerical integration, respectively. The proposed TPM estimation is naturally incorporable into a typical online Bayesian estimation scheme for MJS [e.g., generalized pseudo-Bayesian (GPB) or interacting multiple model (IMM)]. Thus, adaptive versions of MJS state estimators with unknown TPM are provided. Simulation results of TPM-adaptive IMM algorithms for a system with failures and maneuvering target tracking are presented.