Risk-sensitive filtering for jump Markov linear systems

In this paper, a risk-sensitive multiple-model filtering algorithm is derived using the reference probability methods. First, the approximation of the interacting multiple-model (IMM) algorithm is identified in the reference probability domain. Then, the same type of approximation is used to derive the finite-dimensional risk-sensitive filtering algorithm. The derived algorithm reduces to the IMM filter when the risk-sensitive parameter goes to zero and reduces to the risk-sensitive filter for linear Gauss-Markov systems when the number of models is unity. The algorithm performs better in a simulated uncertain parameter scenario than the IMM filter.

[1]  K. Fu,et al.  On state estimation in switching environments , 1968 .

[2]  H. Blom.  An efficient filter for abruptly changing systems , 1984 .

[3]  T. Kailath,et al.  Indefinite-quadratic estimation and control: a unified approach to H 2 and H ∞ theories , 1999 .

[4]  M. Fragoso,et al.  Robust ℋ︁∞ filtering for uncertain Markovian jump linear systems , 2002 .

[5]  C. D. Souza.  A mode-independent H∞ filter design for discrete-time Markovian jump linear systems , 2003, CDC.

[6]  Marcelo D. Fragoso,et al.  H ∞ filtering for Markovian jump linear systems , 2002, Int. J. Syst. Sci..

[7]  Vikram Krishnamurthy,et al.  An improvement to the interacting multiple model (IMM) algorithm , 2001, IEEE Trans. Signal Process..

[8]  Qing Zhang.  Optimal Filtering of Discrete-Time Hybrid Systems , 1999 .

[9]  Y. Bar-Shalom,et al.  Multiple-model estimation with variable structure , 1996, IEEE Trans. Autom. Control..

[10]  J. Speyer,et al.  Optimal stochastic estimation with exponential cost criteria , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[11]  O. Costa.  Linear minimum mean square error estimation for discrete-time Markovian jump linear systems , 1994, IEEE Trans. Autom. Control..

[12]  O. Costa,et al.  Robust linear filtering for discrete-time hybrid Markov linear systems , 2002 .

[13]  Amir Averbuch,et al.  Interacting Multiple Model Methods in Target Tracking: A Survey , 1988 .

[14]  John B. Moore,et al.  Hidden Markov Models: Estimation and Control , 1994 .

[15]  Magdi S. Mahmoud,et al.  Optimal guaranteed cost filtering for Markovian jump discrete-time systems , 2004 .

[16]  Pravin Varaiya,et al.  Stochastic Systems: Estimation, Identification, and Adaptive Control , 1986 .

[17]  Vikram Krishnamurthy,et al.  Expectation maximization algorithms for MAP estimation of jump Markov linear systems , 1999, IEEE Trans. Signal Process..

[18]  X. R. Li,et al.  Online Bayesian estimation of transition probabilities for Markovian jump systems , 2004, IEEE Transactions on Signal Processing.

[19]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[20]  Jitendra Tugnait,et al.  Adaptive estimation and identification for discrete systems with Markov jump parameters , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[21]  Jamie S. Evans,et al.  Finite-Dimensional Filters for Passive Tracking of Markov Jump Linear Systems , 1998, Autom..

[22]  Arnaud Doucet,et al.  Particle filters for state estimation of jump Markov linear systems , 2001, IEEE Trans. Signal Process..

[23]  John B. Moore,et al.  Risk-sensitive filtering and smoothing via reference probability methods , 1997, IEEE Trans. Autom. Control..

[24]  Arnaud Doucet,et al.  Stochastic sampling algorithms for state estimation of jump Markov linear systems , 2000, IEEE Trans. Autom. Control..

[25]  Y. Boers,et al.  Interacting multiple model particle filter , 2003 .

[26]  Y. Bar-Shalom,et al.  The interacting multiple model algorithm for systems with Markovian switching coefficients , 1988 .

[27]  Yaakov Bar-Shalom,et al.  Estimation and Tracking: Principles, Techniques, and Software , 1993 .

[28]  Robert J. Elliott,et al.  Exact hybrid filters in discrete time , 1996, IEEE Trans. Autom. Control..

[29]  Peng Shi,et al.  Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters , 1999, IEEE Trans. Autom. Control..

[30]  M. Fragoso,et al.  ℋ︁∞ filtering for discrete‐time linear systems with Markovian jumping parameters† , 2003 .

[31]  Stelios C. A. Thomopoulos,et al.  Distributed Fusion Architectures and Algorithms for Target Tracking , 1997, Proc. IEEE.

[32]  Oswaldo Luiz V. Costa,et al.  Stationary filter for linear minimum mean square error estimator of discrete-time Markovian jump systems , 2002, IEEE Trans. Autom. Control..