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Mathematical Problems in Engineering
Volume 2013, Article ID 293456, 7 pages
Research Article

State Estimation for Nonlinear Discrete-Time Systems with Markov Jumps and Nonhomogeneous Transition Probabilities

Key Laboratory of Advanced Process Control for Light Industry, Ministry of Education, Institute of Automation, Jiangnan University, Wuxi 214122, China

Received 3 October 2013; Accepted 23 November 2013

Academic Editor: Shuping He

Copyright © 2013 Shunyi Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


State estimation problem is addressed for a class of nonlinear discrete-time systems with Markov parameters and nonhomogeneous transition probabilities (TPs). In this paper, the optimal estimation mechanism of transition probability matrix is proposed in the minimum mean square error sense to show some critical points. Based on this mechanism, the extended Kalman filters are employed as the subfilters to obtain the subestimates with corresponding models. A novel operator which fuses the prior knowledge and the posterior information embedded in observations is developed to modify the posterior mode probabilities. A meaningful example is presented to illustrate the effectiveness of our method.