非线性非齐次Markov跳变系统的贝叶斯滤波

赵顺毅; 刘飞

doi:10.3724/SP.J.1004.2012.00485

非线性非齐次Markov跳变系统的贝叶斯滤波

doi: 10.3724/SP.J.1004.2012.00485

赵顺毅^,,
刘飞

1.
轻工过程先进控制教育部重点实验室江南大学自动化研究所无锡 214122

详细信息

通讯作者:
赵顺毅, 江南大学自动化研究所博士研究生.主要研究方向为复杂系统的滤波及控制. E-mail: shunyizhao@126.com

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出版历程
- 收稿日期: 2011-04-20
- 修回日期: 2011-12-02
- 刊出日期: 2012-03-20

Bayesian Filtering for Non-linear Markov Jump Systems with Non-homogeneous Transition Probabilities

ZHAO Shun-Yi^,,
LIU Fei

1.
Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Institute of Automation, Jiangnan University, Wuxi 214122

摘要

摘要: 针对具有时变不确定转移概率的非线性非齐次Markov跳变系统, 提出一种贝叶斯状态估计方法.该方法首次采用带约束高斯概率密度函数来刻画转移概率的真实特性. 然后,基于参考概率空间法, 将实际的概率测度投影到理想概率空间, 得出信息变量的递归表达式. 同时, 在贝叶斯框架内给出转移概率矩阵的最大后验估计式. 进一步, 采用粒子逼近法求解转移概率矩阵的最大后验估计, 解决非线性函数的多重积分问题, 进而获取状态估计值. 最后, 通过一个仿真示例表明该方法的有效性.
- 非线性非齐次Markov跳变系统 /
- 贝叶斯估计 /
- 参考概率空间 /
- 粒子逼近
Abstract: A method of Bayesian state estimation is presented for non-linear non-homogeneous Markov jump systems where the transition probabilities (TPs) are time-variant and uncertain. The proposed method firstly utilizes constrained Gaussian probability density function to describe the real characters of TPs, and then the recursion of information state is obtained by using the reference probability method by which the actual probability measure is mapped into an ideal one. Meanwhile, the maximum a posterior (MAP) estimate of transition probability matrix is given in the Bayesian framework. To implement the MAP estimation and solve the problem of multiple integral of non-linear function, particle approximation is employed further. Finally, an example is simulated to illustrate the effectiveness of our method.
- Non-linear non-homogeneous Markov jump sys- tems /
- Bayesian estimation /
- reference probability method /
- parti-cle approximation

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参考文献(1)

[1]

Cost O L V, Fragoso M D, Marques R P. Discrete-Time Markov Jump Linear Systems. London: Springer, 2005. 65-83[2] Zhang L X. H∞ estimation for discrete-time piecewise homogeneous Markov jump linear systems. Automatica, 2009, 45(11): 2570-2576[3] Liu H P, Ho D W C, Sun F C. Design of H∞ filter for Markov jumping linear systems with non-accessible mode information. Automatica, 2008, 44(10): 2665-2660[4] Cinquemani E, Micheli M. State estimation in stochastic hybrid systems with sparse observations. IEEE Transactions on Automatic Control, 2006, 51(8): 1337-1342[5] Seah C E, Hwang I. State estimation for stochastic linear hybrid systems with continuous-state-dependent transitions: an IMM approach. IEEE Transactions on Aerospace and Electronic Systems, 2009, 45(1): 376-391[6] Tsantas N. Stochastic analysis of a non-homogeneous Markov system. European Journal of Operational Research, 1995, 85(3): 670-685[7] Dey S, Moore J B. Risk-sensitive filtering and smoothing via reference probability methods. IEEE Transactions on Automatic Control, 1997, 42(11): 1587-1591[8] Shao X G, Huang B, Lee J M. Constrained Bayesian estimation —— a comparative study and a new particle filter based approach. Journal of Process Control, 2010, 20(2): 143-157[9] Zhao Ling-Ling, Ma Pei-Jun, Su Xiao-Hong. A fast quasi-Monte Carlo-based particle filter algorithm. Acta Automatica Sinica, 2010, 36(9): 1351-1356(赵玲玲, 马培军, 苏小红. 一种快速准蒙特卡罗粒子滤波算法. 自动化学报, 2010, 36(9): 1351-1356)[10] Aggoun L, Benkherouf L. Filtering of discrete-time systems hidden in discrete-time random measure. Mathematical and Computer Modelling, 2002, 35(3): 273-282[11] Orguner U, Demirekler M. Maximum likelihood estimation of transition probabilities of jump Markov linear systems. IEEE Transactions on Signal Processing, 2008, 56(10): 5093-5108[12] Luan X, Liu F, Shi P. Finite-time filtering for non-linear stochastic systems with partially known transition jump rates. IET Control Theory and Applications, 2010, 4(5): 735-745

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