Moving horizon estimation for Markov jump systems

In this paper, we study the state estimation problem for a class of nonlinear Markov jump systems with the moving horizon estimation algorithm, which is an optimization-based filtering method. The optimal estimate is obtained by minimizing a quadratic estimation cost function defined on fixed sliding horizon measurements. For this purpose, the quadratic estimation cost function is formulated from the negative logarithm of the joint states distribution, whose particular factorization is represented by a Bayesian network. By analyzing the corresponding full information estimation as a basic problem for nonlinear Markov jump systems, the formulation of the moving horizon estimation is developed. An example is presented to compare the proposed new estimation technique with classical interacting multiple model particle filtering, and show the effectiveness and advantages of the new estimation scheme.

[1]  Jay H. Lee,et al.  A moving horizon‐based approach for least‐squares estimation , 1996 .

[2]  J. Rawlings,et al.  Nonlinear Moving Horizon State Estimation , 1995 .

[3]  Juergen Hahn,et al.  Computation of arrival cost for moving horizon estimation via unscented Kalman filtering , 2009 .

[4]  Giorgio Battistelli,et al.  Moving-horizon state estimation for nonlinear discrete-time systems: New stability results and approximation schemes , 2008, Autom..

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

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

[7]  Manfred Morari,et al.  Moving horizon estimation for hybrid systems , 2002, IEEE Trans. Autom. Control..

[8]  Myo-Taeg Lim,et al.  Improving Reliability of Particle Filter-Based Localization in Wireless Sensor Networks via Hybrid Particle/FIR Filtering , 2015, IEEE Transactions on Industrial Informatics.

[9]  D. Mayne,et al.  MOVING HORIZON OBSERVERS , 1992 .

[10]  Tongwen Chen,et al.  Hinfinity filtering for nonuniformly sampled systems: A Markovian jump systems approach , 2011, Syst. Control. Lett..

[11]  Wook Hyun Kwon,et al.  ${\cal H}_{\infty}$ Finite Memory Controls for Linear Discrete-Time State-Space Models , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[12]  Jinho Choi,et al.  A Cholesky Factorization Based Approach for Blind FIR Channel Identification , 2008, IEEE Transactions on Signal Processing.

[13]  Peng Shi,et al.  Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay , 1999, IEEE Trans. Autom. Control..

[14]  Peng Shi,et al.  Asynchronous I2-I∞ filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities , 2014, Autom..

[15]  George W. Irwin,et al.  Multiple model bootstrap filter for maneuvering target tracking , 2000, IEEE Trans. Aerosp. Electron. Syst..

[16]  Shunyi Zhao,et al.  Risk‐sensitive filtering for nonlinear Markov jump systems on the basis of particle approximation , 2012 .

[17]  Peng Shi,et al.  Novel Neural Control for a Class of Uncertain Pure-Feedback Systems , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[18]  Ligang Wu,et al.  Quantized Control Design for Cognitive Radio Networks Modeled as Nonlinear Semi-Markovian Jump Systems , 2015, IEEE Transactions on Industrial Electronics.

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

[20]  Ligang Wu,et al.  State estimation and sliding mode control for semi-Markovian jump systems with mismatched uncertainties , 2015, Autom..

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

[22]  S. Ungarala.  Computing arrival cost parameters in moving horizon estimation using sampling based filters , 2009 .

[23]  Fei Liu,et al.  Maximum likelihood state estimation for Markov jump systems with uncertain mode-dependent delays , 2016, J. Frankl. Inst..

[24]  L. Biegler,et al.  Constrained particle filter approach to approximate the arrival cost in Moving Horizon Estimation , 2011 .

[25]  Biao Huang,et al.  Moving horizon estimation for switching nonlinear systems , 2013, Autom..

[26]  Kok Lay Teo,et al.  Optimal insulin infusion control via a mathematical blood glucoregulatory model with fuzzy parameters , 1991 .

[27]  Tongwen Chen,et al.  H∞ filtering for nonuniformly sampled systems , 2010, CCECE 2010.

[28]  Huijun Gao,et al.  State Estimation and Sliding-Mode Control of Markovian Jump Singular Systems , 2010, IEEE Transactions on Automatic Control.

[29]  Myo-Taeg Lim,et al.  Switching Extensible FIR Filter Bank for Adaptive Horizon State Estimation With Application , 2016, IEEE Transactions on Control Systems Technology.

[30]  M. Morari,et al.  Moving horizon estimation for hybrid systems , 2002, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[31]  David Q. Mayne,et al.  Constrained state estimation for nonlinear discrete-time systems: stability and moving horizon approximations , 2003, IEEE Trans. Autom. Control..

[32]  Fei Liu,et al.  Unbiased H∞ filtering for neutral Markov jump systems , 2008, Appl. Math. Comput..