A structured filter for Markovian switching systems

In this work, a new methodology for the structuring of multiple model estimation schemas is developed. The proposed filter is applied to the estimation and detection of active mode in dynamic systems. The discrete-time Markovian switching systems represented by several linear models, associated with a particular operating mode, are studied. Therefore, the main idea of this work is the subdivision of the models set to some subsets in order to improve the detection and estimation performances. Each subset is associated with sub-estimators based on models of the subset. In order to compute the global estimate and subset probabilities, a global estimator is proposed. Theoretical developments based on a hierarchical decision, leading to more efficiency in detection and state estimation, are proposed. Naturally, these results can be used for fault detection and isolation, using the activation probabilities of operating modes. These results are applied to detect switches in the centre of gravity for vehicle roll dynamics.

[1]  Y. Bar-Shalom,et al.  Tracking a maneuvering target using input estimation versus the interacting multiple model algorithm , 1989 .

[2]  Huijun Gao,et al.  Distributed H∞ Filtering for a Class of Markovian Jump Nonlinear Time-Delay Systems Over Lossy Sensor Networks , 2013, IEEE Transactions on Industrial Electronics.

[3]  Tan-Jan Ho,et al.  A switched IMM-Extended Viterbi estimator-based algorithm for maneuvering target tracking , 2011, Autom..

[4]  Didier Maquin,et al.  Finite memory observer for switching systems: Application to diagnosis , 2004 .

[5]  HocineA.,et al.  A discrete-time sliding window observer for Markovian switching system , 2008 .

[6]  D. Magill.  Optimal adaptive estimation of sampled stochastic processes , 1965 .

[7]  J. C. Gerdes,et al.  Estimation of vehicle roll and road bank angle , 2004, Proceedings of the 2004 American Control Conference.

[8]  J. Ragot,et al.  A discrete-time Sliding Window Observer for Markovian Switching System , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[9]  A. El Hajjaji,et al.  Road curvature estimation for vehicle lane departure detection using a robust Takagi–Sugeno fuzzy observer , 2013 .

[10]  Robert Shorten,et al.  A design methodology for switched discrete time linear systems with applications to automotive roll dynamics control , 2008, Autom..

[11]  Hans Driessen,et al.  A multiple model multiple hypothesis filter for Markovian switching systems , 2005, Autom..

[12]  X. Rong Li,et al.  Multiple-model estimation with variable structure. II. Model-set adaptation , 2000, IEEE Trans. Autom. Control..

[13]  Zidong Wang,et al.  Exponential Stabilization of a Class of Stochastic System With Markovian Jump Parameters and Mode-Dependent Mixed Time-Delays , 2010, IEEE Transactions on Automatic Control.

[14]  Daniel W. C. Ho,et al.  Robust ${{\cal H}}_{\infty}$ Filtering for Markovian Jump Systems With Randomly Occurring Nonlinearities and Sensor Saturation: The Finite-Horizon Case , 2011, IEEE Transactions on Signal Processing.

[15]  Hamid Reza Karimi,et al.  Robust Delay-Dependent $H_{\infty}$ Control of Uncertain Time-Delay Systems With Mixed Neutral, Discrete, and Distributed Time-Delays and Markovian Switching Parameters , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[16]  X. Rong Li,et al.  General model-set design methods for multiple-model approach , 2005, IEEE Transactions on Automatic Control.

[17]  A. El Hajjaji,et al.  Vehicle dynamic estimation with road bank angle consideration for rollover detection: theoretical and experimental studies , 2013 .

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

[19]  Robert Shorten,et al.  Topics in Automotive Rollover Prevention: Robust and Adaptive Switching Strategies for Estimation and Control , 2007 .

[20]  Liping Pang,et al.  A novel interacting multiple model algorithm , 2009, Signal Process..

[21]  X. Rong Li,et al.  Multiple-Model Estimation with Variable Structure—Part II: Model-Set Adaptation , 2000 .

[22]  Youmin Zhang,et al.  Detection and diagnosis of sensor and actuator failures using IMM estimator , 1998 .

[23]  Zidong Wang,et al.  H∞ filtering with randomly occurring sensor saturations and missing measurements , 2012, Autom..

[24]  Maozhen Li,et al.  Probability-Dependent Gain-Scheduled Filtering for Stochastic Systems With Missing Measurements , 2011, IEEE Transactions on Circuits and Systems II: Express Briefs.

[25]  Hans B. Pacejka,et al.  A New Tire Model with an Application in Vehicle Dynamics Studies , 1989 .