Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements

In this paper, the extended Kalman filtering problem is investigated for a class of nonlinear systems with multiple missing measurements over a finite horizon. Both deterministic and stochastic nonlinearities are included in the system model, where the stochastic nonlinearities are described by statistical means that could reflect the multiplicative stochastic disturbances. The phenomenon of measurement missing occurs in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over the interval [0,1]. Such a probability distribution is allowed to be any commonly used distribution over the interval [0,1] with known conditional probability. The aim of the addressed filtering problem is to design a filter such that, in the presence of both the stochastic nonlinearities and multiple missing measurements, there exists an upper bound for the filtering error covariance. Subsequently, such an upper bound is minimized by properly designing the filter gain at each sampling instant. It is shown that the desired filter can be obtained in terms of the solutions to two Riccati-like difference equations that are of a form suitable for recursive computation in online applications. An illustrative example is given to demonstrate the effectiveness of the proposed filter design scheme.

[1]  Ian R. Petersen,et al.  A Discrete-Time Robust Extended Kalman Filter for Uncertain Systems With Sum Quadratic Constraints , 2009, IEEE Transactions on Automatic Control.

[2]  Konrad Reif,et al.  Stochastic Stability of the Extended Kalman Filter With Intermittent Observations , 2010, IEEE Transactions on Automatic Control.

[3]  Y. I. Yaz,et al.  A new formulation of some discrete-time stochastic-parameter state estimation problems , 1997 .

[4]  Andrey V. Savkin,et al.  Fusion Based 3D Tracking of Mobile Transmitters via Robust Set-Valued State Estimation with RSS Measurements , 2011, IEEE Communications Letters.

[5]  Edwin Engin Yaz,et al.  Recursive estimator for linear and nonlinear systems with uncertain observations , 1997, Signal Process..

[6]  Wei Xing Zheng,et al.  Weighted H∞ model reduction for linear switched systems with time-varying delay , 2009, Autom..

[7]  Edwin Engin Yaz,et al.  Robust minimum variance linear state estimators for multiple sensors with different failure rates , 2007, Autom..

[8]  Andrey V. Savkin,et al.  Vision-Based Target Tracking and Surveillance With Robust Set-Valued State Estimation , 2010, IEEE Signal Processing Letters.

[9]  Uri Shaked,et al.  Robust discrete-time minimum-variance filtering , 1996, IEEE Trans. Signal Process..

[10]  James Lam,et al.  Disturbance Analysis of Nonlinear Differential Equation Models of Genetic SUM Regulatory Networks , 2011, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[11]  Engin Yaz,et al.  On the optimal state estimation of a class of discrete-time nonlinear systems , 1987 .

[12]  Edwin Engin Yaz,et al.  Minimum variance generalized state estimators for multiple sensors with different delay rates , 2007, Signal Process..

[13]  Kai Xiong,et al.  Robust Extended Kalman Filtering for Nonlinear Systems With Stochastic Uncertainties , 2010, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[14]  Giuseppe Carlo Calafiore,et al.  Reliable localization using set-valued nonlinear filters , 2005, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[15]  James Lam,et al.  $H_{\infty}$ Positive Filtering for Positive Linear Discrete-Time Systems: An Augmentation Approach , 2010, IEEE Transactions on Automatic Control.

[16]  Dong Yue,et al.  Network-Based Robust$H_infty$Filtering for Uncertain Linear Systems , 2006, IEEE Transactions on Signal Processing.

[17]  Lihua Xie,et al.  Robust Kalman filtering for uncertain discrete-time systems , 1994, IEEE Trans. Autom. Control..

[18]  Lihua Xie,et al.  Optimal linear estimation for systems with multiple packet dropouts , 2008, Autom..

[19]  X. Kai,et al.  Robust extended Kalman filtering for nonlinear systems with multiplicative noises , 2011 .

[20]  Michael Basin,et al.  Central suboptimal H∞ filter design for nonlinear polynomial systems , 2009, 2009 American Control Conference.

[21]  Peng Shi,et al.  Robust filtering for jumping systems with mode-dependent delays , 2006, Signal Process..

[22]  Peng Shi,et al.  Approximate finite-dimensional filtering for polynomial states over polynomial observations , 2010, Int. J. Control.

[23]  J. Lam,et al.  Fixed-Order Robust Filter Design for Markovian Jump Systems With Uncertain Switching Probabilities , 2006 .

[24]  Wei Xing Zheng,et al.  Exponential stability of nonlinear time-delay systems with delayed impulse effects , 2011, Autom..

[25]  Ian R. Petersen,et al.  Nonlinear state estimation for uncertain systems with an integral constraint , 1998, IEEE Trans. Signal Process..

[26]  David Zhang,et al.  Improved robust H2 and Hinfinity filtering for uncertain discrete-time systems , 2004, Autom..

[27]  LiuXiaohui,et al.  An Extended Kalman Filtering Approach to Modeling Nonlinear Dynamic Gene Regulatory Networks via Short Gene Expression Time Series , 2009 .

[28]  James Lam,et al.  Fixed-order robust H/sub /spl infin// filter design for Markovian jump systems with uncertain switching probabilities , 2006, IEEE Transactions on Signal Processing.

[29]  Zidong Wang,et al.  Robust filtering with stochastic nonlinearities and multiple missing measurements , 2009, Autom..

[30]  Zidong Wang,et al.  An Extended Kalman Filtering Approach to Modeling Nonlinear Dynamic Gene Regulatory Networks via Short Gene Expression Time Series , 2009, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[31]  Daniel W. C. Ho,et al.  Variance-constrained filtering for uncertain stochastic systems with missing measurements , 2003, IEEE Trans. Autom. Control..

[32]  Moshe Idan,et al.  H2/H8 filtering: theory and an aerospace application , 1996 .

[33]  Moshe Idan,et al.  H/sub 2//H/sub /spl infin// filtering: theory and an aerospace application , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[34]  Sirish L. Shah,et al.  Optimal H2 filtering with random sensor delay, multiple packet dropout and uncertain observations , 2007, Int. J. Control.

[35]  Edwin Engin Yaz,et al.  State estimation of uncertain nonlinear stochastic systems with general criteria , 2001, Appl. Math. Lett..

[36]  Konrad Reif,et al.  Stochastic stability of the discrete-time extended Kalman filter , 1999, IEEE Trans. Autom. Control..

[37]  Andrey V. Savkin,et al.  Decentralized robust set-valued state estimation in networked multiple sensor systems , 2010, Comput. Math. Appl..