Distributed weighted robust Kalman filter fusion for uncertain systems with autocorrelated and cross-correlated noises

In this paper, the problem of distributed weighted robust Kalman filter fusion is studied for a class of uncertain systems with autocorrelated and cross-correlated noises. The system under consideration is subject to stochastic uncertainties or multiplicative noises. The process noise is assumed to be one-step autocorrelated. For each subsystem, the measurement noise is one-step autocorrelated, and the process noise and the measurement noise are two-step cross-correlated. An optimal robust Kalman-type recursive filter is first designed for each subsystem. Then, based on the newly obtained optimal robust Kalman-type recursive filter, a distributed weighted robust Kalman filter fusion algorithm is derived for uncertain systems with multiple sensors. The distributed fusion algorithm involves a recursive computation of the filtering error cross-covariance matrix between any two subsystems. Compared with the centralized Kalman filter, the distributed weighted robust Kalman filter developed in this paper has stronger fault-tolerance ability. Simulation results are provided to demonstrate the effectiveness of the proposed approaches.

[1]  Sumit Roy,et al.  Decentralized structures for parallel Kalman filtering , 1988 .

[2]  Bor-Sen Chen,et al.  Minimax robust deconvolution filters under stochastic parametric and noise uncertainties , 1994, IEEE Trans. Signal Process..

[3]  J. Geromel,et al.  H/sub 2/ and H/sub /spl infin// robust filtering for discrete-time linear systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[4]  L. Ghaoui.  State-feedback control of systems with multiplicative noise via linear matrix inequalities , 1995 .

[5]  Victor S. Frost,et al.  A Model for Radar Images and Its Application to Adaptive Digital Filtering of Multiplicative Noise , 1982, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  Yuan Gao,et al.  Reduced-order steady-state descriptor Kalman fuser weighted by block-diagonal matrices , 2008, Inf. Fusion.

[7]  Huijun Gao,et al.  A Parameter-Dependent Approach to Robust $H_{\infty }$ Filtering for Time-Delay Systems , 2008, IEEE Transactions on Automatic Control.

[8]  Kemin Zhou,et al.  H/sub /spl infin// Gaussian filter on infinite time horizon , 2002 .

[9]  James Lam,et al.  $H_{\bm \infty}$ Fuzzy Filtering of Nonlinear Systems With Intermittent Measurements , 2009, IEEE Transactions on Fuzzy Systems.

[10]  Zhisheng You,et al.  The Kalman type recursive state estimator with a finite-step correlated process noises , 2008, 2008 IEEE International Conference on Automation and Logistics.

[11]  Y. Phillis.  Estimation and control of systems with unknown covariance and multiplicative noise , 1989, 26th IEEE Conference on Decision and Control.

[12]  Yunmin Zhu,et al.  The Optimal Kalman Type State Estimator with Multi-Step Correlated Process and Measurement Noises , 2008, 2008 International Conference on Embedded Software and Systems.

[13]  Thiagalingam Kirubarajan,et al.  Estimation with Applications to Tracking and Navigation , 2001 .

[14]  A. Murat Tekalp,et al.  Image restoration with multiplicative noise: incorporating the sensor nonlinearity , 1991, IEEE Trans. Signal Process..

[15]  James Lam,et al.  Robust filtering for discrete-time Markovian jump delay systems , 2004, IEEE Signal Processing Letters.

[16]  Shu-Li Sun,et al.  Multi-sensor optimal information fusion Kalman filter , 2004, Autom..

[17]  Shu-Li Sun,et al.  Multi-sensor optimal fusion fixed-interval Kalman smoothers , 2008, Inf. Fusion.

[18]  Zidong Wang,et al.  Mixed H/sub 2//H/sub /spl infin// filtering for uncertain systems with regional pole assignment , 2005, IEEE Transactions on Aerospace and Electronic Systems.

[19]  Yunmin Zhu,et al.  Optimal Kalman filtering fusion with cross-correlated sensor noises , 2007, Autom..

[20]  Isaac Yaesh,et al.  Hinfinity control and filtering of discrete-time stochastic systems with multiplicative noise , 2001, Autom..

[21]  Mani Srivastava,et al.  Overview of sensor networks , 2004 .

[22]  Jean-Yves Tourneret,et al.  Least-squares estimation of multiple abrupt changes contaminated by multiplicative noise using MCMC , 1999, Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics. SPW-HOS '99.

[23]  Fuwen Yang,et al.  Decentralized robust Kalman filtering for uncertain stochastic systems over heterogeneous sensor networks , 2008, Signal Process..

[24]  N. A. Carlson.  Federated square root filter for decentralized parallel processors , 1990 .

[25]  Dan Simon,et al.  Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches , 2006 .

[26]  K. H. Kim,et al.  Development of track to track fusion algorithms , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[27]  Chuang Li,et al.  Multi-model information fusion Kalman filtering and white noise deconvolution , 2010, Inf. Fusion.

[28]  Chongzhao Han,et al.  Optimal linear estimation fusion .I. Unified fusion rules , 2003, IEEE Trans. Inf. Theory.

[29]  Robert D. Nowak,et al.  Quantized incremental algorithms for distributed optimization , 2005, IEEE Journal on Selected Areas in Communications.

[30]  D. Bertsekas,et al.  Recursive state estimation for a set-membership description of uncertainty , 1971 .

[31]  Yeung Sam Hung,et al.  A Kalman Filter Approach to Direct Depth Estimation Incorporating Surface Structure , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

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

[33]  James Lam,et al.  New approach to mixed H/sub 2//H/sub /spl infin// filtering for polytopic discrete-time systems , 2005, IEEE Transactions on Signal Processing.

[34]  James Lam,et al.  Filtering for Nonlinear Genetic Regulatory Networks With Stochastic Disturbances , 2008, IEEE Transactions on Automatic Control.

[35]  Yurong Liu,et al.  State estimation for jumping recurrent neural networks with discrete and distributed delays , 2009, Neural Networks.

[36]  Gregory J. Pottie,et al.  Instrumenting the world with wireless sensor networks , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[37]  Zidong Wang,et al.  H∞ filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities , 2008, Autom..

[38]  Deborah Estrin,et al.  Guest Editors' Introduction: Overview of Sensor Networks , 2004, Computer.