Optimal and self‐tuning weighted measurement fusion Kalman filters and their asymptotic global optimality

For the multisensor linear discrete time-invariant stochastic systems with unknown noise variances, using the correlation method, the information fusion noise variance estimators with consistency are given by taking the average of the local noise variance estimators. Substituting them into two optimal weighted measurement fusion steady-state Kalman filters, two new self-tuning weighted measurement fusion Kalman filters with a self-tuning Riccati equation are presented. By the dynamic variance error system analysis (DVESA) method, it is rigorously proved that the self-tuning Riccati equation converges to the steady-state optimal Riccati equation. Further, by the dynamic error system analysis (DESA) method, it is proved that the steady-state optimal and self-tuning Kalman fusers converge to the global optimal centralized Kalman fuser, so that they have the asymptotic global optimality. Compared with the centralized Kalman fuser, they can significantly reduce the computational burden. A simulation example for the target tracking systems shows their effectiveness. Copyright © 2010 John Wiley & Sons, Ltd.

[1]  Yuan Gao,et al.  New approach to information fusion steady-state Kalman filtering , 2005, Autom..

[2]  Z. Deng,et al.  Self-tuning Information Fusion Kalman Predictor Weighted by Scalars , 2006, 2006 6th World Congress on Intelligent Control and Automation.

[3]  Zhi Tian,et al.  Performance evaluation of track fusion with information matrix filter , 2002 .

[4]  Tony T. Lee.  A direct approach to identify the noise covariances of Kalman filtering , 1980 .

[5]  C. J. Harris,et al.  Comparison of two measurement fusion methods for Kalman-filter-based multisensor data fusion , 2001 .

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

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

[8]  Andrew P. Sage,et al.  Adaptive filtering with unknown prior statistics , 1969 .

[9]  J. A. Roecker,et al.  Comparison of two-sensor tracking methods based on state vector fusion and measurement fusion , 1988 .

[10]  C. Ran,et al.  Self-Tuning Decoupled Fusion Kalman Predictor and Its Convergence Analysis , 2009, IEEE Sensors Journal.

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

[12]  T. Moir,et al.  Optimal self-tuning filtering, prediction, and smoothing for discrete multivariable processes , 1984 .

[13]  Yuan Gao,et al.  Self-tuning decoupled information fusion Wiener state component filters and their convergence , 2008, Autom..

[14]  Yunmin Zhu,et al.  The optimality for the distributed Kalman filtering fusion with feedback , 2001, Autom..

[15]  Zi-Li Deng,et al.  Optimal and self-tuning white noise estimators with applications to deconvolution and filtering problems , 1996, Autom..

[16]  Xiaojun Sun,et al.  Self-Tuning Multisensor Weighted Measurement Fusion Kalman Filter , 2009 .

[17]  Per Hagander,et al.  A self-tuning filter for fixed-lag smoothing , 1977, IEEE Trans. Inf. Theory.

[18]  R. Mehra.  On the identification of variances and adaptive Kalman filtering , 1970 .

[19]  Michael J. Grimble,et al.  Dynamic ship positioning using a self-tuning Kalman filter , 1983 .

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