Optimal Linear Fusion of Smoothed State Estimates

The work presented here deals with estimation fusion of smoothed state estimates. Two problems of fusion for smoothing are considered: fixed point and fixed interval. Optimal linear fusion rules in the sense of the optimal weighted least squares (OWLS) and the linear minimum mean-square error (LMMSE) are obtained. These rules are in recursive forms convenient for implementation. We also propose a more practical method for real-time smoothing, which in essence is fusing smoothed and filtered estimates. Illustrative numerical results are provided to verify the performance and credibility of the fusion rules.

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

[2]  William Dale Blair,et al.  Fixed-interval smoothing for Markovian switching systems , 1995, IEEE Trans. Inf. Theory.

[3]  Wolfgang Koch,et al.  Fixed-interval retrodiction approach to Bayesian IMM-MHT for maneuvering multiple targets , 2000, IEEE Trans. Aerosp. Electron. Syst..

[4]  X. Rong Li,et al.  Recursibility and optimal linear estimation and filtering , 2004, CDC.

[5]  Peng Zhang,et al.  Optimal linear estimation fusion - part VI: sensor data compression , 2003, Sixth International Conference of Information Fusion, 2003. Proceedings of the.

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

[7]  C. Striebel,et al.  On the maximum likelihood estimates for linear dynamic systems , 1965 .

[8]  Y. Bar-Shalom,et al.  On optimal track-to-track fusion , 1997, IEEE Transactions on Aerospace and Electronic Systems.

[9]  X. R. Li,et al.  Optimal Linear Estimation Fusion — Part III : Cross-Correlation of Local Estimation Errors , 2001 .

[10]  Y. Bar-Shalom.  On the track-to-track correlation problem , 1981 .

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

[12]  Chongzhao Han,et al.  Optimal Linear Estimation Fusion — Part I : Unified Fusion Rules , 2001 .

[13]  X. Rong Li,et al.  Measuring Estimator's Credibility: Noncredibility Index , 2006, 2006 9th International Conference on Information Fusion.

[14]  Yaakov Bar-Shalom,et al.  The Effect of the Common Process Noise on the Two-Sensor Fused-Track Covariance , 1986, IEEE Transactions on Aerospace and Electronic Systems.

[15]  Jitendra Tugnait,et al.  Detection and Estimation with Fixed Lag for Abruptly Changing Systems , 1983, IEEE Transactions on Aerospace and Electronic Systems.

[16]  Arthur Gelb,et al.  Applied Optimal Estimation , 1974 .

[17]  Yunmin Zhu,et al.  Optimal linear estimation fusion. Part V. Relationships , 2002, Proceedings of the Fifth International Conference on Information Fusion. FUSION 2002. (IEEE Cat.No.02EX5997).

[18]  Oliver E. Drummond.  Track and tracklet fusion filtering , 2002, SPIE Defense + Commercial Sensing.

[19]  X. R. Li,et al.  Optimal Linear Estimation Fusion — Part IV : Optimality and Efficiency of Distributed Fusion , 2001 .

[20]  X. Rong Li.  Optimal linear estimation fusion-part VII: dynamic systems , 2003, Sixth International Conference of Information Fusion, 2003. Proceedings of the.

[21]  Chee-Yee Chong,et al.  Track association and track fusion with nondeterministic target dynamics , 2002 .

[22]  Mohammad A. Husain.  Estimation and filtering for digital signals , 1989 .

[23]  S. Mori,et al.  Performance evaluation for MAP state estimate fusion , 2004 .

[24]  R. Saha,et al.  An efficient algorithm for multisensor track fusion , 1998 .

[25]  A. Willsky,et al.  Combining and updating of local estimates and regional maps along sets of one-dimensional tracks , 1982 .

[26]  H. Rauch.  Solutions to the linear smoothing problem , 1963 .