Best linear unbiased state estimation with noisy and noise-free measurements

Numerous state estimation problems (e.g., under linear or nonlinear equality constraints, with correlated or singular measurement noise) can be formulated as the problem with noisy and noise-free measurements. Under the assumption that the initial state and the noise are jointly Gaussian distributed and the coefficient matrix for linear equality constraint has full row rank, some optimal state estimation algorithms were obtained in the literature. Given only the first two moments and without any assumption on the rank of the measurement matrix for noise-free measurement, optimal batch and two sequential forms of the state estimation algorithms in the sense of best linear unbiased estimation (BLUE) are obtained in this paper. Extension to nonlinear measurements is also discussed.

[1]  Thia Kirubarajan,et al.  Estimation with Applications to Tracking and Navigation: Theory, Algorithms and Software , 2001 .

[2]  Bernard Friedland,et al.  Separate-bias estimation with reduced-order Kalman filters , 1998, IEEE Trans. Autom. Control..

[3]  Chun Yang,et al.  Kalman Filtering with Nonlinear State Constraints , 2009 .

[4]  Kazufumi Ito,et al.  Gaussian filters for nonlinear filtering problems , 2000, IEEE Trans. Autom. Control..

[5]  Vesselin P. Jilkov,et al.  A survey of maneuvering target tracking: approximation techniques for nonlinear filtering , 2004, SPIE Defense + Commercial Sensing.

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

[7]  Zhansheng Duan.  Sequential Nonlinear Tracking Filter with Range-rate Measurements in Spherical Coordinates , 2004 .

[8]  Robert R. Bitmead,et al.  State estimation for linear systems with state equality constraints , 2007, Autom..

[9]  Chongzhao Han,et al.  Sequential unscented Kalman filter for radar target tracking with range rate measurements , 2005, 2005 7th International Conference on Information Fusion.

[10]  N. Gupta,et al.  Kalman Filtering in the Presence of State Space Equality Constraints , 2006, 2007 Chinese Control Conference.

[11]  R. Bitmead,et al.  STATE ESTIMATION OF LINEAR SYSTEMS WITH STATE EQUALITY CONSTRAINTS , 2005 .

[12]  Erik Blasch,et al.  Fusion of Tracks with Road Constraints , 2008, J. Adv. Inf. Fusion.

[13]  Dennis S. Bernstein,et al.  State estimation for equality-constrained linear systems , 2007, 2007 46th IEEE Conference on Decision and Control.

[14]  D. Simon,et al.  Kalman filtering with state equality constraints , 2002 .

[15]  F. Chang,et al.  Filtering method for nonlinear systems with constraints , 2002 .

[16]  LI X.RONG,et al.  Best linear unbiased filtering with nonlinear measurements for target tracking , 2004, IEEE Transactions on Aerospace and Electronic Systems.

[17]  Joseph J. LaViola,et al.  On Kalman Filtering With Nonlinear Equality Constraints , 2007, IEEE Transactions on Signal Processing.

[18]  Niels Kjølstad Poulsen,et al.  New developments in state estimation for nonlinear systems , 2000, Autom..

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

[20]  Jie Zhou,et al.  The Linear Minimum Mean-Square Error Estimation with Constraints and Its Applications , 2006, 2006 International Conference on Computational Intelligence and Security.

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

[22]  Hugh F. Durrant-Whyte,et al.  A new method for the nonlinear transformation of means and covariances in filters and estimators , 2000, IEEE Trans. Autom. Control..