Robust Kalman filtering with constraints: a case study for integrated navigation

When certain constraints in the kinematic state parameters of a multi-sensor navigation system exist, they should be taken into account for the improvement of the positioning accuracy and reliability. In this paper, two types of robust estimators for integrated and two stages of Kalman filtering with state parameter constraints are derived based on the generalized maximum likelihood Lagrangian condition, respectively. The properties of the two estimators are discussed. The changes of the state estimates and their covariance matrices as well as the residual vector caused by the constraints are derived and analyzed. It is shown by a simulated example that the precision of the state estimates provided by the Kalman filtering with constraints is better than that provided by the Kalman filtering without considering the state parameter constraints; and the robust Kalman filtering with constraints further improves the reliability and robustness of the state estimates.

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

[2]  Howard E. Doran,et al.  Constraining Kalman Filter and Smoothing Estimates to Satisfy Time-Varying Restrictions , 1992 .

[3]  Z. Wisniewski.  A concept of robust estimation of variance coefficient (VR-estimation) , 1999 .

[4]  Jianjun Zhu,et al.  Robustness and the robust estimate , 1996 .

[5]  Karl-Rudolf Koch,et al.  Parameter estimation and hypothesis testing in linear models , 1988 .

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

[7]  W. Blair,et al.  Use of a kinematic constraint in tracking constant speed, maneuvering targets , 1993, IEEE Trans. Autom. Control..

[8]  Peiliang Xu,et al.  Consequences of constant parameters and confidence intervals of robust estimation , 1993 .

[9]  Werner A. Stahel,et al.  Robust Statistics: The Approach Based on Influence Functions , 1987 .

[10]  Peter J. Huber,et al.  Robust Statistics , 2005, Wiley Series in Probability and Statistics.

[11]  Peiliang Xu.  Sign-constrained robust least squares, subjective breakdown point and the effect of weights of observations on robustness , 2005 .

[12]  G. Lachapelle,et al.  Consideration of time-correlated errors in a Kalman filter applicable to GNSS , 2009 .

[13]  H.J. Chizeck,et al.  Recursive parameter identification of constrained systems: an application to electrically stimulated muscle , 1991, IEEE Transactions on Biomedical Engineering.

[14]  J. Speyer,et al.  Target tracking problems subject to kinematic constraints , 1990 .

[15]  Yuanxi Yang,et al.  Adaptively robust filtering for kinematic geodetic positioning , 2001 .

[16]  S. Hekimoglu.  INCREASING RELIABILITY OF THE TEST FOR OUTLIERS WHOSE MAGNITUDE IS SMALL , 2005 .

[17]  Z. Wiśniewski.  Estimation of parameters in a split functional model of geodetic observations (Msplit estimation) , 2008 .

[18]  Yuan Yunbin,et al.  Application of adaptive filtering by selecting the parameter weight factor in precise kinematic GPS positioning , 2005 .

[19]  Xianqiang Cui,et al.  Adaptively robust filter with multi adaptive factors , 2008 .

[20]  Hugh F. Durrant-Whyte,et al.  Model-based multi-sensor data fusion , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[21]  Yuanxi Yang,et al.  Robust Kalman filter for rank deficient observation models , 1998 .

[22]  Donald L. Simon,et al.  Aircraft Turbofan Engine Health Estimation Using Constrained Kalman Filtering , 2005 .

[23]  P. J. Huber.  Robust Estimation of a Location Parameter , 1964 .

[24]  Burkhard Schaffrin,et al.  On Some Alternatives to Kalman Filtering , 1995 .

[25]  Fernando Sansò,et al.  Geodetic Theory Today , 1995 .

[26]  Yang Yuanxi,et al.  Robust bayesian estimation , 1991 .

[27]  Yang Yuan.  Properties of the Adaptive Filtering for Kinematic Positioning , 2003 .

[28]  Lihua Xie,et al.  Robust Kalman filtering for uncertain systems , 1994 .

[29]  Xu Peiliang,et al.  On robust estimation with correlated observations , 1989 .