Norm-Constrained Kalman Filtering

The problem of estimating the state vector of a dynamical system from vector measurements when it is known that the state vector satisfies norm equality constraints is considered. The case of a linear dynamical system with linear measurements subject to a norm equality constraint is discussed with a review of existing solutions. The norm constraint introduces a nonlinearity in the system for which a new estimator structure is derived by minimizing a constrained cost function. It is shown that the constrained estimate is equivalent to the brute-force normalization of the unconstrained estimate. The obtained solution is extended to nonlinear measurement models and applied to the spacecraft attitude filtering problem.

[1]  Itzhack Y. Bar-Itzhack,et al.  Quaternion normalization in spacecraft attitude determination , 1992 .

[2]  Chieh-Chih Wang,et al.  Stereo-based simultaneous localization, mapping and moving object tracking , 2010, 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[3]  D. Mortari,et al.  Recursive mode star identification algorithms , 2005, IEEE Transactions on Aerospace and Electronic Systems.

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

[5]  P. W. Richards.  Constrained Kalman Filtering Using Pseudo-measurements , 1995 .

[6]  E. J. Lefferts,et al.  Kalman Filtering for Spacecraft Attitude Estimation , 1982 .

[7]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[8]  Daniele Mortari,et al.  Attitude and orbit error in n-dimensional spaces , 2006 .

[9]  Daniele Mortari,et al.  On the Rigid Rotation Concept in n-Dimensional Spaces: Part II , 2001 .

[10]  I. Bar-Itzhack,et al.  Attitude Determination from Vector Observations: Quaternion Estimation , 1985, IEEE Transactions on Aerospace and Electronic Systems.

[11]  On the Singularity in the Estimation of the Quaternion-of-Rotation , 2002 .

[12]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .

[13]  Itzhack Y. Bar-itzhack,et al.  Optimum Normalization of a Computed Quaternion of Rotation , 1971, IEEE Transactions on Aerospace and Electronic Systems.

[14]  M. Psiaki.  Attitude-Determination Filtering via Extended Quaternion Estimation , 2000 .

[15]  R. Farrenkopf.  Analytic Steady-State Accuracy Solutions for Two Common Spacecraft Attitude Estimators , 1978 .

[16]  M. Shuster.  Constraint in attitude estimation part II: Unconstrained estimation , 2003 .

[17]  J. Stuelpnagel.  On the Parametrization of the Three-Dimensional Rotation Group , 1964 .

[18]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[19]  J. Junkins,et al.  Analytical Mechanics of Space Systems , 2003 .

[20]  Charles L. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[21]  P. Furgale,et al.  Pose estimation using linearized rotations and quaternion algebra , 2011 .

[22]  James R. Wertz,et al.  Spacecraft attitude determination and control , 1978 .

[23]  J. Junkins,et al.  Optimal Estimation of Dynamic Systems , 2004 .

[24]  Daniele Mortari,et al.  Information Theoretic Weighting for Robust Star Centroiding , 2011 .

[25]  F. Markley,et al.  Unscented Filtering for Spacecraft Attitude Estimation , 2003 .

[26]  Daniele Mortari,et al.  Quaternion constrained Kalman filter , 2008 .

[27]  F. Landis Markley,et al.  Generalized Linear Covariance Analysis , 2009 .

[28]  Renato Zanetti.  A Multiplicative Residual Approach To Attitude Kalman Filtering With Unit-Vector Measurements , 2009 .

[29]  Daniel Choukroun,et al.  A Novel Quaternion Kalman Filter , 2002 .

[30]  Renato Zanetti,et al.  Quaternion Estimation and Norm Constrained Kalman Filtering , 2006 .

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

[32]  Charles L. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.