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. ∗Presented as paper AIAA 2006-6164 at the 2006 AIAA/AAS Astrodynamics Specialist Conference and paper AAS 08-215 at the 2008 AAS/AIAA Space Flight Mechanics Meeting. †Now Senior Member of the Technical Staff at The Charles Stark Draper Laboratory, 17629 El Camino Real, Suite 470, Houston, Texas 77058 [email protected], AIAA Member. ‡PhD Candidate, Department of Aerospace Engineering, 616D H.R. Bright Building, 3141 TAMU, [email protected], AIAA Student Member. §Professor and Chairman, Department of Aerospace Engineering and Engineering Mechanics, 210 East 24th Street, W. R. Woolrich Laboratories, 1 University Station, [email protected], AIAA Fellow. ¶Associate Professor, Department of Aerospace Engineering, 611C H.R. Bright Building, 3141 TAMU, [email protected], AIAA Associate Fellow.