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.