Quaternion constrained Kalman filter
- Additional Document Info
- View All
The problem of estimating the state vector of a dynamical system from vector measurements, when it is known that the state vector satisfies certain constraints is considered. The case of a linear dynamical system subject to a linear state variable equality constraint is briefly discussed with a review of existing solutions. For the special case of a linear system which evolves with the state subject to constraint of unit norm, a new estimator structure is derived by minimizing a constrained cost function. The resulting estimator structure is subsequently shown to be stable followed by the discussion of important properties of the estimator structure. The filter thus derived is specialized to solve the attitude estimation problem. In this problem, the state vector consists of a four component parametrization of the spacecraft orientation and is found to be naturally constrained to have a unit norm. It is shown that the estimate of the nonlinear observer (which also minimizes the said constrained loss function) is equivalent to the brute force normalization of the unconstrained estimate. Continuous discrete and the discrete attitude estimators are presented using this specialized result. Based on the stability arguments an alternative observer structure is proposed. The projection method for linear constraints is applied to attitude estimation in a multiplicative framework (which we call the linear constrained attitude filter). The stable observers thus developed are compared with the classical Multiplicative Kalman Filter and the linear constrained attitude filter in estimating the states of the rigid body operating under three different situations.
author list (cited authors)