State estimation for linear systems with state equality constraints

This paper deals with the state estimation problem for linear systems with linear state equality constraints. Using noisy measurements which are available from the observable system, we construct the optimal estimate which also satisfies linear equality constraints. For this purpose, after reviewing modeling problems in linear stochastic systems with state equality constraints, we formulate a projected system representation. By using the constrained Kalman filter for the projected system and comparing its filter Riccati equation with those of the unconstrained and the projected Kalman filters, we clearly show, without using optimality, that the constrained estimator outperforms the other filters for estimating the constrained system state. Finally, a numerical example is presented, which demonstrates performance differences among those filters.