Set-Membership Filtering with State Constraints

In this paper, the problem of set-membership filtering is considered for discrete-time systems with equality and inequality constraints between their state variables. We formulate the problem of set-membership filtering as finding the set of estimates that belong to an ellipsoid. A centre and a shape matrix of the ellipsoid are used to describe the set of estimates and the solution to the set of estimates is obtained in terms of matrix inequality. Unknown but bounded process and measurement noises are handled under the inequality constraints by using S-procedure. We apply Finsler's lemma to project the set of estimates onto the constrained surface. A recursive algorithm is developed for computing the ellipsoid that guarantees to contain the true state under the state constraints, which is easily implemented by semi-definite programming via interior-point approach. A vehicle tracking example is provided to demonstrate the effectiveness of the proposed set-membership filtering with state equality constraints.