Moving horizon estimation for bounded noises based on the set-membership approach

Abstract

In this paper, an improved moving horizon estimation (MHE) is proposed for the constrained linear system with bounded noises. To improve the computational efficiency of the numerical algorithms used in the MHE, a set-membership approach is employed to find a suitable search area. A tight set on decision variables is constructed based on the constrained zonotope technique. An optimization method for computing a tight zonotope enclosure of the constrained zonotope is proposed. Then the search area is further simplified into an optimal zonotope. Meanwhile, the cost function is constructed under the scenario of the worst-case noises statistical properties to improve the robustness of the MHE. For the incompletely specified probability distributions, the upper covariance matrix bounds are formulated as matrix inequalities. Finally, a numerical example illustrates the effectiveness of the algorithm.