Quadratic Estimation for Discrete Time System With State Equality Constraints and Composite Disturbances

Abstract

This article investigates the state estimation issue for discrete-time systems subject to composite disturbances (CD) and state equality constraints, in which the CD include unknown inputs and non-Gaussian noise. To enhance the estimation performance under the influence of CD, a quadratic estimator incorporating state equality constraints is proposed. Initially, the Kronecker algebra technique is used to compute the second-order Kronecker powers of the raw vectors and a quadratic dynamical system is formed by combining the original vectors with their corresponding second-order Kronecker powers. Additionally, a specific condition is imposed to suppress the interference caused by unknown inputs. On this basis, a quadratic state unconstrained estimator (QSUE) is developed based on the minimum variance unbiased criterion. Furthermore, a quadratic state constrained estimator (QSCE) is designed by applying the projection technique to the QSUE. Finally, a simulation example demonstrates that the QSCE achieves better estimation performance than the QSUE and exhibits greater adaptability to CD.