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.