Kalman Filtering With Linear State Equality Constraints: A Method Based on Separating Variables

Abstract

This article considers the minimum variance state estimation of linear dynamic systems with linear state equality constraints. The proposed method uses singular value decomposition to divide the constrained system states into deterministic and stochastic parts. The deterministic part can be independently determined through the constraint equations. The stochastic part consists of random variables which have to be determined through a filtering process. The measurement and dynamic equations of the system are also divided into stochastic and deterministic parts. In order to update the mean and covariance of the state vector’s stochastic part, the measurement updating phase of the unconstrained Kalman Filter is used. Then, the deterministic part of the dynamic equation is used as a noisy measurement for the proposed method. Finally, the stochastic part of the dynamic equation is used to predict the mean and covariance of state vector’s stochastic part. Simulations show that the proposed method provides superior performance compared to other methods in the literature especially for estimating the constrained unobservable states.