Some results on Kalman filtering with linear equality state constraints

This paper addresses the estimation problem for linear system with linear equality state constraints. We review the existing state projection method and present a simple way to find the optimal filter gain of the constrained Kalman filter. Then, we transform the constrained system into a reduced-order model and construct a reduced-order Kalman filter for this estimation problem. Next, we discuss the properties and error covariance matrices of different estimates. Finally, a vehicle tracking example is provided to compare the effectiveness of these estimators.