We discuss the pseudo measurement method which is one of the main approaches to equality-constrained state estimation for a dynamic system. We demonstrate by the fundamental theory of Kalman filtering that reviewing the equality constraint as a pseudo measurement seems questionable. The main reason is that the additional pseudo measurement is actually a constant here which cannot help to estimate the state. More specifically, when the states in an unconstrained dynamic system model have already satisfied the equality constraint, the extra constraint is obviously not necessary. When the true equality-constrained states do not satisfy the unconstrained dynamic process equation, the effect of pseudo measurement is projecting the estimate which is not optimal onto the constraint set. However, since the performance of a projected estimate is also certainly influenced by its original estimate, we show through a numerical example that the pseudo measurement method is not always a good choice, especially when the process equation mismatch is large.

In order to settle the requirement of target location and line-of-sight (LOS) rate estimation with multi-angle measurement in terminal guidance process, the state estimation algorithm based on Kalman filter is proposed in this paper. The linearized system model is established, and the extended Kalman filter is used to estimate the position and LOS rate of the target. The simulation results show that this method exhibits high accuracy for position estimation, and it can precisely track the change of LOS angular rate in real time. The algorithm is simple in principle, easy to implement and of high value in practice.