State estimation with incomplete linear constraint

Abstract

A problem of state estimation with destination constraint is considered in this paper. An anti-radiation missile (ARM) often moves towards the target along a trajectory which is almost linear in the X-Y plane. The linear constraint for trajectory and target position are known as priori and can be used to enhance the performance of a tracking filter. In this paper, a destination constrained Kalman filter (DCKF) is first revised for our problem. Then, two methods are proposed to incorporate the prior knowledge by estimating the slope of the trajectory. In the first method, the slope is estimated directly at each time using the point estimated by a unconstrained Kalman filter and the destination point. In the second method, a least square method is used to estimate the slope from all measurements. Several effective linear equality constrained state estimation methods can be used to exploit the estimated slop and the destination point. A typical ARM tracking scenario is established to test the proposed Kalman filter. A comprehensive comparison to recent work is also presented, including unconstrained nonlinear filtering methods and the Posterior Cramer-Rao Lower Bound (PCRLB). Monte-Carlo simulation results are presented to illustrate the effectiveness of the proposed methods for state estimation with destination constraint.