A multiple IMM approach with unbiased mixing for thrusting projectiles

Abstract

This paper presents a multiple interacting multiple model (MIMM) procedure to estimate the state of thrusting/ ballistic projectiles in the atmosphere for the purpose of impact point prediction (IPP). Given a very short time span of observations, the strong interaction between drag and thrust in the dynamic model, in the sense of ambiguity in the estimation, significantly affects the estimation performance and the final IPP accuracy. This leads to the need to use an MIMM estimator with various initial drag coefficient estimates. The modes of each IMM estimator are for the thrusting and the ballistic phases and different extended Kalman filters (EKF) are used as the mode-matched filters with different dimension states. A novel unbiased mixing procedure for an IMM estimator is introduced to deal with state estimates with unequal dimensions, as is the case for the thrusting and ballistic models. The IPP is carried out at the end of the observation period by using the most probable mode of the selected IMM estimator, the latter being the one with the highest likelihood in the MIMM approach.