IMM-LMMSE filtering algorithm for ballistic target tracking with unknown ballistic coefficient

For ballistic target tracking using radar measurements in the polar or spherical coordinates, various nonlinear filters have been studied. Previous work often assumes that the ballistic coefficient of a missile target is known to the filter, which is unrealistic in practice. In this paper, we study the ballistic target tracking problem with unknown ballistic coefficient. We propose a general scheme to handle nonlinear systems with a nuisance parameter. The interacting multiple model (IMM) algorithm is employed and for each model the linear minimum mean square error (LMMSE) filter is used. Although we assume that the nuisance parameter is random and time invariant, our approach can be extended to time varying case. A useful property of the model transition probability matrix (TPM) is studied which provides a viable way to tune the model probability. In simulation studies, we illustrate the design of the TPM and compare the proposed method with another two IMM-based algorithms where the extended Kalman filter (EKF) and the unscented filter (UF) are used for each model, respectively. We conclude that the IMM-LMMSE filter is preferred for the problem being studied.