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.
In tracking applications, target dynamics is usually modeled in the Cartesian coordinates, while target measurements are directly available in the original sensor coordinates. Measurement conversion is widely used to do linearization such that the Kalman filter can be applied in the Cartesian coordinates. A number of improved measurement-conversion techniques have been proposed recently. However, they have fundamental limitations, resulting in performance degradation, as pointed out in Part III of a recent survey conducted by the authors. This paper proposes a recursive filter that is theoretically optimal in the sense of minimizing the mean-square error among all linear unbiased filters in the Cartesian coordinates. The proposed filter is free of the fundamental limitations of the measurement-conversion approach. Results of an approximate implementation for measurements in the spherical coordinates are compared with those obtained by two state-of-the-art conversion techniques. Simulation results are provided.
This paper deals with practical measures for performance evaluation of estimators and filters. Several new measures useful for evaluating various aspects of the performance of an estimator or filter are proposed and justified, including measurement error reduction factors, and success and failure rates. Pros and cons of some widely used measures are explained. In particular, the merits of a measure called average Euclidean error (AEE) over the widely used RMS error is presented and it is advocated that RMS error should be replaced by the AEE in many cases.