Random-point-based filters: analysis and comparison in target tracking

This paper compares state estimation techniques for nonlinear stochastic dynamic systems, which are important for target tracking. Recently, several methods for nonlinear state estimation have appeared utilizing various random-point-based approximations for global filters (e.g., particle filter and ensemble Kalman filter) and local filters (e.g., Monte-Carlo Kalman filter and stochastic integration filters). A special emphasis is placed on derivations, algorithms, and commonalities of these filters. All filters described are put into a common framework, and it is proved that within a single iteration, they provide asymptotically equivalent results. Additionally, some deterministic-point-based filters (e.g., unscented Kalman filter, cubature Kalman filter, and quadrature Kalman filter) are shown to be special cases of a random-point-based filter. The paper demonstrates and compares the filters in three examples, a random variable transformation, re-entry vehicle tracking, and bearings-only tracking. The results show that the stochastic integration filter provides better accuracy than the Monte-Carlo Kalman filter and the ensemble Kalman filter with lower computational costs.