Nonlinear Tracking: The Approach Based on Extended Kalman-Like UFIR Filtering

摘要

Tracking of moving objects is often provided employing the first-order and sometimes the second-order extended Kalman filters. The problem we meet here is associated with the process noise covariance which cannot always be specified correctly and also with the model temporary uncertainties. In this lecture, we show that an efficient remedy against these problems is unbiased averaging associated with finite impulse response (FIR) filtering. For suboptimal nonlinear tracking in discrete-time state-space with additive white noise, we accordingly derive and discuss the first- and second-order extended Kalman-like unbiased FIR filters (EFIR1 and EFIR2, respectively). Unlike the extended Kalman filter (EKF), the EFIR1 one does not require noise covariances and initial errors. By virtue of this, it demonstrates better robustness against temporary uncertainties in real world. Only within a narrow region around an actual process noise covariance, the EFIR filter falls a bit short of EKF and it demonstrates better performance otherwise. We show that the optimal averaging interval for EFIR filters can be determined via measurement in a "learning" circle and then re-determined and updated whenever necessary. We also notice that the second-order approximation can improve the local performance, but it can also deteriorate it. Thus, there can be given no definitive recommendations about its use, at least for tracking problems.