Sigma point Kalman filter for bearing only tracking

Abstract

Relative merits of sigma point Kalman filters (SPKF), also known as unscented Kalman filters (UKF) vis-à-vis extended Kalman filter (EKF) and iterated extended Kalman filter (IEKF) for a bearing-only target-tracking problem using rms error and robustness with respect to outlier initial conditions are explored. After establishing that the rms error performance obtainable by SPKF/UKF and IEKF for this fairly severe non-linear system is similar to those obtainable from other competing techniques, the relative robustness of IEKF, SPKF/UKF and EKF with respect to large initial condition uncertainty (a common occurrence for this class of tracking problems) is investigated. Using several versions of SPKF/UKF, it is shown that SPKF is about 20 times more robust compared to EKF. It is illustrated that the additional design freedom available with a scaled version of SPKF/UKF may be utilised for further improvement of the robustness. The main contribution of this paper is quantification of relative robustness of these non-linear filters. A simplified criterion is suggested and used for quantifying track loss and the relative occurrence of such track loss in batch Monte Carlo simulation has been used as a measure of (lack of) robustness. As the SPKF/UKF does not introduce substantial computational burden, when compared to EKF, it is argued that SPKF/UKF algorithm may become a strong candidate for on-board implementation.