A comparison of several nonlinear filters for re-entry vehicle tracking

Abstract

This paper compares the performance of several non-linear filters for the real-time estimation of the trajectory of a re-entry vehicle from its radar observations. In particular, it examines the effect of using two different coordinate systems on the relative accuracy of an Extended Kalman Filter. Other filters considered are Iterative-Sequential Filters, Single-Stage Iteration Filters and Second Order Filters. It is shown that a Range-Direction-Cosine Extended Kalman filter which uses the measurement coordinate system has less bias and less RMS error than a Cartesian Extended Kalman Filter which uses the Cartesian coordinate system. This is due to the fact that the observations are linear in the Range-Direction-Cosine coordinate system, but nonlinear in the Cartesian coordinate system. It is further shown that the performance of the Cartesian Iterative-Sequential Filter which successively relinearizes the observations around their latest estimates approaches that of a Range-Direction-Cosine Extended Kalman Filter. The use of a single-stage iteration to reduce the dynamic nonlinearity improves the accuracy of both the Extended Kalman filters, but the improvement over the Range-Direction-Cosine Extended Kalman Filter is very small indicating that the dynamic nonlinearity is less significant than the measurement nonlinearity in Re-entry Vehicle Tracking under the assumed data rates and measurement accuracies. The comparison amongst the nonlinear filters is carried out using ten sets of observations on two trajectories based on actual flight test data. The numerical results demonstrate that for RV tracking at normal data rates and normal measurement accuracies, the Range-Direction-Cosine Extended Kalman Filter performs better than other non-linear filters in terms of the trade-off between estimation accuracy, computation time and the radar energy.