A comparison of several nonlinear filters for reentry vehicle tracking

This paper compares the performance of several non-linear filters for the real-time estimation of the trajectory of a reentry 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 that uses the measurement coordinate system has less bias and less rms error than a Cartesian extended Kalman filter that 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 that successively relinearizes the observations around their latest estimates and that of a range-direction-cosine extended Kalman filter are equivalent to first order. The use of a single-stage iteration to reduce the dynamic nonlinearity improves the accuracy of all the filters, but the improvement is very small, indicating that the dynamic nonlinearity is less significant than the measurement nonlinearity in reentry 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 typical trajectories. The performance of the filters is judged by their capability to eliminate the initial bias in the position and velocity estimates.