Ballistic Trajectory Estimation Using Polynomial Chaos Based Square Root Ensemble Filter

The ballistic trajectory estimation problem is challenging, mainly because the dynamic model and the angle-only measurement model are highly nonlinear. In this paper, we propose a polynomial chaos expansion based square root ensemble Kalman filter to solve the ballistic trajectory estimation problem. Between two consecutive measurements, polynomial chaos-based approach is used for uncertainty propagation. Upon a new measurement's arrival, a predicted ensemble generated from the predicted state is corrected through the ensemble square root technique and the obtained analysis ensemble is utilized to form the polynomial chaos representation of the target state. Simulation results show the proposed approach's superiority to previous popular nonlinear estimation methods such as the extended Kalman filter, the unscented Kalman filter, and the polynomial chaos-based ensemble filter with the first order linearization, in terms of the root mean square error (RMSE).