Robust trajectory estimation in ballistic phase using out-of-sequence high-degree cubature huber-based filtering

A novel Out-of-Sequence High-degree Cubature Huber-based Filtering (OOS-HCHF) algorithm is presented and utilized to estimate the trajectory of a ballistic target in the ballistic phase. This novel algorithm makes use of the 5th-degree cubature rule to numerically compute Gaussian-weighted integrals, which are propagated through a nonlinear state equation, and then a weighted mean and covariance are taken. As the radar measurements are accentuated with corrupting glint noise which is essentially non-Gaussian and arriving out-of-sequence, usually caused by communication and processing latency, the novel filtering is carefully designed with the consideration of these factors. First, the solution to the OOSM problem is derived in combination with the 5th-degree cubature rule in time update equations. Second, the Huber technique, which is a combined minimum l₁ and l₂-norm estimation technique, is used to design the measurement update equations. Therefore, the proposed OOS-HCHF could exhibit robustness with respect to deviations from the commonly assumed Gaussian error probability, for which conventional cubature Kalman filtering (CKF) exhibits a severe degradation in estimation accuracy. Furthermore, the out-of-sequence measurements could be incorporated optimally. Finally, in contrast to extended Kalman filtering (EKF), more accurate estimation and faster convergence could be achieved by OOS-HCHF from inaccurate initial conditions. Simulation results are shown to compare the performance of OOS-HCHF with CKF and EKF.