Motivated by the performance degradation of High-degree Cubature Kalman Filtering (HCKF) in coping with randomly delayed measurements in non-Gaussian system, a novel robust filtering named as Randomly Delayed High-degree Cubature Huber-based Filtering (RD-HCHF) is proposed in this paper. At first, the system model is re-written by the Bernoulli random variables to describe the randomly delayed measurements. Then, the Randomly Delayed HCKF (RD-HCKF) is derived based on the rewritten system model and 5th-degree spherical-radial cubature (SRC) rule. In order to enhance the robustness of the filter in glint noise case, the measurement update of RD-HCKF is modified by the Huber technique, which is essentially an M-estimator. Therefore, the proposed RD-HCHF is not only robust to the randomly delayed measurements, but also robust to the glint noise. In addition, the RD-HCHF is applied to the ballistic target tracking in boost phase, and the Gravity-Turn (GT) model is taken as the target model. Finally, the simulation is conducted and the tracking performance of RD-HCHF is compared with that of HCKF, RD-HCKF and High-degree Cubature Huber-based Filtering (HCHF). The results clearly confirm the superiority of the RD-HCHF.
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