Robust Trajectory Estimation in Ballistic Phase using Out-of-Sequence High-degree Cubature Huber-based Filtering

Abstract

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 l 1 and l 2-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.

Robust filtering with randomly delayed measurements and its application to ballistic target tracking in boost phase

“…where x ¯ denotes the mean of x which is a l -dimensional vector. The cubature points w i and its associated weights ξ i have been given by Wang et al (2017).…”

“…Measurement Noise Update. According to Wang et al (2017), the measurement equation can be approximated by…”

Target Tracking in Boost Stage with Quantized Measurements of Space-based Infrared Cameras

“…Among various estimation algorithms, the extended Kalman filtering (EKF), which is based on first-order linearization of the non-linear state model and measurement model, is widely used. 16) Many studies have applied the cubature Kalman filter to target tracking problems [17][18][19] in which the spherical-radial cubature rule is used to compute statistics of a nonlinearly transformed Gaussian random variable.…”

Genetic Resampling Particle Filter with Randomly Delayed Measurements and Its Application to Line-of-Sight Rate Estimation

“…Therefore, many studies have been conducted, and the most common ones were proposed based on backward prediction and forward prediction. [14][15][16] These filters perform well coping with delayed measurements, but the latency time is indispensable. Inspired by the development of Gaussian filters coping with randomly delayed measurements, [17][18][19] the paper reformulates the weight update equation based on the modified measurement model and then the RD-GRPF is obtained.…”