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This paper presents a novel decentralized relative navigation algorithm. The relative motion equations are derived in the Earth-Centered-Inertial frame. The relative measurements contain not only the line of sight and range between the deputy and the chief, but also the ranges among different deputies. This helps to improve the redundancy and accuracy of the relative navigation for spacecraft formation flying. In decentralized estimation algorithm, it is necessary to transmit the global states in the formation to linearize the ranges among the deputies. A sigma-point method is used to account for the uncertainty in the estimated states of other spacecraft. The relative measurements are coupled with the relative motion equation in a novel decentralized filter to determine the relative position and velocity. Simulation shows that the proposed novel decentralized estimation algorithm provides better performance than the traditional iteration algorithm.

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Purpose The time delay would occurs when the measurements of multiple unmanned aerial vehicles (UAVs) are transmitted to the date processing center during cooperative target localization. This problem is often named as the out-of-sequence measurement (OOSM) problem. This paper aims to present a nonlinear filtering based on solving the Fokker–Planck equation to address the issue of OOSM. Design/methodology/approach According to the arrival time of measurement, the proposed nonlinear filtering can be divided into two parts. The non-delay measurement would be fused in the first part, in which the Fokker–Planck equation is utilized to propagate the conditional probability density function in the forward form. The time delay measurement is fused in the second part, in which the Fokker–Planck is used in the backward form approximately. The Bayes formula is applied in both parts during the measurement update. Findings Under the Bayesian filtering framework, this nonlinear filtering is not only suitable for the Gaussian noise assumption but also for the non-Gaussian noise assumption. The nonlinear filtering is applied to the cooperative target localization problem. Simulation results show that the proposed filtering algorithm is superior to the previous Y algorithm. Practical implications In this paper, the research shows that a better performance can be obtained by fusing multiple UAV measurements and treating time delay in measurement with the proposed algorithm. Originality/value In this paper, the OOSM problem is settled based on solving the Fokker–Planck equation. Generally, the Fokker–Planck equation can be used to predict the probability density forward in time. However, to associate the current state with the state related to OOSM, it would be used to propagate the probability density backward either.

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.