Hybrid global navigation satellite systems, differential navigation satellite systems and time of arrival cooperative positioning based on iterative finite difference particle filter

In this study, the authors develop a novel solution for hybrid global navigation satellite systems, differential navigation satellite systems and time of arrival cooperative positioning (CP) based on iterative finite difference particle filter (PF) in GNSS-terrestrial navigation and challenging environments. A variant of finite difference filters called divided difference filter (DDF) was used as an importance density for particle generation. Various proposal distributions have been proposed to improve the performance of PF, but practical situations have encouraged the researchers to design better candidate for proposal distributions in order to gain better performance especially for hybrid CP system. The author´s proposed method named hybrid cooperative particle-based DDF solves the problem of linearisation of non-linear functions that are based on Jacobian matrices which often cannot be applied in practical applications of non-linear estimation techniques. An iterative reweighted information filter based on the extended Kalman filter (KF) was integrated during the measurement update phase to smooth the output of the DDF used for particles update. Simulation results based on a realistic outdoor scenario show that the proposed solution outperforms some well-known state-of-the-art in hybrid CP systems, such as hybrid cooperative unscented KF in terms of accuracy and availability and provides good performance even in challenging conditions.