Improved weighting in particle filters applied to precise state estimation in GNSS

In the last decades, the increasing complexity of the fusion of proprioceptive and exteroceptive sensors with Global Navigation Satellite System (GNSS) has motivated the exploration of Artificial Intelligence related strategies for the implementation of the navigation filters. In order to meet the strict requirements of accuracy and precision for Intelligent Transportation Systems (ITS) and Robotics, Bayesian inference algorithms are at the basis of current Positioning, Navigation, and Timing (PNT). Some scientific and technical contributions resort to Sequential Importance Resampling (SIR) Particle Filters (PF) to overcome the theoretical weaknesses of the more popular and efficient Kalman Filters (KFs) when the application relies on non-linear measurements models and non-Gaussian measurements errors. However, due to its higher computational burden, SIR PF is generally discarded. This paper presents a methodology named Multiple Weighting (MW) that reduces the computational burden of PF by considering the mutual information provided by the input measurements about the unknown state. An assessment of the proposed scheme is shown through an application to standalone GNSS estimation as a baseline of more complex multi-sensors, integrated solutions. By relying on the a-priori knowledge of the relationship between states and measurements, a change in the conventional PF routine allows performing a more efficient sampling of the posterior distribution. Results show that the proposed strategy can achieve any desired accuracy with a considerable reduction in the number of particles. Given a fixed and reasonable available computational effort, the proposed scheme allows for an accuracy improvement of the state estimate in the range of 20–40%.