A Nonlinear Filtering Approach for Robust Multi-GNSS RTK Positioning in Presence of Multipath and Ionospheric Delays

In this paper, we develop a new approach of precise positioning using three carrier phase multi-Global Navigation Satellite System (GNSS) measurements in presence of multipath and ionospheric delays. We propose a new nonlinear filter to estimate the user position as well as all the unknown parameters including the integer ambiguities and the ionospheric errors. First, we use a kernel representation of the conditional density and apply a local linearization which yields a Kalman-like correction enhancing the particle filter correction. This new particle Kalman filter approach, is designed to be efficient for the non-Gaussian state and nonlinear measurements model, reduces the number of needed particles, and reduces the risk of divergence. The proposed procedure for multifrequency ambiguity resolution is based on four steps: 1) at each epoch, we compute the float solution adaptively to the dynamic environment by minimizing the noise level and estimating the ionospheric errors using the proposed robust Bayesian particle Kalman filter (RobPKF); 2) we introduce a new carrier phase multipath indicator and use it to derive a related constraint to reject integers candidates that are affected by multipath errors; 3) we apply the LAMBDA method to search the integer ambiguities; and finally 4) validate the fixed solution using a statistical test. We show in this work that the efficient integration of multifrequency/multisystem carriers provides more redundancy in the measurements and better observability for multipath and ionospheric errors estimation for long-baseline RTK positioning. A major advantage of this method is that it is independent of frequencies choice and therefore can be applied for any multi-GNSS measurements (e.g., Global Positioning System (GPS), Galileo, and their combination). Real-time and postprocessing test results show the effectiveness of the developed overall real-time kinematic (RTK) software.