GNSS pseudorange smoothing: Linear vs non-linear filtering paradigm

Improving the accuracy of position and velocity estimates from single frequency Global Navigation Satellite System (GNSS) receivers is of paramount importance due to their wide spread role in new and emerging real time applications requiring higher levels of accuracy. Single frequency receiver has only two independent measurements: code delay and carrier phase measurements. Pseudorange estimates from code delay measurements are unambiguous but noisy while those from carrier phase measurements are precise but suffer from integer ambiguity problem. In order to obtain high accuracy without explicitly solving for integer ambiguities, Carrier-Smoothed-Code (CSC) methods are very effective. These methods rely on combining the precise but ambiguous carrier phase measurements with noisy but unambiguous code phase measurements to get a smoothed and unambiguous estimate of the pseudorange for each satellite. Several CSC methods have appeared in the last few decades, almost all of them are based on Hatch filter which linearly combines code delay and carrier phase measurements. The main drawback of standard Hatch filter and its variants is the assumption that the receiver is either static or it is slowly moving and there are no cycle-slips. Other than linear filtering solution, a non-linear filtering framework can also be devised for the CSC process. A general framework to analyze and compare the performance of linear and non-linear filtering approaches in the context of CSC techniques especially in the presence of cycle-slips is missing. The main goal of this paper is to provide a contribution to the aforementioned domain. It is shown that the Hatch filter problem can be formulated in terms of the Kalman filtering problem whose performance can be significantly improved after adequate tuning of process noise statistics. The effect of inaccuracies in estimating the measurement noise statistics on the final pseudorange estimates is also presented. A Gaussian sum non-linear filter is studied in detail whose performance is compared with CSC methods based on linear filtering, including the Kalman filter. Simulation results, supported by real GNSS data, are provided showing the trade-off between better noise mitigation, robustness against cycle-slips, convergence speed and computational complexity.