Statistical modeling for the mitigation of GPS multipath delays from day-to-day range measurements

Based on a least-squares model for double-difference GPS pseudoranges and carrier-phases, measurement residuals expressed in time series during an observation session are positively correlated between one sidereal day and the preceding days. As a result of the satellite’s period, the phenomenon, which takes place at a user receiving site, is attributed to multipath interference. Examples from a weekly measurement dataset of control baselines are shown, where the known end-point coordinates also serve as a benchmark for assessing positioning accuracy. The system of error equations for mixed-model adjustment is divided into two subsystems. One set of the error equations is related to the real range measurements, while the other involves the pseudo-observation with an empirical sample variance. According to the existing correlation between day-to-day residual estimates, a multipath-mitigating algorithm is proven to improve the accuracy of the GPS height determination by at least 40%. It is also found that the algorithm depends on a variance-component estimator that adaptively scales an error covariance matrix for both the real range and empirical delay measurements.