Continuous modelling of global navigation satellite system multipath errors for sidereal filtering

Carrier-phase multipath effect is one of the major error sources in static global navigation satellite systems positioning applications. Sidereal filtering is an effective approach for mitigating multipath error, utilising the multipath error of the previous day to improve the positioning result of the next day. In this study two interpolation methods, namely cubic spline interpolation and piecewise linear interpolation, are used for continuous modelling of multipath error in sidereal filtering, which can further improve the performance of the filter. Sidereal filtering approach adopting the first-order derivative Tikhonov regularisation is applied in this work. Two issues, namely the different sampling intervals or the non-synchronisation between the data for modelling and the data to be mitigated, are solved by applying the continuous multipath models. Then the effects of two interpolation methods are compared and the feasibility of the proposed method is illustrated in the real data processing.