Fig. 1 Simulated GPS three-frequency (red: L1, blue: L2, green: L5) multipath error in PRN02 in the LCPC dataset (relative permittivity =3.9) Phase multipath is one of the most crucial error sources in centimetre or millimetre level GNSS high precision positioning. Short-delay multipath is still especially difficult to detect or mitigate by the state-of-the-art hardwarebased techniques. Therefore, processing algorithm-based multipath mitigation methods are crucial for the further improvement of positioning accuracy, either integrated with other techniques or in a stand-alone mode. The effectiveness of some of these is, however, limited by the degrees of freedom in currently available solutions, i.e. insufficient satellites and signals. This problem is similar to the un-robustness and unreliability of some outlier detection techniques used in RAIM and other integrity algorithms in the current GPS system.