Three-dimensional mapping-aided (3DMA) Global Navigation Satellite System (GNSS) positioning improves the positioning in urban canyons for non-precision GNSS receivers. However, the 3DMA GNSS algorithms often produce a multimodal position solution, and simply taking the average of these modes reduces accuracy. A further problem, named ‘solution shifting’, is the effect of large numbers of low-scoring candidates shifting the overall position solution away from high-scoring regions. This study uses a clustering method to separate the different modes and exclude low-scoring regions from the position solution. Factor graph optimisation (FGO) is then used to integrate clustered 3DMA GNSS position and GNSS Doppler measurements or estimated velocity over multiple epochs. Positioning performance is assessed using data collected in London. The results show that the clustering method can successfully mitigate the multimodal effect, and integrating the FGO can mitigate the occurrence of multimodality and solution shifting. Static experiments in London achieve an RMSE of approximately 10 m for FGO 3DMA GNSS with clustering and 11 m without clustering.

Global navigation satellite system (GNSS) positioning in dense urban areas remains a challenge due to the signal reflection by buildings, namely multipath and non-line-of-sight (NLOS) reception. These effects degrade the performance of low-cost GNSS receivers such as in those smartphones. An effective three-dimensional (3D) mapping aided GNSS positioning method is proposed to correct the NLOS error. Instead of applying ray-tracing simulation, the signal reflection points are detected based on a skyplot with the surrounding building boundaries. The measurements of the direct and reflected signals can thus be simulated and further used to determine the user's position based on the measurement likelihood between real measurements. Verified with real experiments, the proposed algorithm is able to reduce the computational load greatly while maintaining a positioning accuracy within 10 metres of error in dense urban environments, compared with the conventional method of ray-tracing based NLOS corrected positioning.