3D map-aided smartphone GNSS positioning using TDCP-constrained clustering and factor graph multi-observation fusion

Abstract High-density urban environments severely impair smartphone Global Navigation Satellite System (GNSS) positioning due to Non-Line-of-Sight (NLOS) signals and limited satellite visibility, leading to reduced accuracy and continuity. Three-Dimensional Map-aided (3DMA) GNSS methods partially solve the problems but still much rely on noisy pseudorange measurements, while the resolution of carrier-phase ambiguities remain challenging, limiting their robustness in complex urban areas. To overcome these challenges, this study introduces a novel Factor Graph Optimization (FGO) framework that tightly integrates 3D map constraints with multiple GNSS observations. First, a Shadow Matching (SDM) scoring strategy is proposed by incorporating Time-Differenced Carrier Phase (TDCP) constraints. Second, a map-matching probability approach is applied to identify a unique candidate road segment, thereby reducing solution ambiguity. Third, a Random Sample Consensus (RANSAC)-based region growing clustering algorithm is designed to manage multimodal high-score points and ensure unique clustering. Finally, a factor graph model is constructed that fuses pseudorange, Doppler, and TDCP observations with 3D map constraints, significantly enhancing positioning accuracy and stability. Field experiments in typical urban scenarios show that the proposed method outperforms existing SDM techniques such as road constraint and region-growing clustering, as well as advanced GNSS optimization frameworks, in terms of both positioning accuracy and trajectory continuity. Specifically, the proportion of horizontal positioning errors within 3 m and 5 m reached 76.7% and 93.1%, respectively, substantially exceeding those achieved by the advanced GNSS multi-source fusion framework (63.4% and 79.3%).