Abstract
To address the topological mismatch between signal space and physical space caused by uneven signal feature distribution in indoor non-line-of-sight and complex topological environments, this paper proposes an indoor positioning algorithm based on Energy-domain Fingerprint Manifold Graph Total Variation (EFM-GTV). To mitigate neighborhood distortion caused by uneven high-dimensional signal feature distribution, a UMAP manifold topology graph construction method based on fuzzy simplicial sets is designed to establish a graph basis consistent with physical space topology. To reduce false matching risks in global search, a physical topology pruning strategy combining Jaccard similarity is proposed, effectively eliminating pseudo-connections. Building upon this foundation, we introduced an optimization model based on graph total variation, reformulating the positioning problem as a graph signal recovery task. This approach effectively overcomes signal fluctuation interference in complex topologies like U-shaped corridors, achieving robust position estimation. Experiments demonstrate that this algorithm effectively leverages manifold structure constraints to correct NLOS errors. On real-world field test datasets, compared to traditional weighted algorithms, the average positioning accuracy improves to 1.4267 m, with maximum positioning error reduced by over 50%, achieving high-precision robust positioning.