Total Variational Indoor Localization Algorithm for Signal Manifolds in the Energy Domain

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.