A Fast and Efficient Residual Learning Framework Driven by Approximate Nearest Neighbor Search for Large-Scale Fingerprint-Based Visible Light Positioning

Localization based on received signal strength using the k-Nearest Neighbor method is quite common in indoor localization systems. However, as the fingerprint dataset grows, finding the nearest neighbors becomes time-consuming. In this study, we use Approximate Nearest Neighbor (ApNN) methods to accelerate nearest-neighbor search in RSS-based localization. We further propose a residual learning framework driven by ApNN search, where ApNN provides coarse position estimates and the residual model compensates for the nonlinear relationship between RSS measurements and spatial coordinates. Simulation results show that, compared to the Brute k-Nearest Neighbor method, ApNN algorithms significantly reduce computation time. KD-Tree is the fastest algorithm, with an improvement of approximately 96% compared to kNN and WkNN. Other methods such as HNSW and Ball-Tree also achieved high performance with improvements of around 93–94%, while LSH improved by approximately 84.8%. Regarding positioning error, KD-Tree achieved the best positioning error after applying residual learning, with the highest RMSE reduction of approximately 22.5%. These results demonstrate that the proposed ApNN-based residual learning framework is an effective solution for large-scale received signal strength positioning systems.