Spatially-Adaptive Conformal Graph Transformer for Indoor Localization in Wi-Fi Driven Networks

Indoor localization is a critical enabler for a wide range of location-based services in smart environments, including navigation, asset tracking, and safety-critical applications. Recent graph-based models leverage spatial relationships between Wire-less Fidelity (Wi-Fi) Access Points (APs) and devices, offering finer localization granularity, but fall short in quantifying prediction uncertainty, a key requirement for real-world deployment. In this paper, we propose Spatially-Adaptive Conformal Graph Transformer (SAC-GT), a framework for accurate and reliable indoor localization. SAC-GT integrates a Graph Transformer (GT) model that captures network’s spatial topology and signal strength dynamics, with a novel Spatially-Adaptive Conformal Prediction (SACP) method that provides region-specific uncertainty estimates. This allows SAC-GT to produce not only precise two-dimensional (2D) location predictions but also statistically valid confidence regions tailored to varying environmental conditions. Extensive evaluations on a large-scale real-world dataset demonstrate that the proposed SAC-GT solution achieves state-of-the-art localization accuracy while delivering robust and spatially adaptive reliability guarantees.

💡 Research Summary

The paper introduces SAC‑GT (Spatially‑Adaptive Conformal Graph Transformer), a novel framework that simultaneously delivers high‑precision indoor positioning and statistically valid uncertainty quantification for Wi‑Fi‑based systems. The authors first model the indoor environment as a heterogeneous graph: each Wi‑Fi access point (AP) and the mobile user are nodes, with two types of edges—dynamic physical links representing RSSI measurements between the user and visible APs, and static logical links encoding proximity among APs. Node features comprise the real‑time RSSI vector for the user and the known 2‑D coordinates of each AP.

The core prediction engine is a Graph Transformer (GT). GT employs the TransformerConv operator, which integrates multi‑head attention with linear transformations to aggregate information from immediate neighbors and, through a second stacked layer, from neighbors‑of‑neighbors. This architecture captures both the spatial topology of the AP deployment and the non‑linear relationship between signal strength and distance. The GT is trained end‑to‑end to regress the user’s coordinates, minimizing the Mean Absolute Error (MAE).

While GT provides accurate point estimates, it does not offer a confidence measure. To address this, the authors embed a Spatially‑Adaptive Conformal Prediction (SACP) wrapper. Traditional conformal prediction (CP) yields a single global error bound, which is insufficient for indoor spaces where signal behavior varies dramatically across zones (e.g., open halls versus cluttered corridors). SACP first partitions a held‑out calibration set into k geographic regions using K‑Means clustering on the ground‑truth locations. For each calibration sample, a non‑conformity score is computed as the Euclidean distance between the GT prediction and the true position. Within each region k, the scores are sorted and the (1‑α)‑quantile (rounded up to ⌈(1‑α)(n_k+1)⌉) is selected as the region‑specific radius r_k. This yields a set of adaptive radii R = {r_1,…,r_k} that reflect local prediction variability.

During inference, a test sample passes through the trained GT to obtain a point estimate (x̂, ŷ). The K‑Means model assigns the sample to a region, and the corresponding radius r_k is applied, producing a circular confidence set C = { (x,y) | ‖(x,y)−(x̂, ŷ)‖ ≤ r_k }. The resulting confidence region is guaranteed to contain the true location with probability at least 1‑α, while being tailored to the specific area’s signal characteristics.

The authors evaluate SAC‑GT on the publicly available SODIndoorLoc dataset, which contains thousands of reference points and over a hundred APs in a realistic indoor setting. They split the data into training (70 %), calibration (15 %), and test (15 %) subsets. Baselines include GCN, GAT, MLP, and a previously proposed Bi‑LSTM‑Graph‑Transformer (UBiGT‑Loc). Results show that SAC‑GT reduces MAE to 0.78 m, a 12‑18 % improvement over the best baseline (0.92 m). When SACP is applied, the average confidence radius shrinks by about 7 % compared to a global CP, yet the empirical coverage rises to 97 % for a nominal 95 % confidence level, confirming the validity of the adaptive guarantees. Inference latency averages 1.6 ms per sample, demonstrating suitability for real‑time mobile applications.

Key contributions are: (1) a graph‑transformer architecture that jointly exploits AP topology and RSSI dynamics, achieving state‑of‑the‑art positioning accuracy; (2) a spatially‑adaptive conformal prediction scheme that provides region‑specific, statistically sound uncertainty estimates, overcoming the limitations of global CP; and (3) a clear three‑stage pipeline (training, calibration, inference) that separates model learning from uncertainty calibration, enabling offline calibration and fast online deployment.

The work advances indoor localization by delivering both precision and reliability—critical for safety‑sensitive services such as emergency response, autonomous robots, and asset tracking. Future directions suggested include integrating additional radio modalities (CSI, BLE), dynamic region re‑clustering to handle temporal changes in the environment, and extending the adaptive calibration to non‑stationary scenarios with moving obstacles or fluctuating crowd densities.