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

Technical Summary: Spatially-Adaptive Conformal Graph Transformer for Indoor Localization

Problem Statement
Indoor localization is essential for smart environment services such as navigation and asset tracking, yet it remains challenging due to the obstruction of Global Positioning System (GPS) signals. While Wi-Fi Received Signal Strength Indicator (RSSI) offers a cost-effective alternative to Channel State Information (CSI), traditional RSSI-based methods like multilateration and fingerprinting struggle with signal attenuation, multipath effects, and dynamic environmental fluctuations. Furthermore, existing deep learning approaches often treat signal data as flat vectors, ignoring the underlying graph structure of the wireless network. Crucially, most current models lack a rigorous framework for quantifying prediction uncertainty, a requirement for safety-critical real-world deployments. Existing uncertainty estimation techniques, such as Monte Carlo dropout, often lack formal statistical guarantees, and Conformal Prediction (CP) methods typically apply global uncertainty margins that fail to account for the spatial heterogeneity of indoor environments (e.g., varying signal behaviors in open areas versus complex hallways).

Methodology: The SAC-GT Framework
The authors propose the Spatially-Adaptive Conformal Graph Transformer (SAC-GT), a unified framework designed to provide both high-precision point localization and statistically valid, region-specific confidence regions. The framework operates in three stages:

1. Graph Transformer (GT) Model:
   The core localization engine models the environment as a graph where nodes represent a mobile user and $m$ Wi-Fi Access Points (APs). The graph includes two link types:

   • Physical links: Dynamic connections between the user and detectable APs, weighted by RSSI values.
   • Logical links: Static connections between APs in close physical proximity, encoding the spatial topology of the infrastructure.
     The model employs stacked Graph Transformer layers using the TransformerConv operator with multi-head attention. This allows the model to aggregate features from immediate neighbors and neighbors-of-neighbors, learning a direct end-to-end mapping from the graph structure to precise 2D coordinates $(\hat{x}, \hat{y})$. The model is trained to minimize Mean Absolute Error (MAE).

2. Spatially-Adaptive Conformal Prediction (SACP):
   To address the lack of uncertainty quantification, the authors introduce SACP, a wrapper applied to the GT model. Unlike global CP methods, SACP partitions the indoor environment into $k$ distinct geographical regions using K-Means clustering on ground truth coordinates.

   • A calibration set is used to compute nonconformity scores (Euclidean distance between predicted and true locations) for each sample.
   • For each region, the scores are sorted, and a unique prediction radius ($r_k$) is calculated to satisfy a desired confidence level ($1-\alpha$).
   • This results in a set of adaptive radii, where complex regions receive larger uncertainty margins and simpler regions receive tighter ones.

3. Inference Stage:
   For a new test sample, the GT model generates a point prediction. The prediction is assigned to a specific geographical region via the trained K-Means model. The pre-calibrated radius for that region is applied to generate a circular confidence region centered at the predicted location, guaranteeing that the true location falls within the circle with probability $1-\alpha$.

Key Contributions

• Robust GT Model: A graph-based architecture that leverages fixed AP spatial locations and dynamic RSSI signals to learn direct mappings to 2D coordinates, capturing network topology better than flat-vector deep learning models.
• SACP Framework: A novel method that extends Conformal Prediction to be spatially adaptive. It partitions the environment and calibrates unique, statistically valid confidence radii for each zone, providing granular uncertainty estimates tailored to local signal conditions.
• Empirical Validation: Extensive evaluation on the SODIndoorLoc dataset, demonstrating state-of-the-art performance in both accuracy and reliability.

Experimental Results
The framework was evaluated on the SODIndoorLoc dataset (HCXY building), comprising 56 APs and over 11,000 training samples.

• Accuracy: SAC-GT achieved a Median Error of 1.37 m and an MAE of 1.76 m. This represents a significant improvement over the best baseline Graph Convolutional Network (GCN), which had a median error of 2.05 m, and traditional methods like Random Forest (3.20 m MAE).
• Robustness: The 95th percentile error for SAC-GT was 4.40 m, nearly half that of the GCN (8.03 m) and Random Forest (8.29 m), indicating superior handling of outliers.
• Adaptive Reliability: The SACP framework successfully calibrated distinct radii for five regions, ranging from 1.70 m (low error zones) to 3.78 m (high ambiguity zones). The framework achieved an overall test coverage of 84.8% against a target confidence level of 90%, confirming its statistical validity and spatial adaptability.
• Parameter Sensitivity: Experiments showed that a signal strength threshold ($\tau$) of -75 dBm provided the optimal trade-off between feature richness and noise, while varying the significance level ($\alpha$) demonstrated that the framework maintains clear distinctions between easy and challenging regions across different confidence requirements.

Significance and Claims
The paper claims that SAC-GT addresses a critical gap in indoor localization by moving beyond point predictions to provide reliable, spatially adaptive confidence regions. The authors emphasize that while previous graph-based models offered improved accuracy, they lacked formal uncertainty quantification. Conversely, existing uncertainty methods often applied a single global margin, ignoring the reality that different indoor regions exhibit different signal behaviors. By integrating a Graph Transformer with a region-aware Conformal Prediction mechanism, SAC-GT delivers a solution that is not only precise but also trustworthy for real-world deployment, offering statistically valid guarantees tailored to specific environmental conditions. The authors modestly note a current limitation: the framework does not yet provide strict conditional coverage guarantees per region, a focus for future work.