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

A GNN-based regression framework for indoor localization with rigorous uncertainty guarantees. Accepted to IEEE ICC 2026.

This project introduces a reliable indoor localization framework that performs continuous position regression while providing formal, user-defined uncertainty guarantees, enabling safer deployment in real-world systems. Click for the full paper.

Problem

Most indoor localization models output a single point estimate of the user’s location ((x, y)) without quantifying how reliable that estimate is.
In practice, sensor noise, multipath effects, and environmental ambiguity can cause large localization errors that are indistinguishable from confident predictions.

This lack of calibrated uncertainty is a major limitation for safety-critical applications such as robotics, navigation, and human–machine interaction.

Key Idea

We design an indoor localization system that performs precise coordinate regression while explicitly modeling uncertainty through adaptive confidence regions.

Our approach combines two core components:

  1. Graph Neural Networks (GNNs) for Indoor Modeling:
    The indoor environment is represented as a graph where nodes correspond to fixed infrastructure elements (e.g., WiFi access points) and the mobile user, while edges capture physical proximity, signal relationships, and network connectivity.
    This allows the model to reason jointly over sensor measurements and the structure of the indoor network.

  2. Conformal Prediction for Regression:
    We apply conformal prediction on top of the regression output to produce confidence regions around the predicted ((x, y)) location.
    These regions come with formal statistical guarantees, ensuring that the true location lies within the region with a user-specified confidence level (e.g., 95%).

Crucially, the confidence regions are adaptive: they remain tight in well-observed areas and expand automatically in regions with noisy or ambiguous signals to maintain the desired coverage guarantee.

Sensor measurements (e.g., WiFi, IMU) are processed by a Graph Neural Network that models the indoor network structure, including access points and their relationships to the mobile user. Conformal Prediction converts point estimates into adaptive confidence regions with rigorous coverage guarantees.

Technical Details

This framework was implemented with a focus on probabilistic regression, structured modeling, and uncertainty calibration:

  • Framework: PyTorch, PyTorch Geometric
  • Model: Graph Neural Networks for continuous ((x, y)) regression
  • Graph construction: Nodes represent access points and the mobile user; edges encode spatial proximity and signal relationships
  • Uncertainty modeling: Conformal Prediction applied to regression outputs (distribution-free, coverage-guaranteed)
  • Calibration strategy: Data-driven residual modeling with adaptive region sizing
  • Clustering: KMeans used for structural or calibration-related preprocessing
  • Data processing: NumPy and Pandas for large-scale sensor and localization datasets
  • Evaluation: Empirical coverage, localization error, and region adaptivity analysis

The design explicitly separates representation learning from uncertainty calibration, allowing the confidence mechanism to remain statistically valid even under distribution shifts.

Results and Behavior

The model learns spatially varying uncertainty across the indoor environment.
Regions with strong and consistent signal geometry yield compact confidence regions, while ambiguous areas produce larger regions that preserve the user-defined confidence level.

Localization error map illustrating region-dependent uncertainty. Areas with lower error correspond to tighter confidence regions, while ambiguous regions exhibit larger uncertainty, which is explicitly captured by the conformal prediction mechanism.

This framework provides a principled and practical solution for reliable indoor localization, enabling downstream systems to reason explicitly about positional uncertainty.
A full technical analysis and experimental evaluation have been submitted for publication.

References