# Reconstructing Spatial Localization Error Maps via Physics-Informed Tensor Completion for Passive Sensor Systems

## TL;DR

This paper introduces a new method to map localization errors in sensor systems using physics-informed tensor completion, improving accuracy over existing techniques.

## Contribution

A novel physics-informed tensor completion framework for reconstructing high-fidelity localization error maps from sparse data.

## Key findings

- The proposed framework improves localization error map accuracy by at least 27.96% over existing methods.
- Physics-informed regularization enhances robustness in recovering error maps from incomplete data.

## Abstract

Accurate mapping of localization error distribution is essential for assessing passive sensor systems and guiding sensor placement. However, conventional analytical methods like the Geometrical Dilution of Precision (GDOP) rely on idealized error models, failing to capture the complex, heterogeneous error distributions typical of real-world environments. To overcome this challenge, we propose a novel data-driven framework that reconstructs high-fidelity localization error maps from sparse observations in TDOA-based systems. Specifically, we model the error distribution as a tensor and formulate the reconstruction as a tensor completion problem. A key innovation is our physics-informed regularization strategy, which incorporates prior knowledge from the analytical error covariance matrix into the tensor factorization process. This allows for robust recovery of the complete error map even from highly incomplete data. Experiments on a real-world dataset validate the superiority of our approach, showing an accuracy improvement of at least 27.96% over state-of-the-art methods.