Robust Indoor Localization via Conformal Methods and Variational Bayesian Adaptive Filtering

Indoor localization is critical for IoT applications, yet challenges such as non-Gaussian noise, environmental interference, and measurement outliers hinder the robustness of traditional methods. Existing approaches, including Kalman filtering and its variants, often rely on Gaussian assumptions or static thresholds, limiting adaptability in dynamic environments. This paper proposes a hierarchical robust framework integrating Variational Bayesian (VB) parameter learning, Huber M-estimation, and Conformal Outlier Detection (COD) to address these limitations. First, VB inference jointly estimates state and noise parameters, adapting to time-varying uncertainties. Second, Huber-based robust filtering suppresses mild outliers while preserving Gaussian efficiency. Third, COD provides statistical guarantees for outlier detection via dynamically calibrated thresholds, ensuring a user-controlled false alarm rate. Theoretically, we prove the Semi-positive Definiteness of Huber-based Kalman filtering covariance and the coverage of sliding window conformal prediction. Experiments on geomagnetic fingerprint datasets demonstrate significant improvements: fingerprint matching accuracy increases from 81.25% to 93.75%, and positioning errors decrease from 0.62-6.87 m to 0.03-0.35 m. Comparative studies further validate the framework's robustness, showing consistent performance gains under non-Gaussian noise and outlier conditions.