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Robust Indoor Localization via Conformal Methods and Variational Bayesian Adaptive Filtering

Zhiyi Zhou, Dongzhuo Liu, Songtao Guo, Yuanyuan Yang

TL;DR

Indoor localization under realistic indoor noise is challenging due to non-Gaussian disturbances and outliers. The authors propose a hierarchical framework that combines Variational Bayesian Adaptive Filtering (VB-UKF) for real-time noise learning, a Huber M-estimation layer for mild outliers, and Conformal Outlier Detection with sliding-window calibration for statistical guarantees. Key contributions include a VB-UKF that jointly estimates state and noise covariance via the ELBO objective, a dual-layer outlier handling mechanism with theoretical guarantees, and empirical results showing fingerprint matching accuracy improving from 81.25% to 93.75% and positioning error shrinking from 0.62–6.87 m to 0.03–0.35 m, even under non-Gaussian noise. The approach provides robust, distribution-free uncertainty quantification and real-time outlier rejection, enabling reliable indoor localization for IoT applications in dynamic environments.

Abstract

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.

Robust Indoor Localization via Conformal Methods and Variational Bayesian Adaptive Filtering

TL;DR

Indoor localization under realistic indoor noise is challenging due to non-Gaussian disturbances and outliers. The authors propose a hierarchical framework that combines Variational Bayesian Adaptive Filtering (VB-UKF) for real-time noise learning, a Huber M-estimation layer for mild outliers, and Conformal Outlier Detection with sliding-window calibration for statistical guarantees. Key contributions include a VB-UKF that jointly estimates state and noise covariance via the ELBO objective, a dual-layer outlier handling mechanism with theoretical guarantees, and empirical results showing fingerprint matching accuracy improving from 81.25% to 93.75% and positioning error shrinking from 0.62–6.87 m to 0.03–0.35 m, even under non-Gaussian noise. The approach provides robust, distribution-free uncertainty quantification and real-time outlier rejection, enabling reliable indoor localization for IoT applications in dynamic environments.

Abstract

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.
Paper Structure (20 sections, 3 theorems, 40 equations, 8 figures, 1 table, 2 algorithms)

This paper contains 20 sections, 3 theorems, 40 equations, 8 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Indoor Localization Technologies
  4. Adaptive and Robust Filtering
  5. Uncertainty Quantification and Outlier Detection
  6. System Design
  7. Geomagnetic characteristics and data preprocessing
  8. Variational Bayesian Adaptive Filtering Framework
  9. Hierarchical Outlier Handling Mechanism
  10. Huber Robust Update
  11. Conformal Outlier Detection
  12. Problem Formulation
  13. Conformal Prediction Framework
  14. Extension to Filtering Framework
  15. Outlier Handling Mechanism
  16. ...and 5 more sections

Key Result

Theorem 1

Given the Huber-modified posterior covariance matrix: where: Then $P_{k|k}$ remains positive semi-definite, i.e., $P_{k|k} \succeq 0$.

Figures (8)

  • Figure 1: Geomagnetic strength characteristics.
  • Figure 2: Conformal outlier detection results with $\alpha=0.05$.
  • Figure 3: Comparison of measurements with different noise.
  • Figure 4: The simulation results of VB-based AUKF filters for the four different types of measurement noise. (a) Case a. (b) Case b. (c) Case c. (d) Case d.
  • Figure 5: The simulation results of different filters for the four different types of measurement noise. (a) Case a. (b) Case b. (c) Case c. (d) Case d.
  • ...and 3 more figures

Theorems & Definitions (5)

  • Theorem 1: Huber-Weighted Posterior Covariance
  • Theorem 2: Time-Varying Coverage
  • proof
  • Theorem 3
  • proof