Variational Bayesian Joint Measurement Anomaly and Noise Inference Filter for Robust Cellular/MEMS-INS Localization

In Global Navigation Satellite Systems (GNSS)-denied urban environments, cellular/microelectromechanical system-inertial navigation system (MEMS-INS) integrated positioning provides a promising solution for continuous navigation. However, in such environments, signal propagation is severely affected by multipath, blockage, and environmental dynamics, leading to heterogeneous measurement uncertainties, including time-varying noise, impulsive outliers, and persistent NLOS biases, which are difficult to handle within conventional estimation frameworks. To address these challenges, this paper proposes a Variational Bayesian Joint Measurement Anomaly and Noise Inference Filter (VB-JMANIF) for robust positioning. The proposed method explicitly models NLOS-induced biases, impulsive outliers, and time-varying measurement noise, and jointly integrates anomaly classification, bias estimation, noise adaptation, and state update within an error-state cubature Kalman filter (CKF) framework. Simulation results demonstrate that VB-JMANIF consistently outperforms the conventional CKF and several state-of-the-art robust and noise-adaptive methods in terms of positioning accuracy, estimation stability, and robustness. Field experiments using real cellular signals further validate the effectiveness of the proposed approach, achieving horizontal positioning Root Mean Square Error (RMSE) values of 4.7 m and 6.1 m under moderate and severely degraded urban measurement conditions, respectively, thereby demonstrating its practical applicability in real-world environments.