Enhanced Robust State Estimation via Spatio-Temporal Constraint EM Under Adverse Measurement Conditions

Abstract

This study proposes an enhanced robust filtering algorithm based on spatio-temporal constraint expectation maximization to address the degradation of state estimation in multi-sensor localization systems (MSLS) caused by adverse measurement conditions, primarily incomplete data and heavy-tailed non-Gaussian noise. First, an incomplete measurement model grounded in a dual-state Markov process is constructed, and the approximate posterior Cramér-Rao lower bound is derived to quantify the impact of the Markovian arrival probability and the Student’s t tail parameter on the available information. Second, to overcome the limitations of the existing variational Bayesian robust Student’s t Kalman filter (VB-RSTKF) relying on nominal process noise, an approximate moment-matching method is proposed for the adaptive closed-loop posterior estimation of noise covariance matrices. Furthermore, to fully utilize implicit spatio-temporal information during measurement losses, a Q-function is constructed based on temporal information and spatial structural constraints. The expectation maximization (EM) algorithm is then employed to correct the prior inverse scale matrices. Through the alternate iteration of VB updates and EM corrections, the proposed method significantly enhances the robustness and accuracy of MSLS. Theoretical analysis and three-dimensional positioning experiments demonstrate the superiority of the proposed framework. Note to Practitioners—This work is motivated by the challenges faced by multi-sensor localization systems in complex real-world environments, such as autonomous navigation, uncrewed vehicles, and target tracking. In practical applications, sensor measurements are often unreliable due to signal blockage, communication constraints, or environmental interference, leading to incomplete data and unpredictable, severe noise (often called outliers). Existing filtering methods typically struggle to handle both missing data and extreme noise simultaneously, and they often fail to sufficiently exploit the temporal and spatial structural information. To overcome these issues, we propose a robust state estimation algorithm that adaptively learns noise characteristics on the fly, reducing the reliance on accurate prior system knowledge. Furthermore, when some sensor data is missing, the algorithm leverages the temporal information and spatial structural constraints of the sensor network to infer the missing information, thereby maintaining high localization accuracy. The proposed method significantly enhances system robustness under adverse conditions, the additional computational overhead introduced by the iterative process is acceptable and does not compromise real-time performance. Furthermore, the algorithm avoids the need for extensive parameter fine-tuning, making it highly suitable for direct deployment in practical systems. In future applications, this approach could be extended to accommodate heterogeneous sensor networks (e.g., fusing cameras, radars, and lidars) and further validated using real-world hardware platforms to fully realize its potential in industrial deployment.