State estimations and noise identifications with intermittent corrupted observations via Bayesian variational inference

2026-04-03

AI Summary

This work addresses the challenging problem of state estimation in distributed sensor networks where packet losses, corrupted observations, and unknown noise covariances coexist. To tackle this issue, the paper proposes a Variational Bayesian Adaptive Kalman Filter (VB-AKF) that, for the first time, jointly models the system state, noise statistics, and network reliability within a unified framework. The method introduces a dual Bernoulli masking mechanism to explicitly distinguish between communication outages and data corruption, and leverages concurrent multi-source observations to enhance parameter identifiability. Both theoretical analysis and experimental results demonstrate that the proposed approach achieves asymptotic convergence to the Cramér–Rao lower bound in both state estimation and noise parameter identification, with performance approaching optimality as the number of sensors increases.

Abstract

This paper focuses on the state estimation problem in distributed sensor networks, where intermittent packet dropouts, corrupted observations, and unknown noise covariances coexist. To tackle this challenge, we formulate the joint estimation of system states, noise parameters, and network reliability as a Bayesian variational inference problem, and propose a novel variational Bayesian adaptive Kalman filter (VB-AKF) to approximate the joint posterior probability densities of the latent parameters. Unlike existing AKF that separately handle missing data and measurement outliers, the proposed VB-AKF adopts a dual-mask generative model with two independent Bernoulli random variables, explicitly characterizing both observable communication losses and latent data authenticity. Additionally, the VB-AKF integrates multiple concurrent multiple observations into the adaptive filtering framework, which significantly enhances statistical identifiability. Comprehensive numerical experiments verify the effectiveness and asymptotic optimality of the proposed method, showing that both parameter identification and state estimation asymptotically converge to the theoretical optimal lower bound with the increase in the number of sensors.

Problem

• state estimation
• intermittent observations
• corrupted data
• noise identification
• distributed sensor networks

Innovation

• variational Bayesian inference
• adaptive Kalman filter
• intermittent observations
• noise identification
• distributed sensor networks