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

arXiv stat.ML / 4/6/2026

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Key Points

The paper addresses joint state estimation in distributed sensor networks under intermittent packet dropouts, corrupted observations, and unknown noise covariance.
It formulates estimation of system states, noise parameters, and network reliability as a Bayesian variational inference problem and introduces a variational Bayesian adaptive Kalman filter (VB-AKF).
VB-AKF improves over prior adaptive Kalman filter approaches by using a dual-mask generative model with two independent Bernoulli variables to model both communication loss and latent observation authenticity/outlier behavior.
By incorporating multiple concurrent measurements into the filtering process, the method improves statistical identifiability of the latent parameters.
Numerical experiments in the paper support effectiveness and asymptotic optimality, showing convergence of both parameter identification and state estimation toward a theoretical optimal lower bound 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.