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

TL;DR

This paper introduces a Bayesian variational inference approach with a novel Kalman filter for improved state estimation and noise identification in sensor networks with intermittent and corrupted data.

Contribution

It proposes a dual-mask variational Bayesian Kalman filter that explicitly models communication losses and data authenticity, enhancing robustness and identifiability.

Findings

The method effectively estimates states and noise parameters in sensor networks.

It achieves asymptotic convergence to the theoretical optimal lower bound.

Numerical experiments confirm the effectiveness and optimality of the approach.

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.