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

Peng Sun, Ruoyu Wang, Xue Luo

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.

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

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.

Paper Structure

This paper contains 18 sections, 28 equations, 6 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem setting-up and Preliminaries
  3. Problem setting-up
  4. Preliminary: Variational Inference (VI)
  5. Structured VI at time instant $k$
  6. Bayesian Mixture of Gaussians (BMG) and inference of clean rate
  7. Inferences of global parameters ($\rho_k$, $\beta_k$, $R_k$ and $Q_k$)
  8. Rates inference $\rho_k$ and $\beta_k$
  9. Observation covariance matrix $R_k$
  10. State covariance matrix $Q_k$
  11. Gated Kalman gain and state's fusion
  12. Iteration of variational inference (VI) and pseudo code
  13. Numerical experiments
  14. Asymptotic optimality
  15. Transient robustness
  16. ...and 3 more sections

Figures (6)

  • Figure B1: Generative model of the linear filtering problem \ref{['eq:state_hd']}-\ref{['eq:obs_hd']} with packet dropout and corrupted noises. Shaded nodes: observable variables; unshaded circles: latent parameters to be estimated; rectangles: hyper-parameters in priors.
  • Figure C1: Latent parameters dependency. Global parameters shared across all sensor nodes, while local parameters (subscript $i,k$) are different among individual sensors.
  • Figure D1: The RMSE of the state convergence comparison between the oracle KF and the proposed VB-AKF with different numbers of observation nodes $N$.
  • Figure D2: State estimation and noise variance inferences under non-stationary perturbations with $N=5$ sensor nodes. Top: State trajectory tracking; Middle: Inference of observation noise variance $R_k$; Bottom: Inference of process noise variance $Q_k$.
  • Figure D3: Performance of the proposed VB-AKF under severe data degradation (60% packet dropout and 60% data corruption). Top: Dropout rate inference; Second: Data clean rate identification; Third: Joint inference of process noise $Q_k$ and observation noise $R_k$; Bottom: State estimation via centralized sequential fusion.
  • ...and 1 more figures