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

Peng Sun; Ruoyu Wang; Xue Luo

stat.MLApr 3, 2026

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

Authors: Peng Sun, Ruoyu Wang, Xue Luo

Organizations: School of Mathematical Sciences, Beihang University, Beijing, P. R. China 102206. · School of Mathematical Sciences, Beihang University, Beijing, P. R. China 102206, and Key Laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, P. R. China 100191.

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.

Figures & tables

Panel of Figure 1 — Fig. 1: Generative model of the linear filtering problem ( 1 )-( 2 ) with packet dropout and corrupted noises. Shaded nodes: observable variables; unshaded circles: latent parameters to be estimated; rectangles: hyper-parameters in priors.

Panel of Figure 2 — Fig. 2: Latent parameters dependency. Global parameters shared across all sensor nodes, while local parameters (subscript $i,k$ ) are different among individual sensors.

	$\displaystyle\hat{x}_{k\|k-1}^{(j)}=$	$\displaystyle F_{k}\hat{x}_{k-1\|k-1},$
	$\displaystyle P_{k\|k-1}^{(j)}=$	$\displaystyle F_{k}P_{k-1\|k-1}F_{k}^{T}+(\mathbb{E}{Q_{k}}^{(j-1)})^{-1}.$

Algorithm 1 Our proposed VB-AKF

Fig. 3: The RMSE of the state convergence comparison between the oracle KF and the proposed VB-AKF with different numbers of observation nodes $N$ .

Panel of Figure 5 — Fig. 4: 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 $Q_{k}$ .

Panel of Figure 6 — Fig. 5: 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.

Panel of Figure 7 — Fig. 6: Sensitivity analysis and statistical identifiability of corruption rate inference. (a) Identifiability degradation under strong baseline observation noise. (b) Exponential error convergence beyond the anomaly intensity threshold. (c) Identifiability degradation under intense process noise variations.

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Apr 30, 2026J/K move · Enter open · S save

Neural Aided Kalman Filtering for UAV State Estimation in Degraded Sensing Environments

Akhil Gupta, Erhan Guven

Whiting School of Engineering EP Program, Johns Hopkins University, Baltimore, Maryland, USA

Bayesian Neural Networks Kalman Filtering Uncertainty Quantification Robot State Estimation

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Accurate state estimation of nonlinear dynamical systems is fundamental to modern aerospace operations across air, sea, and space domains. Online tracking of adversarial unmanned aerial vehicles (UAVs) is especially challenging due to agile nonlinear motion, noisy and sparse sensor measurements, and unknown control inputs; conditions that violate key assumptions of classical Kalman filter variants and degrade estimation performance. Neural networks (NNs) can learn complex nonlinear relationships from data, but lack principled uncertainty quantification, which is critical for state estimation tasks where confidence bounds drive downstream decisions. We address this with Bayesian Neural Networks (BNNs), which model uncertainty through distributions over network weights and produce predictive means and uncertainties via Monte Carlo sampling. Building on this, we propose the Bayesian Neural Kalman Filter (BNKF): a hybrid framework coupling a trained BNN with a Kalman correction step for robust online UAV state estimation. Unlike related neural Kalman approaches, BNKF produces full state predictions and incorporates Bayesian uncertainty directly into covariance propagation, improving robustness under high noise conditions. We evaluate BNKF under varying radar noise levels and sampling rates using synthetic nonlinear UAV flight data. Five fold cross validation demonstrates that BNKF outperforms Extended and Unscented Kalman Filters in accuracy, precision, and truth containment under degraded sensing. An ensemble variant (BNKFe) further improves precision in high-noise edge cases at a slight accuracy tradeoff. Runtime analysis confirms minimal inference overhead, supporting real-time deployment feasibility.

	$\displaystyle\hat{x}_{k\|k-1}^{(j)}=$	$\displaystyle F_{k}\hat{x}_{k-1\|k-1},$
	$\displaystyle P_{k\|k-1}^{(j)}=$	$\displaystyle F_{k}P_{k-1\|k-1}F_{k}^{T}+(\mathbb{E}{Q_{k}}^{(j-1)})^{-1}.$

Abstract

Explore similar work

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