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.

翻译：本文聚焦于分布式传感器网络中的状态估计问题，其中间歇性数据丢包、异常观测与未知噪声协方差并存。为应对这一挑战，我们将系统状态、噪声参数与网络可靠性的联合估计建模为贝叶斯变分推断问题，并提出了一种新型变分贝叶斯自适应卡尔曼滤波器（VB-AKF），用以逼近潜在参数的联合后验概率密度。与现有分别处理缺失数据和测量异常值的自适应卡尔曼滤波器不同，所提出的VB-AKF采用双掩码生成模型，通过两个独立的伯努利随机变量显式刻画可观测的通信丢失与潜在的数据真实性。此外，VB-AKF将多并发多次观测集成到自适应滤波框架中，显著增强了统计可辨识性。全面的数值实验验证了所提方法的有效性与渐近最优性，结果表明随着传感器数量的增加，参数辨识和状态估计均渐近收敛至理论最优下界。