This article investigates state estimation in islanded microgrids (ImGs) over peer-to-peer sensor networks, focusing on scenarios involving unknown noise characteristics and measurement data corrupted by random outliers. To address this issue, a novel distributed robust state estimation algorithm is introduced. First, the inverse Wishart distribution serves as the prior distribution for estimating the unknown noise covariance matrix. The prediction probability density function (PDF) adopts a Gaussian framework, while the measurement PDF is characterized by a Gaussian–Student’s t mixture model. Furthermore, a variational Bayesian methodology is implemented to concurrently compute posterior estimations for both the state vector and associated model parameters. Besides, the alternating direction method of multipliers is utilized to achieve consensus among sensor nodes based on estimation results, while reducing communication bandwidth requirements. Finally, simulation experiments on an ImG with two distributed generation units demonstrate the effectiveness of the proposed algorithm through comparative simulations with existing methods.

This paper focuses on the design of a privacy-preserving distributed Kalman filtering algorithm for a class of linear time-varying systems in signal-to-interference-plus-noise ratio (SINR)-based sensor networks, where packet dropouts may occur in information transmission between neighboring sensor nodes. Considering the potential occurrence of eavesdropping attacks during information transmission, which is common due to the inherent vulnerability of SINR-based sensor networks, a new class of distributed secure Kalman filtering algorithm has been developed. The presented algorithm incorporates a modified ElGamal cryptosystem and adaptive fusion weights to significantly enhance security, resist privacy leakage, and bolster robustness against packet dropping. Then, a detailed performance analysis for the presented distributed secure Kalman filtering algorithm is conducted, where the security and unbiasedness of the designed algorithm are discussed. Sufficient conditions for the stability of the estimation error are further established to ensure that the estimation error is ultimately bounded in the almost sure sense. Finally, numerical examples are given to illustrate the effectiveness of the proposed algorithm.