Robust distributed extended Kalman filter based on adaptive multi-kernel mixture maximum correntropy for non-Gaussian systems

As one of the most advanced variants in the correntropy family, the multi-kernel correntropy criterion demonstrates superior accuracy in handling non-Gaussian noise, particularly with multimodal distributions. However, current approaches suffer from key limitations-namely, reliance on a single type of sensitive Gaussian kernel and the manual selection of free parameters. To address these issues and further boost robustness, this paper introduces the concept of multi-kernel mixture correntropy (MKMC), along with its key properties. MKMC employs a flexible kernel function composed of a mixture of two Students t-Cauchy functions with adjustable (non-zero) means. Building on this criterion within multi-sensor networks, we propose a robust distributed extended Kalman filter-AMKMMC-RDEKF based on adaptive multi-kernel mixture maximum correntropy. To reduce communication overhead, a consensus averaging strategy is incorporated. Furthermore, an adaptive mechanism is introduced to mitigate the impact of manually tuned free parameters. At the same time, the computational complexity and convergence ability of the proposed algorithm are analyzed. The effectiveness of the proposed algorithm is validated through challenging scenarios involving power system and land vehicle state estimation.

Adaptive Robust Unscented Kalman Filter for Dynamic State Estimation of Power System

Non-Gaussian noise and the uncertainty of noise distribution are the common factors that reduce accuracy in dynamic state estimation of power systems (PS). In addition, the optimal value of the free coefficients in the unscented Kalman filter (UKF) based on information theoretic criteria is also an urgent problem. In this paper, a robust adaptive UKF (AUKF) under generalized minimum mixture error entropy with fiducial points (GMMEEF) over improve Snow Geese algorithm (ISGA) (ISGA-GMMEEF-AUKF) is proposed to overcome the above difficulties. The estimation process of the proposed algorithm is based on several key steps including augmented regression error model (AREM) construction, adaptive state estimation, and free coefficients optimization. Specifically, an AREM consisting of state prediction and measurement errors is established at the first step. Then, GMMEEF-AUKF is developed by solving the optimization problem based on GMMEEF, which uses a generalized Gaussian kernel combined with mixture correntropy to enhance the flexibility further and resolve the data problem with complex attributes and update the noise covariance matrix according to the AREM framework. Finally, the ISGA is designed to automatically calculate the optimal value of coefficients such as the shape coefficients of the kernel in the GMMEEF criterion, the coefficients selection sigma points in unscented transform, and the update coefficient of the noise covariance matrices fit with the PS model. Simulation results on the IEEE 14, 30, and 57-bus test systems in complex scenarios have confirmed that the proposed algorithm outperforms the MEEF-UKF and UKF by an average efficiency of 26% and 65%, respectively.