Iterative Unscented Kalman Filter With General Robust Loss Function for Power System Forecasting-Aided State Estimation

Unscented Kalman filter (UKF) plays a vital role in power system forecasting-aided state estimation (FASE). Given that the minimum mean-square error (MMSE) criterion adopted in the conventional UKF handles Gaussian noise, but when face non-Gaussian noise, Laplace noise, outliers, and sudden load change, it is less sensitive. To address this problem, an iterative UKF algorithm (GR-IUKF) is developed by using a general robust loss function. The general robust loss function can simulate a variety of different robust functions in M estimation, which make GR-IUKF effectively cope with non-Gaussian noise problems and has greater scalability. In addition, due to the highly nonlinear nature of the power system, the traditional linear regression model may lead to a degradation of the SE accuracy, so the algorithm employs a nonlinear regression model to unify the state error and the measurement error. Furthermore, the mean error behavior and the mean-square error behavior of the GR-IUKF algorithm are analyzed to determine its convergence. Finally, extensive experiments on the IEEE 14, 30, and 57 systems and comparisons with traditional nonlinear filtering algorithms have established that our proposed algorithm is more robust.