Robust Fusion Kalman Estimator For Multi-Sensor Fractional-Order System

The research results of Kalman filter can be applied in many fields such as weather forecasting,satellite positioning,aerospace,etc.Traditional Kalman filters generally consider integer-order systems,but Kalman estimation using fractional-order systems can get estimates that are closer to the real system,thus reducing the actual system error,so the Kalman estimation theory of fractional-order systems has aroused the interest of many scholars.This paper focused on linear fractional order systems after discretization by the Grunwald-Letnikov(7)G-L(8)difference method.When studying the Kalman filtering of fractional order systems,the uncertainty in the system may cause the filtering effect of the Kalman filter to deteriorate or even diverge,so it is necessary to study the robustness of the uncertain system.In this paper,based on the existing theory,we will further propose a robust fusion Kalman estimator for multi-sensor fractional-order systems with uncertain noise variance.The main contents of this paper are as follows:1.A local robust fractional Kalman filter is proposed for linear discrete fractional order systems with uncertain noise variance and uncorrelated noise,and its robustness is proved by the minimax robust filtering method based on Lyapunov equation.Then the fusion estimation of the fractional order system is realized by using centralized fusion algorithm,distributed matrix weighted fusion algorithm and distributed weighted measurement fusion algorithm.2.For linear discrete fractional order systems with uncertain noise variance and noise correlation,a local robust fractional Kalman filter is proposed by transforming correlated noise into uncorrelated noise.The fusion estimation of some local fractional order systems is realized by using centralized fusion algorithm,distributed matrix weighted fusion algorithm and distributed weighted measurement fusion algorithm.3.For linear discrete fractional order systems with noise variance uncertainties with colored process noise and colored observation noise respectively,the colored noise is processed by constructing augmented vectors defined by state vector and noise vector,and robust local Kalman filters are proposed for two kinds of fractional order systems with different colored noise.For the local fractional system with colored process noise,the fusion estimation is realized by centralized fusion algorithm,distributed matrix weighted fusion algorithm and distributed weighted measurement fusion algorithm,and for the local fractional system with colored measurement noise,the fusion estimation is carried out by centralized fusion algorithm and distributed matrix weighted fusion algorithm,respectively.