Information Fusion Kalman Estimator For Multi-sensor Time-delay Fractional-order System

Fractional calculus has the advantage of accurately describing the memory and heredity of the system,and has a good effect in depicting the physical changes related to history.In the process of information transmission,time delay is usually unavoidable,leading to poor system performance and disrupting the stability of fractional order systems.This article focuses on the problem of system information fusion estimation for multi-sensor delay fractional order systems under the linear minimum variance criterion.The main research content is as follows:For the observation constant delay multi-sensor fractional order systems with uncorrelated noise,the state space expression of the fractional order systems with time delays was derived by the discretization method which was defined by Grunwald-Letnikov(G-L).By using the method of state augmentation,the delayed fractional order system was transformed into a non-delayed augmented fractional order system.For the new system with state augmentation,the cross-covariance matrix between the local filter and the subsystem was derived.Furthermore,centralized and distributed fusion filters for the system were proposed,effectively improving local estimation accuracy.For the observation multi-time delay single sensor fractional order system with uncorrelated noise,a Kalman filter based on non-augmented suboptimal fractional order systems was proposed by introducing suboptimal prediction estimators through a non-augmented method,avoiding the increase in system dimensionality and the calculation of complex smoothers.Furthermore,for the observation multi-time delay multi-sensor fractional order systems,the cross-covariance matrix between subsystems was derived,in addition,centralized and distributed fusion filters were proposed for the system,effectively improving local estimation accuracy.For the state and observation multi-time delay multi-sensor fractional order system with correlated noise,a decorrelation method is used to convert the fractional order model with correlated noise into a fractional order model with uncorrelated noise.For the transformed new system,the cross-covariance matrix between the local suboptimal Kalman filter and the subsystem was derived by introducing one-step suboptimal state prediction estimators and observation prediction estimators.Furthermore,centralized and distributed fusion filters for the system were proposed,effectively improving local estimation accuracy.