A state update method for fractional linear discrete-time systems dealing with non-Gaussian lévy noise

Abstract

The invention discloses a method for updating the state of a fractional order linear discrete system for processing non-Gaussian Levy noise. The method comprises the steps that firstly, a state prediction initial value and a prediction error covariance initial value are given; secondly, an approximation method is used for conducting decomposition to obtain a decomposition value of the non-Gaussian Levy noise, a state approximate value and a measurement output approximate value are deduced, and corresponding system noise covariance and corresponding measurement noise covariance are calculated accordingly; thirdly, a current state estimation value is used for calculating a next moment state prediction value, and current moment estimation error covariance and current moment system noise covariance are used for calculating next moment prediction error covariance; lastly, the state estimation value is updated by combining the obtained state prediction value, and the prediction error covariance is used for updating the estimation error covariance. By means of the method, due to the fact that the problem of the state estimation of the fractional order linear discrete system under the non-Gaussian Levy noise is solved, the application range of the fractional order theory is expanded, and the method can be easily combined with existing state estimation software.

Description

technical field [0001] The invention relates to a fractional-order linear discrete system state update method for processing non-Gaussian Lévy noise, belonging to the technical field of system analysis and processing. Background technique [0002] System analysis and processing aims to study the interaction of various parts (subsystems) in a specific system structure, the external interface and interface of the system, as well as the behavior, functions and limitations of the system as a whole, so as to provide information for the future changes of the system and related decisions. One of the goals is to improve the decision-making process and system performance, so as to achieve the overall optimum of the system. In the field of system analysis and processing, state estimation plays a vital role. According to the relative relationship between the observed data and the estimated state in time, the state estimation can be divided into three situations: smoothing, filtering a...

AI Technical Summary

Problems solved by technology

The traditional Kalman filtering method requires the system to be of integer order, and both the system noise and the measurement noise are Gaussian white noise. These ideal requirements are difficult to meet in the actual system

In contrast, real-world systems are often subject to non-Gaussian noise, and not all systems can be modeled in integer order

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