Filter Design And Simulation Of Characteristic Function For A Class Of Nonlinear Dynamic Systems

Filtering is a common algorithm in fault diagnosis,target tracking and other fields.It plays an important role in the practical application of some dynamic systems that need to pursue high precision and accuracy.In the development history of filtering algorithms,there are endless filtering algorithms for dynamic systems with different characteristics.At present,the common filtering algorithms are Kalman Filtering,Unscented Kalman Filter,Cubature Kalman Filtering and so on.Most of the nonlinear filtering algorithms based on Kalman Filtering are aimed at Gaussian system,but in the non Gaussian system filtering algorithm,the recently developed Characteristic Function Filtering method needs to take the linear state equation as the premise,which affects its further development.Therefore,in this paper,for the state equation is non-linear non Gaussian,and the measurement system is a non-linear non Gaussian system composed of multiple sensors,the corresponding centralized and distributed filtering methods based on the characteristic function are established,and the simulation and application research are carried out.The main work of this paper is as follows:(1)An Characteristic Function Filtering method is proposed in which both state equation and measurement equation are nonlinear and non Gaussian.Firstly,the UT transformation form of nonlinear transfer function and the Taylor expansion method based on high dimension and high order are studied.Secondly,the propagation equation of state variable estimation error is derived,and the characteristic function recursive model of state error variable is constructed accordingly.Secondly,the objective function is established,and the real-time recursive filter of nonlinear non Gaussian system is deduced.Finally,the digital simulation experiment is used to verify The validity of the method is proved.(2)A nonlinear non Gaussian filter with multiple observers is established.Firstly,according to the existing design method of multi-sensor filter based on Kalman Filtering,a parallel filter and a sequential filter based on the Characteristic Function Filtering are designed;then,the solution method for the nonlinear state equation in the Characteristic Function Filtering proposed in(1)is incorporated to make it applicable to the nonlinear system;finally,the effect is verified by the simulation experiment.(3)An adaptive updating method of neural network parameters based on Characteristic Function Filtering is proposed.Firstly,the output equation with parameters is regarded as the transcendental equation with parameters as state variables;secondly,a dynamic model with parameters to be evaluated as variables is established,which can realize the centralized and distributed estimation of model parameters by combining(1)and(2);finally,a hierarchical estimation method is designed to update the parameters of each layer step by step.