Research On New Filtering Algorithm Based On Interval Process Model

Kalman filtering is one of the basic methods of state estimation problem,which achieves the recursive minimum variance estimation of system state by continuously predicting and correcting the observed values and is widely used in many fields.In the traditional Kalman filtering analysis,it is usually necessary to know the precise statistical characteristics of the random noise.If its statistical characteristics are deviated,the estimation results will be inaccurate or even divergent.However,due to the limitation of testing conditions or costs,it is often difficult or even impossible to get enough testing samples to obtain accurate statistical characteristics of the random noise in many practical engineering.Although the self-adaptive filtering technology developed subsequently does not need the prior statistics of the random noise,the accuracy and validity of the adaptive estimation results lack of strict evaluation methods.At the same time,it is a suboptimal filter method that cannot give consideration to both the speed and precision of operation.Therefore,the classical Kalman filtering and its improved algorithms based on the stochastic system framework are faced with some challenges in practical engineering applications under the limitation of the number of samples.In view of the above problems,this paper uses the interval process model to describe the uncertainty of the system state and the random noise,and completes the following research work:(1)The interval process model is applied to the linear filtering problem,and a new filtering algorithm is proposed,which can achieve the real-time filtering estimation of the linear system state under the condition of insufficient sample information.Firstly,the linear state space equation with interval process noise is constructed.Secondly,in the new filtering algorithm,the middle point of the system state is used as its optimal estimation value,and the variance of the estimation error is used to represent the fluctuation degree of the optimal estimation value.Finally,the recursive filtering algorithms for one-dimensional linear discrete systems and multi-dimensional linear discrete systems are derived respectively in the sense of minimum estimation error variance.(2)The problem of nonlinear system filtering is studied in this paper,and a new nonlinear discrete system filtering algorithm based on interval process model is proposed.Firstly,the nonlinear state space equation with interval process noise is constructed.Secondly,based on the Taylor series expansion method,the first-order term of the nonlinear state-space equation is intercepted and the linearized state-space equation is obtained.Finally,the new linear discrete system filtering algorithm proposed above is used in the obtained approximate linearized model,and then the system state estimates and variance estimates are approximately calculated to achieve the state estimation of nonlinear discrete systems.