Filtering Performance Research Based On Nonlinear System

Nonlinearity,as the typical performance of the complex nature,is the essence of the plenty of the systems in our real life,among which the majority is the strong nonlinear system.There is a wide range of practical studies on the filtering based on the nonlinear system in all fields,such as data assimilation in the field of earth science,target tracking and navigation in the field of military and so on.With the development of science and technology,there is a more and more highly demand to the filtering performance and accuracy of the nonlinear system.On the basis of the linearization,it is difficult to solve the problems of complex filtering in the real life,thus no perfect result can be attained.Therefore,it is obvious to mention the importance of the nonlinear filtering.What's more,there is a long way to go on the treatment of the filtering.In the basis of data assimilation in the system,expert and scholar from the abroad and home pay more and more attention to the filtering performance of the nonlinear system as well as it has become the key point in the study of the basic theory.The author will focus on the nonlinear method to implement research the performance of it from the point of the data assimilation.There are three kinds of ways mentioned to filter the nonlinear system in the thesis: Ensemble Kalman Filter,Reduced Order Kalman Filter and Robust Filter.The essence of these three kinds of the nonlinear system is the following: The first step is to obtain the estimation of state variable covariance in the light of ensemble predicted values.The second step is to update predicted values based on latest observation.The last step is to acquire predicted values and covariance matrix.By making use of transition matrix and evolving from background covariance,Ensemble Transform Kalman Filter is aimed to analyze covariance.The Reduced Order Kalman Filter,which is intended to achieve the effect of the filtering through reducing the order of the Kalman Filter,is aimed to measure the standard of the filtering by minimizing the estimation the trace of the error covariance.Robust Filter refers to implement the filtering by means of using the performance of the Robust norm in the Robust control method.What Robust Filter is introduced is to resolve the problems of the uncertainty and randomness existed in the system.The method of Robust Filter regards noise as random signal,thus to make sure that the system interference is reduced to minimize.The main details of the thesis are as follows:(1)On the basis of Kalman Filter,the Reduced Order Kalman Filter is introduced to improve the performance of filtering by means of reducing the order number of the filtering model.On the specific occasion,taking second-order system as an example is to explain the performance of Reduced Order Kalman Filter is superior to that of Kalman Filter.On the premise of reduced order gain and convergence,the author can calculate the off0 line steady-state values as well as conduct calculation.(2)In order to change the traditional simple model of the maneuvering system,based on the system model is already completely well-known and there is a hundred times larger than the real system,the author compares the sensitivity of Kalman Filter and Robust Filter in the case of settling mismatching problems considering parameters of position,velocity,standard deviation and so on.(3)In view of the performance of the nonlinear system and Lorenz-96,the author makes a further research on the Ensemble Transform Kalman Filter and examines the robustness of data assimilation by changing the values of forcing items to generate different kinds of model error.Considering the magnification of background covariance and analysis covariance existed in the Ensemble Transform Kalman Filter,the author verifies the effectiveness of the filtering while both assemble numbers are changing and amplification factors are enlarging in the system.The author does some research on the performance of three nonlinear filtering system and compares them with traditional filtering system.In the end,the author confirms the effectiveness of enlarging covariance in the Ensemble Transform Kalman Filter.Based on the three main details,the author makes a further discussion on how to utilize nonlinear filtering system in the system of data assimilation.