Research On Several Filtering Algorithms With Non-linear System

With the rapid development of modern science and technology, especially the widespread application of communication technology, information technology and computer technology in numerous civilian and defense sectors, signals from modern control systems often exhibit non-linear, non-Gaussian noise-related and other complex features. Accordingly, it results in the design of nonlinear filtering algorithms faces many new problems and challenges, and it has important theoretical significance and application value.For the relevant characteristics of the system and non-Gaussian noise, many existing nonlinear filtering algorithms cannot satisfy the application requirements of complex systems. As a result, the study to design nonlinear filtering algorithms for the systems with related noises and non-Gaussian case becomes an effective way to improve application capabilities. In response to these problems, this thesis develops the following main work:Firstly, for linear Gaussian systems, we propose a new cubature information filtering algorithm with noise-related. We consider a kind of system with related process noise and measurement noise, then an extended information filter is derived for this system. After that, a cubature information filter with noise correlation is presented by embedding the extended information filter in the cubature Kalman filter. Then, some simulation examples with bearings-only tracking are demonstrated to validate the proposed filters.Secondly, for a kind of nonlinear non-Gaussian systems, a novel design algorithm of nonlinear filter is presented under a new performance. The algorithm takes symmetric K-L distance as the performance index and introduces the concept of the real distance. Selection ranges of weighting function and the filter gain matrix are given. Some simulation results are provided to validate the new algorithm.Thirdly, for a kind of nonlinear non-Gaussian system, a filtering algorithm of multidimensional observation distribution function is proposed based on a mix characteristic function. For one dimension case, a filter design method is presented. By introducing the weighted function vector under high-dimension observation condition, a new performance index is established and the selecting range of the weighted function vector to guarantee the consistent boundedness of the performance index. A gain matrix solution is presented under minimizing the new performance index. The simulation results show that the application ability of the proposed filtering algorithm is greatly improved.