Research On Observable Degree Analysis Method Of Nonlinear System With Noise Correlation

Modern control has been proposed for decades by Mr.Kalman since the last century.In modern control theory,observability and controllability have always been the focus of many researchers.However,in the modern control theory founded by Mr.Kalman,it is only explained how to determine whether a linear system is observable or controllable,and no calculation method is given for the observable degree.The research on observable degree theory of nonlinear systems is rarely studied by scholars.In engineering practice,control systems often have nonlinear characteristics and noise correlation.Without analysis and processing,the estimation and filtering of the control system will become inaccurate and the reliability of the results will be reduced.As the depth of research continues to expand,the observable degree theory of more complex systems should be established.Aiming at the problems described above,this article mainly improves and perfects the existing observable degree theory through the following three aspects:(1)In view of the imperfection of the current nonlinear observable degree theory research,some scholars did not consider the influence of noise when they proposed the theory.Some researchers also take first-order approximations when dealing with nonlinear systems.This approach may lead to large errors in the presence of nonlinear control systems.In this regard,this content considers a new fusion method to properly fuse the two pseudo matrices,so that the observable degree calculation after fusion processing is more accurate.(2)Aiming at the research of nonlinear observable degree theory,noise-related issues are not considered.However,noise-related control systems often exist in the background of practical engineering applications.This chapter mainly analyzes the calculation of nonlinear observable degree when there is a correlation between process noise and observation noise.First,the decorrelation processing is performed on the non-linear system with noise correlation,and then the observable degree defined by cramer-rao lower bound under noise correlation is used.Further analysis of the observable degree under spectral decomposition is consistent with our definition method.Finally,the chapter uses observable degree to define adaptive adjustment factors to improve the performance of nonlinear filtering.(3)For the multi-sensor fusion analysis method,the problem of observabledegree is not considered.This chapter discusses the observable degree theory of multi-sensor fusion,analyzes the existing observable degree methods of multi-sensor fusion,and considers the observable degree of a single sensor as the fusion matrix.The method is applied to the ship's GPS navigation and positioning system to verify the rationality of the method.The multi-sensor fusion of noise correlation system is also analyzed.