Multicollinearity Diagnosis Method Of Regression Model And Its Application In Inertial Navigation Error Separation

Multicollinearity is a kind of problem that a regression model has high linear correlation among part of independent variables.Multicollinearity problem commonly exits in the field of natural science with non-experimental data,such as geodesy,economics,medicine,biology,atmospheric science and weapon equipment test and identification.Due to the multicollinearity,the estimation of regression coefficients in models can be distorted or difficult to be estimated accurately.Hence,as the premise and key to achieve the high-accuracy parameter estimation and the application of multicollinearity models,the research and development of multicollinearity diagnosis and measurement,and the corresponding estimation methods of model parameters are very important.The main research of this paper focuses on the parameter estimation of the multicollinear regression model,aiming at further enriching and developing the diagnosis and measurement methods of the multicollinearity,and proposing some new parameter estimation methods,estimation algorithms and estimation strategies of the ill-conditioned models.The main work and innovations of this paper are as follows:1.Using the theory of data fusion and model decomposition,propose a new parameter estimation strategy of multicollinearity regression model.Setting the guidance system error separation of moving-base inertial missile as the application background,validate the effectiveness and the superiority of the new strategyFirstly,the optimal weighting and parameter estimation of the fusion processing of unequal precision linear measurement are studied for various precision measurement models.The optimal estimation of the parameters of the unequal precision data fusion model is given.The existence and uniqueness of the optimal fusion weights are proved,and the accuracy of the optimal estimation of the unequal precision linear fusion model is analyzed.Secondly,from the point of view of model decomposition,based on certain assumptions,a new piecewise parameter estimation strategy and an iterative parameter estimation strategy for the multicollinear regression model are proposed,and the numerical simulation of the optimal fusion estimation and the piecewise parameter estimation is given according to the theoretical analysis,which proves the feasibility of the proposed method and strategy.Finally,considering the initial error of the moving-base inertial missile,the coupling between the initial error and the guidance system error is analyzed.The piecewise estimation strategy and the iterative estimation strategy are applied to the separation of the guidance system error.The applicability of the error estimation strategy for the guidance system of the moving-based missile is verified by the data simulation test.2.Aiming at the diagnosis and measurement of multicollinearity,a collinearity identification and diagnosis method based on Conditional Index-Variance Decomposition Proportion(CI-VDP)is proposed and applied to the problem of linear separation of inertial missile guidance system errorFirstly,the concepts and properties of SVD decomposition,conditional number and hypothesis test of correlation analysis are given theoretically.On this basis,the definitions and forms of conditional index and variance decomposition proportion are analyzed,and a method of multicollinearity identification and diagnosis based on CI-VDP is proposed.Secondly,combined with the correlation numerical simulation,the theoretical basis of key parameters setting in the identification and diagnosis of multicollinearity is given.Finally,the multicollinearity identification and diagnosis method based on the CI-VDP is applied to the collinearity processing of the guidance system error model,and the partitioning least squares estimation algorithm for the separation of guidance errors is realized according to the identification and diagnosis results.The method can not only detect whether the design matrix in the model has collinear relationship,but also accurately diagnose the related variables contained in the linear correlation,which effectively improves the separation accuracy of guidance system errors.3.Building a nonlinear joint model for guidance system error based on telemetering and external ballistic measurement.Based on the nonlinear model,combining with the coupling between initial error and guidance system error of moving-based guidance system,a parameter separation method based on artificial fish swarm intelligent bionic algorithm is proposedFirstly,the nonlinear joint model of guidance system error with high accuracy is established by using telemetry and external measurement data.On this basis,the Bayes maximum a posterior(MAP)parameter estimation algorithm of the traditional nonlinear regression model is given.Secondly,aiming at the characteristics of the nonlinear joint separation model and the shortcomings of the traditional Gauss-Newton iteration method,an artificial fish swarm intelligent bionic algorithm is proposed to estimate the parameters.The convergence and global optimality of the algorithm are theoretically analyzed,and the detailed algorithm steps are given.Finally,based on the nonlinear guidance system error model,the artificial fish swarm algorithm is used to separate the guidance error of the moving-base aircraft,which effectively improves the separation accuracy.