On homotopy method to parameter estimation for generalized nonlinear Gauss-Helmert model
The generalized nonlinear Gauss-Helmert model is a unified expression of explicit and implicit nonlinear function ad-justment models that consider the errors of the dependent variable or the whole variable.Aiming at the problem of non-conver-gence of its Gauss-Newton iterative solution algorithm when the difference between the initial value and the true value is large,the parameter estimation method of the generalized nonlinear Gauss-Helmert model that integrates the homotopy method and nonlinear least squares is proposed.Starting from the nonlinear least-squares adjustment criterion that introduces the homotopy parameter,the system of differential equations for solving the generalized model parameters and the fixed-step prediction for-mula for tracking the homotopy curve with the Newton's correction formula are derived,and the approximation formula for cal-culating the residual vector of the implicit function model is given.The complexity of computing the system of differential equations is reduced by introducing the Kronecker product and the matrix straightening operation into the derivation process in order to avoid computing the cubic matrix.The feasibility of the method is verified through three experiments,including dis-tance positioning that only considers the error of the independent variable,pseudo-distance positioning that considers the satel-lite coordinate error and ranging error,trilateration network that considered the errors in the known coordinates,and circular curve fitting that considers the error of plane coordinates.The experimental results show that the new method converges to a larger range of initial values.
万方数据
维普
