Improved Fitting Method of Elevation Anomaly Based on Variable Projection Algorithm
In order to improve the least squares fitting accuracy in the calculation of elevation anomaly fitting,this paper is on the basis of the conventional logarithmic function model,and combined with the variable projection algorithm to improve and study the elevation anomaly algorithm,first of all,the known point data is substituted into the logarithmic function fitting model to form a separable non-linear equation system,and then the matrix is SVD decomposed,under the principle of least squares the variable projection function based on SVD decomposition is iteratively solved,the nonlinear parameters are obtained,and finally the solved parameters are brought back,and the coordinate values to be fixed are brought in to find the fitting value of elevation anomaly. The calculation results show that the sum of squares of the predicted residuals of the variable projection method is 2.657×10-7 m2,and the prediction RMS error is 3.645×10-4 m. Compared with the prediction results of other models,the variable projection method has the highest prediction accura-cy. As compared with the abnormal plane of elevation,the plane obtained by the variable projection method is relatively smooth and most in line with the distribution of point positions.
万方数据
维普
