基于变量投影算法的高程异常改进拟合方法  

Improved Fitting Method of Elevation Anomaly Based on Variable Projection Algorithm

作　　者：翟耀红 ZHAI Yaohong(China Railway 12th Bureau Group No.1 Engineering Co.,Ltd.,Xi'an 710054,China)

机构地区：[1]中铁十二局集团第一工程有限公司,陕西西安710054

出　　处：《测绘与空间地理信息》2024年第9期182-184,187,共4页Geomatics & Spatial Information Technology

摘　　要：为提高高程异常拟合计算中的最小二乘拟合精度,在常规的对数函数模型的基础上,结合变量投影算法对高程异常算法进行改进和研究:首先将已知点数据代入对数函数拟合模型形成可分离非线性方程组,然后将矩阵进行SVD分解,在最小二乘原则下对基于SVD分解的变量投影函数进行迭代解算,求得非线性参数,最后将求解的参数回代,将待定点的坐标值代入,求得高程异常拟合值。计算结果表明,变量投影法的预测残差平方和为2.657×10^(-7)m^(2),预测均方根误差为3.645×10^(-4)m,与其他模型的预测结果相比较,变量投影法预测精度最高;通过高程异常平面对比,变量投影法获得的平面比较平滑,最符合点位分布情况。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 nonlinear 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) m^(2),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 accuracy.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.

关 键 词：高程异常 似大地水准面 正常高 变量投影 

分 类 号：P216[天文地球—测绘科学与技术]