大地测量病态线性问题解算的奇异值修正

An improved singular value decomposition method for solving ill-linear problem in geodesy

Tikhonov方法和截断奇异值方法是处理大地测量病态线性最小二乘问题常用的两种方法。基于两种方法处理病态问题的思想,根据奇异值分布空间差异性,提出了一种混合正则化算法。该算法通过对奇异值进行差异性修正,提高参数估计解的精度和稳定性,最后采用数值案例验证了该方法的有效性。

The Tikhonov method and the truncated singular value method are two common methods to deal with the linear least squares problem of geodetic measurement. Based on the idea of the two algorithms to deal with morbid problems, and according to the spatial difference of singular value distribution, a hybrid regularization algorithm is proposed, which improves the accuracy and stability of the parameter estimation solution by modifying the singular value.The validity of the method is verified by numerical example.