误差限的病态总体最小二乘解算

A Regularization Method to Ill-posed Total Least Squares with Error Limits

大地测量和地球物理数据解算中时常会涉及病态问题的处理。基于客观的观测精度,利用设计矩阵与观测向量的误差限制,一方面降低了病态性对求解造成的波动;另一方面避免引入正常数,从而提高整个解算过程的客观性与可靠性。计算表明,本文提出的方法可以有效地处理病态总体最小二乘问题,并且具有较高的稳定性。

Based on the objective measurement accuracy,we attempt to use the residuals of measurements in both design matrix and observation value to replace the positive constant.A few numerical experiments are carried out to demonstrate the performance and efficiency of the new method.