基于最小二乘的选权迭代抗差拟合模型研究

目的提出基于最小二乘的选权迭代抗差推估GPS水准高程拟合方法,并检验可靠性.方法利用数值分析方法和GPS水准拟合过程分析软件对相关平面、二次曲面和三次曲面抗差推估数学模型进行对比分析研究.结果二次曲面抗差的结果要好于相关平面与三次曲面抗差的结果精度,并非抗差模型阶次越高有效性越高.抗差模型的精度与点位分布有关.在进行抗差计算时要结合多种模型进行比较分析,特别点要进行多次抗差计算,通过抗差计算有效剔出了粗差点,提高了GPS水准拟合精度.结论基于最小二乘的选权迭代抗差拟合模型解决了常规拟合模型不稳定的缺点,实际数据证明,模型结果能够达到等级几何水准的精度.

Anti Error Fitting Model Analysis Based on Least Squares

The paper aims to bring forward anti error fitting model based on least squares and test reliability.Using numerical analysis method and GLSPA the paper researches into the plane,conicoid and three cubed anti error fitting model.The result indicates that conicoid anti error is smaller than that of plane and three cubed anti error fitting model,but the validity of the model doesn't necessarily have relationship with model steps.Anti error fitting model precision relates to point distribution.We compare the anti error fitting model with other models.The special point needs more anti error calculations.The model improves the height simulation precision.So the model modifies the precarious disadvantage of general simulation model.Practice data proves that the model can obtain the precision of grade geometry level.