In the field of practical engineering, the moving least-squares (MLS) and moving total least-squares (MTLS) methods are widely used to approximate the measurement data. However, the fitting accuracy and robustness are affected inevitably by random errors and outliers, which results in distorted estimation. To solve this problem, we present an improved MTLS (IMTLS) method, in which a newly constructed parameter is introduced to characterize the geometric feature of abnormal points in each influence domain. The total least-squares (TLS) method is used to generate the fitting points at first. The corresponding variance of each node is then calculated, and the connection between abnormal degree and random errors is established to trim the nodes with a certain abnormal degree. The remaining nodes are used to find the local coefficients. This proposed algorithm can avoid the negative effects of outliers without human intervention and overelimination. The final results of the measurement experiments and numerical simulations demonstrate that the improved algorithm has better robustness and accuracy than the MLS and MTLS method.

中文翻译：

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基于几何的测量数据剖面分析重建方法

在实际工程领域，移动最小二乘法（MLS）和移动总最小二乘法（MTLS）方法被广泛用于近似测量数据。然而，拟合精度和鲁棒性不可避免地受到随机误差和异常值的影响，从而导致估计失真。为了解决这个问题，我们提出了一种改进的 MTLS（IMTLS）方法，其中引入了一个新构造的参数来表征每个影响域中异常点的几何特征。首先使用总最小二乘法 (TLS) 生成拟合点。然后计算每个节点对应的方差，建立异常度与随机误差的联系，对具有一定异常度的节点进行修剪。其余节点用于查找局部系数。该算法可以避免异常值的负面影响，无需人工干预和过度剔除。最终的测量实验和数值模拟结果表明，改进后的算法比MLS和MTS方法具有更好的鲁棒性和准确性。