关键词: 最小二乘, 加权总体最小二乘, PEIV模型, 计算效率, 坐标转换

Abstract: At present, the weighted total least-squares (WTLS) adjustment is a relatively rigorous method used for estimating parameters in the errors-in-variables (EIV) model. However, the required matrix operations involved in the iteration process are extremely time-consuming, particularly when processing large data sets. Using partial errors-in-variables (PEIV) is conducive to improve the computational efficiency of WTLS. Based on the PEIV model and the least squares criterion, this study derived an algorithm for weighted total least squares problemin a concise way. The algorithm is simple in the concept and involves fewer matrix operations because it doesn't demand matrix reconstruction in the iteration process. Finally, simulated experiment is used to test the performance of the proposed algorithm. The results show that the proposed algorithm can achieve the same results as the existing algorithms and has higher computational efficiency.

Key words: least squares, weighted total least squares, partial errors-in-variables model, computational efficiency, coordinate transformation