Enhancement of Computational Efficiency for Weighted Total Least Squares

Abstract

Weighted total least-squares (WTLS) adjustment is a rigorous method used for estimating parameters in the errors-in-variables (EIV) model. However, its computational efficiency is limited due to the large number of matrix operations involved, which are extremely time-consuming, particularly when processing large data sets. Based on the structural characteristics of the EIV model, the design matrix is divided into a constant matrix and a random matrix. Then the EIV model is rewritten as a general structured model and reformulate it as an efficient WTLS algorithm, which only attaches a weight matrix to the random matrix to reduce the size of the matrices involved in the iterative process. In addition, the proposed algorithm does not reestimate the random matrix in each iteration. All of this helps to improve computational efficiency. Numerical results confirm that the proposed algorithm can obtain the same accuracy as other existing improved algorithms, but using the same hardware, which requires significantly less time and memory.