Multivariate Weighted Total Least Squares Based on the Standard Least-Squares Theory
Publication: Journal of Surveying Engineering
Volume 149, Issue 4
Abstract
The weighted total least squares (WTLS) has been widely used in many geodetic problems to solve the error-in-variable (EIV) models in which both the observation vector and the design matrix contain random errors. This method is widely applied in its univariate form, where the observations and unknown coefficients appear in vector forms. However, in some geodetic problems, data sets appear in more than one dimension, and the vector representation of the univariate model may not be suitable to efficiently solve the problem. The observation and unknown parameter vectors can then be replaced with their counterparts in matrix representations in a multivariate model. In this paper, we propose a simple, fast, and flexible procedure for solving the multivariate WTLS (MWTLS) problem using the standard least squares theory. The method has the capability of applying to large-size and high-dimensional data sets. Our numerical experiments on both simulated and real datasets demonstrate the high performance of the proposed method for solving multivariate WTLS problems. In terms of computational complexity, our method outperforms the existing state-of-the-art methods, both numerically and analytically.
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Data Availability Statement
Some or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request. The available data are: (1) generating synthetic data, and (2) MATLAB code for MWTLS.
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© 2023 American Society of Civil Engineers.
History
Received: Nov 14, 2022
Accepted: Apr 13, 2023
Published online: Jun 16, 2023
Published in print: Nov 1, 2023
Discussion open until: Nov 16, 2023
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