Weighted total least-squares joint adjustment with weight correction factors

• Published in: Communications in statistics. Simulation and computation Vol. 48; no. 9; pp. 2689 - 2707
• Main Authors: Wang, Leyang, Yu, Hang
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 21.10.2019; Taylor & Francis Ltd
• Subjects: Affine transformations; Algorithms; Data points; Datasets; Errors-in-variables model; Helmert variance component estimation; Iterative algorithms; Iterative methods; Joint adjustment; Least squares; Parameter estimation; Stochastic models; Weight; Weight correction factor; Weighted total least squares
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1080/03610918.2018.1468450

A joint adjustment involves integrating different types of geodetic datasets, or multiple datasets of the same data type, into a single adjustment. This paper applies the weighted total least-squares (WTLS) principle to joint adjustment problems and proposes an iterative algorithm for WTLS joint (WTLS-J) adjustment with weight correction factors. Weight correction factors are used to rescale the weight matrix of each dataset while using the Helmert variance component estimation (VCE) method to estimate the variance components, since the variance components in the stochastic model are unknown. An affine transformation example is illustrated to verify the practical benefit and the relative computational efficiency of the proposed algorithm. It is shown that the proposed algorithm obtains the same parameter estimates as the Amiri-Simkooei algorithm in our example; however, the proposed algorithm has its own computational advantages, especially when the number of data points is large.