Partial Total-Least-Squares Adjustment of Condition Equations with Application to a Rectangular Building Adjustment in a GIS

Abstract

This paper presents a partial total-least-squares adjustment method for condition equations (PTLSC) in which the observation vector and coefficient matrix contain linearly correlated errors. In the proposed method, the functionally independent variables in the observation vector and the coefficient matrix of the condition equations are abstracted to form a collected observation vector. The PTLSC method is formulated by minimizing the sum of the weighted squared errors of the collected observation vector by the use of a Lagrangian multiplier algorithm. The estimation of the covariance matrix based on linear approximation for the collected observation vector is also derived. The proposed PTLSC method was tested in an example of rectangular building adjustment in a geographical information system (GIS). The results indicate that the proposed PTLSC method can adjust the interior angles of the digitized buildings so they are right angles, and it can be used to maintain the correlations among the elements in the observation vector and the coefficient matrix.