Adjustment of numerous measurements in steps

Abstract

A technique for addressing adjustment problems involving large data sets is developed. The adjustment-in-steps approach of the least-squares method, applied to observation adjustments only, is optimized. The core idea of the optimization process is to group the condition equations in a way that minimizes the computational effort required for adjustments. A detailed theoretical framework of the adjustment-in-steps technique is refined, covering both linear and non-linear condition equations. In addition, an optimization methodology is developed to support the implementation of the proposed technique. Numerical experiments, including line-fitting and the determination of equipotential curves, are conducted. The proposed technique is implemented in the C programming language, and the results demonstrate its numerical equivalence and improved computational efficiency compared to the classical method.