Least Squares Adjustment

Least Squares Adjustment is a mathematical estimation method used to determine the most probable values of unknown parameters from redundant and noisy observations by minimizing the sum of the squared residuals. It provides a statistically optimal solution under the assumption of normally distributed observation errors.

In geodesy, least squares adjustment is the fundamental method for processing observations from surveying, GNSS, VLBI, SLR, levelling, and gravity measurements. It is used to estimate station coordinates, velocities, Earth orientation parameters, gravity field coefficients, and other geodetic quantities. The method also delivers precision measures such as variances and covariance matrices, enabling rigorous quality assessment and reference frame realization.