Least squares adjustment is a technique for deriving a unique, best estimate of a desired quantity from redundant (multiple, non-minimal) sets of observations, by minimizing the weighted sum of squared residuals (φ = vᵀWv), where weights are inversely related to observation variance; for equally weighted, uncorrelated observations this criterion reduces to the arithmetic mean. Redundancy — the excess of actual observations (n) over the minimum required (n₀) to define a model, r = n − n₀ — is necessary to detect and control errors, but a model with redundancy is not automatically solvable unless the observations actually constrain the desired quantities; adjustment is then carried out via one of two formal approaches, the condition equation method (equations relating only observation estimates, numbering r) or the observation equation method (equations relating observation estimates to model parameters, numbering r + u, where u is the number of unknowns). This is a foundational topic in surveying computation and adjustment theory, generalizing basic error-propagation and weighting concepts into a systematic framework for combining observations into consistent, optimal estimates.
Least squares adjustment is a technique for deriving a unique, best estimate of a desired quantity from redundant (multiple, non-minimal) sets of observations, by minimizing the weighted sum of squar…