The observation equation (indirect/parameter) method is a least-squares adjustment technique in surveying that formulates one independent functional-model equation per observation, each relating that observation's residual to the full set of unknown parameters via coefficients (zero where a parameter does not appear), rather than relating observations to each other directly as in the condition equation method. These equations are assembled into the matrix form v + Bδ = f, where v is the residual vector, B is the coefficient (design) matrix of parameter coefficients, δ is the vector of unknown parameters, and f is the vector of known constants; the stochastic model is represented separately by a weight matrix W. The method belongs to the broader theory of adjustment computations, which addresses redundant observations that fail to exactly satisfy a functional model due to random errors, by finding the parameter estimates that minimize the weighted sum of squared residuals (v'Wv), with the closed-form least-squares solution δ = (B'WB)⁻¹B'Wf.
The observation equation (indirect/parameter) method is a least-squares adjustment technique in surveying that formulates one independent functional-model equation per observation, each relating that…