Observation Equation

An observation equation is the mathematical relationship that links a geodetic observation (measured quantity) to the unknown parameters to be estimated within a defined functional model. It expresses how the observed value depends on physical, geometric, or dynamical quantities and typically includes a residual term representing measurement errors.

In geodesy, observation equations form the foundation of least squares adjustment and parameter estimation. They are used to model GNSS pseudorange and carrier phase measurements, VLBI time delays, SLR ranges, leveling height differences, and gravity observations. A consistent formulation of observation equations is essential for precise positioning, reference frame realization, orbit determination, and gravity field modeling.