What is the purpose of including constraint equations in a least squares adjustment?

• A. To fix known quantities or relationships (e.g., fixed control points) and improve solution stability.
• B. To maximize residuals and test the model.
• C. To add random variables to the system.
• D. To replace observations with fixed parameters regardless of data.

Answer: (A)

Constraint equations bring in a priori information by expressing known quantities or exact relationships as additional equations in the adjustment. This anchors the solution to places we already know well—such as fixed control point coordinates or relationships like collinearity or known distances—so the unknowns are constrained to satisfy those facts. By reducing the freedom of the system and aligning it with solid prior information, the adjustment becomes more stable and the estimated parameters gain precision. If a constraint is not exact but has uncertainty, it can be included with appropriate weighting to act as a soft constraint, still guiding the solution without overpowering the observations. This is why the purpose is to fix known quantities or relationships and improve solution stability.