In least squares adjustment, what is the impact of adding constraint equations?

• A. To fix known quantities or relationships and improve solution stability.
• B. To increase computation time without benefit.
• C. To introduce bias into the solution.
• D. To remove the need for weighting.

Answer: (A)

Constraint equations bring in prior information about known quantities or relationships among the unknowns. In a least squares adjustment, you’re solving for parameters that best fit the observations, but sometimes the network alone doesn’t determine all parameters well or they are highly correlated. By adding constraints, you fix certain values or linkages, narrowing the set of feasible solutions to those that satisfy these known facts. This grounding reduces ambiguity, improves the conditioning of the normal equations, and makes the solution more stable and reliable in the presence of measurement noise or limited data.

If the constraints accurately reflect true facts and are applied with appropriate emphasis (a high weight or exact equality when warranted), they reduce the uncertainty in the estimated quantities. If a constraint is incorrect, it can pull the solution away from reality, effectively biasing the result. So constraints are powerful because they incorporate reliable prior information to stabilize and improve the solution, not because they eliminate the need to consider observation quality or because they merely slow things down.