In a post-adjustment network, what does the standard deviation of a coordinate correspond to?

• A. The square root of the diagonal element in the covariance matrix for that coordinate.
• B. The value on the diagonal itself.
• C. The sum of all covariances.
• D. The determinant of the covariance matrix.

Answer: (A)

In a post-adjustment network, the standard deviation of a coordinate reflects its uncertainty and comes from the covariance matrix of the estimated parameters. The diagonal elements of this matrix are the variances of each coordinate, so the standard deviation is the square root of the corresponding diagonal element. In other words, take the i-th diagonal entry, which is Var(x_i), and its square root gives SD(x_i). The diagonal value is the variance itself, not the standard deviation; the sum of covariances isn’t the per-coordinate uncertainty, and the determinant describes the overall error ellipsoid volume for the whole network, not the uncertainty of an individual coordinate. For example, if the diagonal element for a coordinate is 0.04 m^2, the standard deviation is 0.2 m.