How does the covariance matrix describe a post-adjustment network's uncertainty?

• A. The covariance matrix contains variances of coordinates on the diagonal and covariances between coordinates; square roots give standard deviations and off-diagonal terms show correlations.
• B. It lists the residuals for each observation.
• C. It stores the mean coordinates and their standard errors.
• D. It is only used to color-code mapping results.

Answer: (A)

Uncertainty in a post-adjustment network is captured by the covariance matrix, which encodes variances and covariances among estimated quantities. The diagonal elements are the variances of each parameter, and their square roots are the standard deviations that reflect the typical size of the estimation error. The off-diagonal elements are covariances between pairs of parameters, showing how their errors co-vary; nonzero covariances indicate that the errors in two quantities are linked, which you can also express as correlation coefficients to understand the strength and direction of that relationship. This matrix lets you propagate uncertainty to any derived quantity and quantify how confident you are in the network’s results.

Residuals describe the differences between observed and computed values and are not what the covariance matrix itself contains. The means (best estimates) are stored separately as the estimated coordinates; the covariance matrix provides their uncertainties, not the means. And the covariance matrix’s purpose goes beyond any aesthetic use like color-coding mapping results.