What does a nonzero covariance between coordinates indicate in a network adjustment?

• A. It indicates that the errors in those coordinates are correlated; a change in one tends to be associated with a change in the other.
• B. It indicates independent errors with no relation.
• C. It indicates a systematic bias in all coordinates.
• D. It indicates a measurement residual.

Answer: (A)

Covariance between coordinates tells you how their estimation errors move together. When the covariance is nonzero, those errors are correlated: a disturbance that increases one coordinate’s error tends to increase or decrease the other’s error as well, depending on the sign of the covariance. In a network adjustment, this arises from common error sources—such as atmospheric effects, clock or instrument biases, or the geometry of the network—that simultaneously affect multiple coordinates. The result is a nonzero off-diagonal term in the error covariance matrix, indicating that the coordinates do not vary independently. This is not about a single measurement residual, which is the difference for one observation, nor does a single systematic bias imply correlation by itself; a consistent bias would shift all coordinates in the same way, whereas correlation describes how their errors co-vary. If the coordinates were independent, the covariance would be zero.