Precisions of Adjusted Quantities

Introduction After a least squares adjustment, the covariance matrix for the computed unknowns can be computed from N-1 Then apply GLOPOV to obtain precisions of indirectly determined quantities

Covariance Matrix Population Sample The standard deviation for computed unknown, xi is:

Example – Leveling: Unweighted

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Covariance of Computed Values

Numerical Example

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Final Summary

Computing Standard Deviations for Observations That Were Not Made Say we wanted the standard deviation for the elevation difference from A to C. The equation is: C – A = 1.05 Note that only the 4 corner values from N-1 were used.

Summary For a computed unknown, the standard deviation is S0 times the square root of the corresponding diagonal term from N-1 For functions of unknowns (observed or not) we need the corresponding variances and covariances – then apply GLOPOV (along with standard deviation of unit weight)