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STAR*NET V6 - Circe

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Appendix C Additional Technical Information<br />

C.4 Instrument and Target Centering Errors<br />

Centering Error values entered in the Instrument Options, cause standard errors for<br />

turned angles, distances, directions, delta elevations, and zenith angles to be inflated.<br />

In all following formulas:<br />

I = Horizontal Instrument Centering Error<br />

T = Horizontal Target Centering Error<br />

V = Vertical Centering Error at Instrument and at Target<br />

As described below, the standard error of horizontal turned angles, directions, azimuths<br />

and horizontal distances are affected only by horizontal centering. The standard error of<br />

delta elevations are affected only by vertical centering.<br />

Horizontal Turned Angles: The standard error contribution for an angle due to the<br />

horizontal centering error of the instrument is equal to:<br />

Inst StdErr = d3/(d1*d2) * I<br />

Where: d1 and d2 are the horizontal distances to the targets<br />

d3 is the horizontal distance between the two targets<br />

The standard error contribution for an angle due to the horizontal centering error of both<br />

targets is equal to the following:<br />

Target StdErr (Both) = Sqrt(d1 2 +d2 2 ) / (d1*d2) * T<br />

Combining the entered standard error for an angle with the standard error contributons<br />

from the instrument and target centering, we get the total standard error for an angle:<br />

Total Angle Std Err = Sqrt( AngStdErr 2 + InstStdErr 2 + TargetStdErr 2 )<br />

Directions: Total standard error, where “d” is the horizontal distance, is equal to:<br />

Total Dir StdErr = Sqrt( DirStdErr 2 + I 2 /d 2 + T 2 / d 2 )<br />

Where: d is the horizontal distance to the target<br />

Azimuths: Same as directions, but using azimuth standard error the in the formula.<br />

Horizontal Distances: Total standard error is equal to:<br />

Total Dist StdErr = Sqrt( DistStdErr 2 + I 2 + T 2 )<br />

Delta Elevations: Total standard error is equal to:<br />

Total DeltaElev StdErr = Sqrt( DeltaElevStdErr 2 + V 2 + V 2 )<br />

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