Error propagated into latitude and departure from errors in an angle and a distance
One course, one distance uncertainty and one azimuth uncertainty, carried through the general propagation formula with partial derivatives - and a rotation argument that checks the answer without repeating it.
Analyze· about 26 minutes by hand· 5 steps
Given
A single traverse course was observed as: distance D = 1284.62 ft, azimuth α = 63°14′30″ clockwise from north.
The distance has a standard error of σ_D = ±0.025 ft.
The azimuth has a standard error of σ_α = ±8″.
The two errors are independent: the distance came from an EDM observation and the azimuth from an angular observation on an independently oriented backsight.
Distances in US survey feet.
Required
The latitude and departure of the course.
The standard error of each, propagated from both sources.
The resultant positional uncertainty of the far end of the course.
Work it through yourself before reading on - the solution below shows every step, so there is no way to skim it without giving the answer away.
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