Manual Error Propagation
Hello,
I’m trying to make an excel spreadsheet that will calculate the expected standard deviation in the Northing and Easting of an observed coordinate based on the expected errors in my measurements. I’m getting stuck when applying the law of error propagation on my horizontal angles. It’s been too long since I’ve dove into partial derivatives and Im sure im making a mess of things.
Does anyone know of a spreadsheet that exists out there or formula I can look at to get me past my sticking point?
For example the formula I have right now for the std. dev of the northing of my observed point is…
?NB?ý = ?NA?ý + ?CEI?ý + ?CET?ý + (??NB / ??HD)?ý*?HD?ý + (??NB / ??AZ)?ý*?AZ?ý + (??NB / ??AZ)?ý*?AET?ý
as NB = NA + HD*COS(AZ)
NA = Northing of my setup point
CEI = Centering error of the instrument
CET = Centering error of the target
HD = Horizontal distance
AZ = Azimuth
AET = Angular error of the prism
ZA = ZENITH ANGLE
& the standard deviation of my HD is…
?HD?ý =(??HD / ??SD)?ý*?SD?ý + (??HD / ??ZA)?ý*?ZA?ý
The end goal is to turn the spreadsheet into a simple app I can have in the field (and available free to everyone) to help decide what combination of # of rounds, distance from target, what equipment to select, ect to meet a required error. I will compile a database inside of it with the precisions provided by the manufactures for common targets, totals stations, poles, ect
(??NB / ??AZ) Im getting messed up on this one. In Excel I have it as HD*-sin(radians(az)) but it’s putting way too much error in my final result.
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