Hello,
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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.
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Does anyone know of a spreadsheet that exists out there or formula I can look at to get me past my sticking point?
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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
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as NB = NA + HD*COS(AZ)
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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
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& the standard deviation of my HD is...?ÿ
?HD?ý =(??HD / ??SD)?ý*?SD?ý + (??HD / ??ZA)?ý*?ZA?ý
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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?ÿ
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(??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.
I haven't studied your equations, but the first thing that comes to mind is that math angles and azimuths are reckoned differently so you have to be careful about sin vs cos and signs.
It's definitely something along those lines. Whenever I take the sin of an azimuth at or near 90/270 degrees I get a value at or near 1. So when I multiply that factor by my HD its applying a relatively large error.
Its like the HD shouldn't be there in that equation.
?ÿ I have no idea if this will help you. I had this as a study guide and a few others and I have not looked at it close just briefly but it has several formulas for error propagation. I apologize if its not of help. I had read this the other day and while out checking cows today it clicked i had some files . If this works great if it doesn??t i will try and remember to look on my old control for something. ?ÿI know I have all kinds of documents and studies etc.?ÿ
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.
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?ÿ
The description of your task almost sounds like working backwards from an average/arbitrary Relative Positional Precision standard/number between x pairs of tested points within a survey network to guide you towards the correct measurement strategy? I'm not sure anyone has done that, or what you are proposing.
The concept is fascinating, but, all of your well placed intentions won't account for blunders (4:45pm on Friday), systemic errors (Did they really adjust all the gear, and was it done correctly?), and most importantly, crew willingness to participate (see blunders and systemic errors), etc.
Modern survey measurement theory already includes proper mission planning: equipment selection, error budgeting, LSA, etc., and is the obvious "going-forward-process".
It seems that both processes (forward/backward) require measurements, redundancy, and variables you can't possibly anticipate, until you navigate the field survey, complete the data collection, and assess the data set after the fact?
No iPhone app will replace knowledge, skills, and experience.
This is a great example of training and spending time with staff to assess their abilities.
I hope you prove me wrong and successfully develop the app. Please let me know; I will be the first to buy it.
The description of your task almost sounds like working backwards from an average/arbitrary Relative Positional Precision standard/number between x pairs of tested points within a survey network to guide you towards the correct measurement strategy? I'm not sure anyone has done that, or what you are proposing.
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Seems like StarNET's Preanalysis function, except with a desired relative positional precision value input at the beginning.
I developed a very crude version in Matlab back in school for one of my projects (and just to see if I could do it), but I lacked the coding skillz to take it to a compiled version with a user-friendly GUI.
You note that the error seems too large at 1 but that partial derivative value gets multiplied by the associated error component, such as error in the AET or AZ as noted in your original equation for the error of NB.
Your partial derivate is correct.
