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RPP, Round 2 (Calculation?)
Posted by michiganleft on December 28, 2022 at 7:09 pmReading the thread about “ALTA Measurement Standards” got me thinking more about the computation of RPP. I posted what I thought was the proper method, and @olemanriver suggested something slightly different (which appears to be TBC way?).
Does anyone have a definitve source on how to calculate the RPP with respect to the points as the proper method?
I’ve not seen any documentation (other than the Trimble help files) that discusses the topic further.
Stipulate the following:
We get through the properly weighted LSA portion and arrive at the magnitude of the semimajor axis for each point.
Semimajor axis for Point 1 = 0.02′;
Semimajor axis for Point 2 = 0.03′;
Reported (measured) line length = 100.00′;
50ppm (0.00005′) * line length = 0.005′;
Allowable RPP = (0.07′ + 0.005′) = 0.075′.
Now what?
Pythagoras?
Distance formula plus 50ppm * line length?
sqrt((0.02′)^2 + (0.03′)^2) = 0.036′
0.036’+0.005 = 0.041′ (Tested; passed)
Addition?
Add each semimajor axis and the 50ppm * line length?
0.02’+0.03′ = 0.05′
0.05’+0.005′ = 0.055′ (Tested; passed)
Mean Squared?
Average the sum of each semimajor axis squared and add the 50ppm * line length?
((0.02′)^2 + (0.03′)^2)/(2) = 0.00065′
0.00065’+0.005′ = 0.00565′ (Tested; passed)
Root Mean Squared? (Estimate of Standard Deviation of Random Variable)
Square root of the average of the sum of each semimajor axis squared and add the 50ppm * line length?
sqrt(0.00065′) = 0.025′
0.025’+0.005′ = 0.030′ (Tested; passed)
GaryG replied 1 year, 4 months ago 8 Members · 30 Replies 
30 Replies

It will be interesting to see if someone in the know posts how different software packages approach this.
I have been in professional development courses where it is suggested that the addition method you posted is the way to go. But I think that was mainly because it was the simplest to convey.
With the computing power we now have at our finger tips, are the software developers using the error ellipse orientation and calculating along the point on the ellipse towards the other point? That seems like overkill for the small numbers we should hopefully be dealing with, but given the computing power of a PC would that not be possible?

The way I understood it and asked in a different place here and I was asking if i was correct on what TBC was doing. The .036 is how much error you have. Then 50ppm devided by 1 million times the 100 gives you the .005 now that you have the scaler add that to .07 so your allowable is .075. .036 to .075 you passed. The factor or ratio I can??t remember now. Comes to be less than 1 so pass. If greater than 1 it would fail if I understood all of it correctly. I am out dealing with foot rot on cows because of the long wet spell the. Long freeze. If my memory serves me correct there is a few videos on the almighty you tube one with nsps about this and after asking here cking the math on TBC report and those videos i have been doing it that way. Maybe someone else could confirm. I am still not sold on the whole rpp vs rpa and the math. I understand what they are trying to do. But at one time they called it relative p accuracy or something vs relative position precision. It was a whole thing people were upset about. Fgcc standards have a way to compute relative positioning accuracy as well. I can??t remember that formulas for network vs local or absolute off the top of my head. Thats the hardest thing is land surveyors will state accuracy but it is used slightly different than accuracy as I learned. We can be within 95% confidence to the datum. So we can never achieve accuracy greater in that regard higher than the order of monument we came off of. Like harn 2nd order monument. Then there local accuracy on our network itself. Which tends to be more about the relative type we use on land surveying side. In a way. Hopefully bill or rover or john some of those smart folks correct me where i am wrong.

From Starnet Output
Inverse From: HLS1 Desc: RBCS
To: HLS2A Desc: RBCSBearing: S581138.38E
GridDist: 286.9671
ElevDiff: 9.8752Station Coordinate Error Ellipses (FeetUS)
Confidence Region = 95%Station SemiMajor SemiMinor Azimuth of Elev
Axis Axis Major AxisHLS1 0.019532 0.000003 6756 0.034637
HLS2A 0.026576 0.013663 8016 0.025257Relative Error Ellipses (FeetUS)
Confidence Region = 95%Stations SemiMajor SemiMinor Azimuth of Vertical
From To Axis Axis Major Axis
HLS1 HLS2A 0.032828 0.014029 7503 0.042867Now I’m curious.

@gary_g if i use the method i am very close to your relative answer from starnet i get .03298155. For relative. I compute the allowable to be on that grid distance as .0843486. Which I don??t see allowable in that but its close to what it is by long hand and I might have fat fingered my phone calculator. But it is something to ponder. Starnet might be using the covariance matrix. I am usually very close on tbc as well I think i ck to third decimal place in that alta report as i just spot ck. And if I understand correctly by using the semi major and using the method it is only estimating it. Being that close it could be a significant figure and or rounding issue. Does starnet compute the allowable as well on any two given points. Man it has been years since i read a starnet file.
I did it to 3 decimal places and 4 so I think the squaring of both semi major adding together and square root is basically the same if you round starnet to 3 decimal places in relative.033 so a rounding or significant figure on my part long hand makes a difference. of course my eye ball enhancers are in the truck and i am watching a rerun of bonanza so my weighting could be off lol.

Starnet calculates the Station and Relative error ellipses on everything but side shots. You can use inline options to compute relative error ellipses between any two points. I did not show the ALTA test part of the report, sorry I can do that when I’m back at the computer.
I did a quick search for starnet formula on error ellipse co putions but came up with nothing.
I started thinking if there was a way to do an adjustment, set your boundary, input computed coordinates for corners not found and re run the adjustment to get relative error ellipsesand the ALTA test report for the entire boundary. As I’m typing this that probably won’t work since there would be no new raw data.
Just thinking outloud.

@gary_g i have asked that question as well. Ok i do a alta and have a non found monument but everything i have traverse control passes alta requirements on rpp. I set the missing corner. Do inl need to reobserve that corner add that a re do my network adjustment and re check all RPP values to technically meet the standards. I guess technically i would. In reality i would set corner ck my bs. Either do a new set up bs a different point or measure some rounds to bs fs and new set corner as a ck. Heck most are not even computing RPP many are not even doing a least squares. So much to learn for sure. I do know every corner i have ever set i have re bs and re observed or bs the monument itself and cked into a known control point as a check as i have always felt if i set this wrong my LS could be in a pickle. It would be my fault not his but he would be to blame. I usually get asked why i do the extra checks by a manager in office when i was in the field years ago and at the last place. I said well every measurement has error. And i can live with that but if someone comes behind me they better not have an excuse of not hitting my rebar and cap because I messed up. We use to set a bunch for subdivisions and chain at minimum between fronts and then backs. As robots got better we would set a bunch then move locations and re ck them all looking for a blunder. Etc we would find one here and there.

Here’s a RPP report from TBC and my dataset’s error ellipses at 95%.
The RPP report states that relative precision is the rootmeansquare of the semimajors, but I’m not so sure that it’s calculating that. It appears that TBC adds the two semimajor axes, squares it, divides it by 2, then takes the root of the whole thing.
EDIT3: adding the squares of the major axes and then taking the root of the resulting sum as @olemanriver thinks fits the examples given, but still isn’t an RMS computation that TBC is claiming it’s doing (if its definition noted within its ALTA/NSPS Allowable Relative Tolerance Report is to be taken at face value). Either way my “suspected method” doesn’t work. Shame on me.
Example:
504>605 = 0.04071 ft per the report
RMS: sqrt((((0.02682)^2)+(0.03062^2))/2)) = 0.02878704>705 = 0.03881 ft per the report
RMS: sqrt((((0.02701)^2)+(0.02788^2))/2)) = 0.02745
EDIT: quick conclusion because I forgot to add this in… so in reality per the above: you could say that TBC’s RPP report is more stringent than actually calculating RMS. *IF* my suspected calculation method is correct.
EDIT2: @michiganleft by how I interpret the ALTA minimum standards, it calls for RMS. See snippet from minimum standards below.
Relative Positional Precision can be estimated by the standard deviation of the distance between the monument or witness marking any boundary corner of the surveyed property and the monument or witness marking an immediately adjacent boundary corner of the surveyed property (called local accuracy) that can be computed using the full covariance matrix of the coordinate inverse between any given pair of points, understanding that Relative Positional Precision is based on the 95 percent confidence level, or approximately 2 standard deviations.
EDIT3: removed “suspected method” (sqrt(((major axis1+major axis2)^2)/2). It doesn’t work 100% of the time. The result is close, but no cigar.

I stakeout to set a new corner then reobserve what I stakedout as if I found the corner. So I might have point number 300. I store a 300SO from the stakeout routine. Then my boundary location point is 300LOC. I was thinking I could put that 300LOC data back in the adjustment to calc the error ellipses. But, then all the statistics will update and the adjustment will be a little different.
I can’t get back to this till next week but I’m gonna contact StarNet for any input.

Ok i do a alta and have a non found monument but everything i have traverse control passes alta requirements on rpp.
The key here is that the MONUMENTS need to pass muster, not your traverse control. Yes, you could intuit that if your traverse control passes muster you’re probably fine… but horseshoes and hand grenades.
Quoting the minimum standards for everyone’s reference.
The following measurement standards address Relative Positional
Precision for the monuments or witnesses marking the corners of the surveyed property.EDIT: if it was me in that situation I’d see 2 potential options moving forward: [1] readjust after setting the monument (readjusted values of other coordinates would probably be minimal if your initial work was tight to begin with… I usually see a couple thousandths at worst if you see deltas larger than that you could argue your initial adjustment may not have been as good as you thought it was…), or [2] just have a separate adjustment where the control points you used to set the monument are held using the standard errors derived for those points from your initial adjustment. In essence you’re processing your asstaked positions as secondary control. From there spit out a report and you’re off.

And @steinhoff uncovers the real issue: Monuments.
So we have “today technology” and “today measurement” standards. That’s nice.
So what?
What if the original survey was to the nearest 0.1′, or nearest 1 link, or nearest 1′?
It’s nice that I can report some math about how well I did today, but if that math does not relate to 125+ years ago, what good is it?
(i.e. if they were lucky to hit the top of the 4″x4″ cedar post for a PLSS corner within 1′ – xx+’, who cares that I can hit 0.07’+50ppm, or better today?)
(This is about the ability to measure (correctly), not what is the correct monument in a boundary survey, etc. but those matter too?!)
Which is probaby one of the reasons why they switched from RPAccuracy to RPPrecision.
I still want to know the the proper procedure is for RPP, but I also don’t understand why tight RPP matters for boundary/title lines in 2023 vs early 1800’s techniques?

marking an immediately adjacent boundary corner of the surveyed property (called local accuracy) that can be computed using the full covariance matrix
My understanding is that the full covariance matrix also addresses the correlation of the measurements between the two error ellipses of the tested points such that the probablility of the magnitude of both error ellipses together @ 95% combined is much larger than the actual/probable realtionship between them, as set in the ground. (all things being equal, rpp is a “worst case” type scenario.)

@steinhoff so when i take your two points listed and square both add to together and then take the square root i match what your tbc report sais. I don??t get the divide by 2 yet. But i am barely reading the numbers. So 8 6 could be transposed i know on my end. But i match the exact tbc numbers. I did not compute the allowable because I think we all have that down. Its the relative between programs that seem to be slightly different which could be a number of things. Starnet could be aligning all rotation of error ellipse or using that as part of the equation as well. I have never missed a spot ck yet on a tbc report long hand but that doesn??t mean i am 100% correct either. You and others all come very close and truly our differences so far are so far in the decimals place. I guess the divide by 2 could be technically correct but it states i am going from memory. A direct line between the two on semi major axis. So when i was reading the problem and building my first formula i intrepid it as if we are basically inversing. But the thing that trips me up is we only use the semi major axis and not both semi major and minor which the first time i did this I set it up as semi major and semi minor as a delta major delta minor. But that didn??t work either lol. Once i did it the way i have stated it worked and then i we went out and asked Trimble rep asked here and such. I don??t usually check much pass the 4th decimal place i am usually at 3. I work mostly in feet now use to meters so its more comfortable looking at 3 decimal as i am use to it. It??s one place further than I would put on a plat or sketch of any kind. I guess if i were working in meters i would possibly show 3 decimal places. But once we start saying we are measuring to a half a hundredth of a foot on a typical boundary we are fooling ourselves.
I could do the readjust like you say and watch after setting and re observing and understand that for sure. I can really easily get down in the weeds on measuring. That comes from the curse of metrology measurements. Think of it like this we collect as a surveyor say a haf a million points by scanning around a building. Take and scan something the size of a pencil eraser and have a half a million points on that. Thats my metrology side of my brain. I would create tin and surfaces on fragments from bullets and such. Talking about a surveyor like me walking into that hornets nest. I did learn a lot though i need to get my books out there is a author that I trained under that was a bug least squares person in that arena. It was pretty neat. Except trying to look at all those digits past the decimal. I used my redneck calculator a lot counting on my toes and fingers. Those laser trackers are some very precise pieces of equipment. And you don??t have to level them in some cases as its all 3d xyz. Not earth center earth fixed. Just relative. You can mount the to walls equipment upside down sideways etc. if they ever get those for longer distances at that accuracy we will be doing some amazing stuff. But they are a toll designed to do what they do. I know NGS has used them in conjunction with other tools on measuring some antennas and sensors.
the use of the as staked point. In adjustment. Hhhhhmmmmm i don??t think you can adjust an as staked point in tbc. Now if you mean re observe to your as staked point then adjust gotcha. I don??t think any keyed in or as staked point can have anything much done to it in tbc. I know observations and any offsets etc stored as vectors or hz angle vertical angle slope distance you can. I seen a lot of people do things like off set a power pole by cogo and store as grid. But the pole computed point never moved when they adjusted a traverse or translate rotate etc.

the use of the as staked point. In adjustment. Hhhhhmmmmm i don??t think you can adjust an as staked point in tbc.
Sure you can. Convert your asstaked point in TBC. Boom. Standard sideshot.

when i take your two points listed and square both add to together and then take the square root i match what your tbc report sais.
Either way that’s not an RMS computation, which TBC says it’s doing.

@michiganleft you may have answered a question. Why RPP and not a positional accuracy statement. Precision is what they ask for in alta. As last of the 4 requirements etc. in a boundary survey if i retrace a 1800??s section and i find original stones that have been accepted and such i am not the one to say I measured better than the last guy. I become accurate by following the blue bible(blm manual) i was taught it was the surveyors blue bible. guidelines and boundary retracement principles and that is my truth my accuracy. I do like to make good measurements though. But even on east coast running a line behind a late 1800??s or early 1900??s survey chains links etc I don??t sweat when our measurements don??t match i do try and make sure my measurements are good but i am not setting another corner a half a foot away from a axel that was set by chain and transit up and down hills and hollars just because I measured better or think I measured better. If all evidence points to that original survey monument beyond the stated distance or direction i have no desire to change that now when i find a pin cushion of several rebars all the right size and i have to try and guess which one is correct or senior or oldest i get a little disgusted lol . Had one year ago 3 rebars all touching literally so tight i truly don??t know how the flagged them dental floss would not fit between them. I did hear the story on that one someone had found about a tenth difference in a quarter mile line with several angle points along the way and thought the surveyor before did sloppy work . Don??t know about the other rebars one had to be original or close to original what do you do throw a quarter up and say heads i hold this one tails that one or bring in 3 different employees and play paper rock scissors I mean honestly anyone of them could be accepted and not one thing would change 3 5/8? rebars all squished together . I can almost understand when you find one and find another rebar a half foot down etc maybe locator didn??t work bad day hung over . But sticking out of the ground nope just not smart. The direction and distance depends on plss vs metes bounds is not the top of even priority of calls . I do though care that i make the best measurements possible within realistic means a big rural boundary vs property in the city I approach a little different now i get an alta on a rural track that i know client is about to do something with commercially develop i tend to be much tighter on I don??t want my measurements to cause issues .

@olemanriver I don’t think any of these standards from ALTA mean you modify your boundary determination.

I don’t think any of these standards from ALTA mean you modify your boundary determination.
Agreed. In my eyes this standard is just a matter of proving out that the relationships between monuments/witness you??re reporting (IE your measurements) are repeatable.
What you do for boundary determination..? Whole different ballgame.

@gary_g yes sir I don??t believe that either. It is just one portion of the alta the reason for rpp is to just try and get better quality data and ensure quality a bit better. I mean in most states the precision of 1:10000 or 1: 5000 or 1:20000 precision ratio statements were developed under the days of chains rods and 20? transits. The 1:20000 is not a lot different than the .07 50ppm just a different way of looking at it. Versus the old compass rule. I do believe that they should have made it an either or type thing versus mandatory least squares in some regards. I like least squares but I don??t believe its the almighty gold standard either.


@mathteacher thank you for posting for sure. I will enjoy reading this tonight. I did see it was 2011 but it should help us all see where we need to be focused. I think from 2011 to now they made a few changes wording mostly as if my memory serves me correct it was almost impossible not completely impossible to meet the standards of precision in some situations where small boundaries lot surveys and or property corners were very close together on the boundary. It is not uncommon to have a good size boundary here in the east say 15 acres more or less but on that boundary to have property corners only a few feet from one another. In that case or situation it usually blows up the rpp between those sometimes of allowable. Just to small a distance. There is a clause in the new standards that gives a surveyor an out in these situations because of terrain and such size shape all plays into this.
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