Free-Stationing 


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RichVanDam
Posts: 11

Joined: 1/9/2009
Topic  Free-Stationing       Flag »  Reply »

I am in the final year of my degree and are studying the accuracy of Free Stations in Total Stations for my dissertation.

I am struggling drawing hypothesis’s in relation and are wondering if you could offer me some advice.

 

Basically, i can not find a mathematical reason why a Free-Station should not be as accurate as a Regular set up for surveying and setting out in the Easting and Northings directions.

I am however struggling with the Zenith.

Engineers on site would tell me to keep the instrument height as Zero when performing a Freestation set up but could not explain why is there anyway you could shed light on this?

As the research i have conducted seems to indicate that  you do indeed require the instrument height. At the same time however i do not see how it is possible to obtain accurate instrument heights when working on land that is not solid. I.e. difficult locations such as clay.

I have conducted a number of practical analysis’s and it seems to confirm that indeed the zenith is out by about 10 – 20mm and are now wondering if it is because i have set the instrument height to zero.

 

Is there any help you could possible offer because there does not seem to be a lot of readily available information in regards to this topic whatsoever.

  Friday, January 09, 2009 at 2:22:24 PM
Thomas LaCorte
Posts: 62

Joined: 10/17/2008
Reply  Re: Free-Stationing Flag »  Reply »

Define "free stations" please. Do you mean a set up on an arbitrary point? I would love to answer your question, and believe I can. I'm just not understanding it do to a difference in terminology. I believe this is why no one has responded to you. Perhaps you can reword it somehow? when you talk about setting the HI to zero do you mean in the data collector? you should only need the HI for Z value's not X and Y.

This what I mean but not understanding your question but I would really like to try and help you. Hope it is not to late for your dissertation. 

 

  Monday, January 12, 2009 at 8:59:00 PM
RichVanDam
Posts: 11

Joined: 1/9/2009
Reply  Re: Free-Stationing Flag »  Reply »

Thomas,
Thank you for your response.

Free-stationing (resection) is a process whereby you set up on a arbitary point yes. I.e. you are not setting up your total station on a control point - the total station is computing the station location using the sine rule from two known points.
Like you say this does not affect X and Y at all only the Z values.
When you set up conventionally, you input the total station height measured using a tape measure from the control station to a point on the total station and also the Height of the target.
I do not mean the height of data collected, i.e. the pogo height when you start surveying.

Engineers i have been working with have told me to keep the instrument height to zero when setting up the total station using the Free-Station method (resection), but i am at a loss as to why they are doing this?

regards

Richard Dale

  Tuesday, January 13, 2009 at 12:13:19 AM
Isleno
Posts: 42
Location: Gonzales, La USA

Joined: 10/20/2008
Reply  Re: Free-Stationing Flag »  Reply »

    It might be because the truth hurts.  A resection from two points using the sign rule has no redundency, so the answer you get seems fine (no matter how off it really is).  The height can be determined from one observation, but there are two observations (solutions) and they will not agree.  Try a resection from three are more points, if the program will alow it, and you'll get the same fuzzy result.  The "Free-Station" method does not discover the measurement errors in x & y because there is only one solution.  The heights have two conflicting solutions (becasue of measurement error) so it is easier to disregard both by setting the value at zero.

    The 10-20mm variation you are finding in the height exists in the horizontal as well, you just don't know it.

  Tuesday, January 13, 2009 at 9:07:20 AM
RichVanDam
Posts: 11

Joined: 1/9/2009
Reply  Re: Free-Stationing Flag »  Reply »
Isleno,
I am comparing the method to a conventional setup of an instrument by surveying 15 points using both methods and same stations.
The values are identical X and Y just not in the zenith.
Plus there is redundancy as the total station uses a Least Squares Adjustment to obtain the most likely value for the stations and reports by how much each was altered on the display using a resection, in addition, a third station is sighted to see how accurate the resection (freestation) has been in regards to the local grid, all have been within 1mm including the height.
Regardless of that though,

I am just trying to understand basically why you need to put your instrument height as zero before you perform a resection (freestation) when the manual tells you to measure it.


  Tuesday, January 13, 2009 at 10:53:01 AM
Isleno
Posts: 42
Location: Gonzales, La USA

Joined: 10/20/2008
Reply  Re: Free-Stationing Flag »  Reply »
RichVanDam:
                In that case, the answer is "I don't know".  If you figure it out, please post it.
  Tuesday, January 13, 2009 at 3:47:22 PM
RichVanDam
Posts: 11

Joined: 1/9/2009
Reply  Re: Free-Stationing Flag »  Reply »
:(


Any experts out there that can help me
  Tuesday, January 13, 2009 at 3:50:46 PM
Isleno
Posts: 42
Location: Gonzales, La USA

Joined: 10/20/2008
Reply  Re: Free-Stationing Flag »  Reply »
RichVanDam:
            I don't think I understand what you are asking.  There is no way a redundent set of observations for 15 stantions has a standard deviation of 1 mm.  A total station with optical or plumbob centering can not be taken down and reset to within 1 mm.  If you have fixed stations (concrete posts with a tribrack reciever poured in place), maybe.  Most total stations have a standard deviation of 5mm in distance measurement alone.

            Maybe somebody out there can help.  As for me, yo no se.
  Tuesday, January 13, 2009 at 4:23:46 PM
RichVanDam
Posts: 11

Joined: 1/9/2009
Reply  Re: Free-Stationing Flag »  Reply »
????


Ok

When you set up a Total Station, you either set-up conventionally (over a station and backsight another) or your can perform a free-station (resection - sight two points the total station computes its most likely co-ordinates based on the sine rule adn with a least square adjustment applied).

I am comparing the two methods!

So i am surveying 15 pegs with targets set on them.

I survey them using both methods from stations i have set up.

  I am trying to understand the mathemetics behind why you set your total station with a instrument height of zero and not measure it with a tape measure ad input it into the total station before it performs the program.


Conventional set up - input instrument height, and target height

Freestation (Resection) - Instrument height = 0, and input target height   WHY?
  Tuesday, January 13, 2009 at 4:30:23 PM
Isleno
Posts: 42
Location: Gonzales, La USA

Joined: 10/20/2008
Reply  Re: Free-Stationing Flag »  Reply »
OK:
    If you only sight two targets to compute the resection, it is a simple soultion.  Least Squares adjustments don't occur because there is no redundency.  The program runs, but no adjustement is made to the simple solution.  More than two targets must be observed before a solution is computed in order to arrive at a least squares "adjusted" position for the Total Station.  
    The Instrument elevation can be computed from a single observation from a free-station set-up.  Trigonometry tells us that the elevation of the farsight + the height of the target above the farsight - the sin(zenith angle) x slope distance = elevation of the instrument.      
    Two observations (the minimum to establish an x & y), will produce two height values for the free-station which are adjusted by the program.
    The elevation of the point occupied = instrument elevation - instrument height.  If you are not interested in the elevation of the point over which you have placed the instrument then instrument height is zero.
    This is my last stab at it.
  Tuesday, January 13, 2009 at 4:55:57 PM
RichVanDam
Posts: 11

Joined: 1/9/2009
Reply  Re: Free-Stationing Flag »  Reply »

Isleno,  this is just the answer i was looking for.

 

Just for reference there is redundancy;

http://www.leica-geosystems.com.cn/newsletter/System1200_28_Resection_1.pdf

The Sokkia SET4130R3 also displays the redundancy correction after the freestation (resection) has been performed - which is the instrument i am using to perform the studies.
 
The redundancy in values of Eastings and Northings to which the two point resection (FreeStation) i have been getting redundancy's of upto 1mm. Mostly they have been less than 1mm.


Thank you again

 

 

  Tuesday, January 13, 2009 at 7:08:10 PM
Thomas LaCorte
Posts: 62

Joined: 10/17/2008
Reply  Re: Free-Stationing Flag »  Reply »
It is amazing how a question "pops to life" when you reword it!! GOOD JOB ISLENO!! I am sure RichVanDam appreciated your sticking to it!! You have great patience. My hat is off to you.
  Tuesday, January 13, 2009 at 8:32:53 PM
Isleno
Posts: 42
Location: Gonzales, La USA

Joined: 10/20/2008
Reply  Re: Free-Stationing Flag »  Reply »

RichVanDam:

            The redundency that the publication you refrred to requires three or more, prefferedly more, observations to arrive at a Least Squares solution.  If you only use two observations the is only one unique solution so the variations will always be near zero (roundoff prevents it from being perfectly zero).  Perform the resection using four or more observations to known stations and you will see what I mean. 

  Wednesday, January 14, 2009 at 1:25:22 PM
RichVanDam
Posts: 11

Joined: 1/9/2009
Reply  Re: Free-Stationing Flag »  Reply »
Isleno
I was under the impression that this was occurring in two point resection as well.
To what is the total station displaying when a Free-Statino has been performed on the display?

I interpreted as a adjustment of the three points (computed from two control stations).

The display looks like this when i do a freestation:-

N = 0.0008
E = 0.0002

Indicating what i thought that the 3 point system have been adjusted by those values using a least squares adjustment?
Am i wrong?
  Wednesday, January 14, 2009 at 1:36:29 PM
Isleno
Posts: 42
Location: Gonzales, La USA

Joined: 10/20/2008
Reply  Re: Free-Stationing Flag »  Reply »

    Yes.  Locations computed from two control stations have no redundency.  The data is sufficient for a unique solution.  Resection solutions do not compute or adjust the locations of the control stations, only the "Free Station's" x, y and z values are calculated.  

    If minimum input is applied to a Least Squares program the Free Station has only one solution.  So the average is the solution.  When the deviation of the solution from the average is computed (the solution is also the average) the result is zero.  Round off in the computations present N=0.0008 and E = 0.0002 because of the significant figures being calculated.  The true answer is N = 0 and E = 0.  Try using three or more control stations.
  Wednesday, January 14, 2009 at 2:06:57 PM
sloppy
Posts: 8

Joined: 5/12/2009
Reply  Re: Free-Stationing Flag »  Reply »
Hi

I am another so called student studying Civils as opposed to Surveying.
I am after information on how the total station actually positions itself using a two point resection and one with three or more points. I sort of grasp least squares, but struggle a little when it comes to applying it to surveying. My aim is as to prove that I can calculate and understand two point and three point resections with least squares adjustments.

I will be forever grateful if someone could help me, as I feel like i have hit a brick wall.

Kind Regards
 S
  Tuesday, May 12, 2009 at 8:59:30 AM
RichVanDam
Posts: 11

Joined: 1/9/2009
Reply  Re: Free-Stationing Flag »  Reply »
Sloppy.
I am actually studying civils; the study's i was doing here were a set of practical experiments that i abandoned where i was trying to negate distance as a variable in regards to free-stationing where i was getting 20mm error in the zenith.
The guys on the board really helped me out in regards to the fundamentals of how it all happened.
Applying a Least Squares Adjustment shouldn't be too difficult if you have the write software to do it, mathematically its a itterative process that is open to massive amount of errors as you know.
The total station uses a program called free-stationing whereby it utilises the sine rule, so maybe thats a good starting point, higher end machines also apply a least squares regression after to the co-ordinates once the values for the stations have been achieve.

It would be just a simple case of applying the sine rule to two points based on the distance from those control points, and then performing a least square regression. If you want i will post exactly the information i have on how a total station computes its co-ordinates based on such?

  Tuesday, May 12, 2009 at 12:37:14 PM
sloppy
Posts: 8

Joined: 5/12/2009
Reply  Re: Free-Stationing Flag »  Reply »
Ill take any information you can give me. Thanks.

Correct me if i am being dense, but when the instrument uses the sine rule for two known stations, it has one angle and two distances.... If you apply the sine rule you can effectively find out the as-built distance of your base line between the stations. Say for example it is 10mm short, how does the instrument compute the residuals and position itself?

My thoughts were that it splits the difference and will give you the same error on both stations. Then I know for a fact that when the Trimble S6 calculates a 2point resection it will spit out both the error found and its correction, E, N, Orientation.

Does the instrument take on least squares of a 2point resection?

Kind Regards

S
  Tuesday, May 12, 2009 at 12:53:32 PM
RichVanDam
Posts: 11

Joined: 1/9/2009
Reply  Re: Free-Stationing Flag »  Reply »
You seem to know plenty about free-stationing i thought you were looking for infomation on it, i could have used your knowledge! Too late now though. What are you doing at this point in your studies that requires this information?

Its my understanding that:-
Yes it has one angle and two distances - the distances are measured using the EDM of the total station however, your not actually "working out" the distance. I think you have answered your own question in stating a equal adjusment of the co-ordinates has occured with the onboard program of the total station.
As you state the residuals are CLEARY stated once setting up has completed and must be carefully evaulated anything over 1-3mm and i would perform another freestation.

I was under the impression a Trimble S6 (funny you should mention that) can perform a least squares regression of the three co-ordinates once obtained to compute the "most likely" co-ordinate for each.

If you apply traversing to the situation and solution maybe you can image the process

Richard



  Tuesday, May 12, 2009 at 1:15:50 PM
RichVanDam
Posts: 11

Joined: 1/9/2009
Reply  Re: Free-Stationing Flag »  Reply »
Sorry i read your statement incorrect - yes you are working out the distance between the Control Stations, this used in conjunction with the angle the rest can be achieved!
I'd just like to point out that i am pretty far from an expert on surveying and just offering a opinion based on my interpretation of my studies.
  Tuesday, May 12, 2009 at 1:19:52 PM
sloppy
Posts: 8

Joined: 5/12/2009
Reply  Re: Free-Stationing Flag »  Reply »
well thanks for trying to help me out. Maybe an expert wil reply in the near future.

Refering back to your statement about re-doing a resetion between 1-3mm, I really dont know what instruments you have been using, but i believe that 1-3mm on a 3" instrument that has a distance of +-3mm 2ppm is not that bad.

I have ased quite a few people about this problem I have, but they all refer me to starnet or just to give up. I don't really want to do that. Thanks again for your feedback,  will endeavour to get to the bottom of it.

Kind Regards

S


  Tuesday, May 12, 2009 at 3:56:21 PM
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