I've been tinkering with an idea this past week & was hoping to get some input on why it's a terrible idea or what I've overlooked.
Im not a fan of conveying ideas strictly via text, especially technical ones so bear with me if I do a poor job of explaining myself.
When carrying elevations using a total station in most circumstances your Hi/Ht measure up is the largest source of error introduced into the vertical axis. What if we could eliminate this source of error from "compounding" through the traverse?
With 3D traversing/trig levelling, we typically take the elevation from a point on the ground and project it to the trunnion axis of the TS with a zenith angle, SD & HT. Then we can define the height of our physical setup point using the Hi to project the elevation from the trunnion axis to that point we're setup over then carry the elevation to the next point using another ZA, SD and Ht. Then we move to the next setup and project the elevation from that control point up to the trunnion axis via the Hi measurement and carry on from there.
But I propose we don't have to do this. Every Ht and Hi adds unnecessary error that stays in the network so that points further along in the network are not only influenced by the 10+ other sources of error that affect height determination from a total station but also the Hi/Ht measure ups.
Why not use a braced traverse with common points on each leg and post-process your data in a way so that the networks elevation is carried through these common points from trunnion axis to trunnion axis of each setup and while the elevation of each point is being defined by the Hi/Ht, the network elevation that's being carried along stays in those common points.
I ran a 1500m traverse over the weekend through a neighborhood with 15 setups using ball prisms on power poles for my common points and fixed height targets for every other BS/FS. That traverse closed out to 1.1mm vertically when I processed the data as is with no manipulation to the raw observations (15mm horizontally but I wasn't testing for that).
I then post processed the data in the way I described above and it closed to 0.2mm. Keep in mind this is the traverse closure, not the accuracy of each point. Of course Im not/cannot measuring each point's Hi to 0.2mm but it's an indication that error is going down. Albeit a weak one because these values are ridiculously small.
I then degraded the Hi/Ht measure ups at random for about 60% of the setups to a max of 3mm error and took away the common points. I did this to highlight the effectiveness of this method for those not using fixed height targets or maybe not being as careful on Hi measure ups. It closed to 6.7mm.
I added those common points back in and it closed to 3.5mm.
I then post processed it using the method described above and it closed to 0.2mm, same as without the bad Hi/Ht's introduced because those Hi/Ht's are not altering the final closure of the traverse (provided your initial and final Hi/Ht dont have "extra" error as the Hi is still being used to define the elevation of each individual point from the trunnion axis).
This was all based off a paper I read from Jesse Kozlowski. Im just tweaking his idea a bit so I can get the advantages for eliminating Hi/Ht from the total error equation and but still create a traverse, not just trig levelling.
This test was only one example so the sample size is weak but as far as I can tell, the theory behind the mathematics of it holds up. Those common point ball prisms I used aren't changing elevations to over 0.3mm between shots. Basically the question this method asks is "what's more accurate vertically, the Hi/Ht measure ups of the vertical centering accuracy between shots on your common points as all other factors are equal or smaller using the braced traverse method described here.
As I understand your proposal - we have a traditional point to point traverse, but between each instrument setup station we have an intermediate station which we shoot, both forward and back, using a fixed height rod to cancel out measure up errors.
I see this working in theory. Starnet doesn't allow completely freeing the measure up values, I believe, but does allow a standard error of any value. Nevertheless I'm left wondering if running levels though your control wouldn't be quicker and - at least - equally effective.
If you really need that level of accuracy, just use a level on your tripod heads at each setup
As I understand your proposal - we have a traditional point to point traverse, but between each instrument setup station we have an intermediate station which we shoot, both forward and back, using a fixed height rod to cancel out measure up errors.
I see this working in theory. Starnet doesn't allow completely freeing the measure up values, I believe, but does allow a standard error of any value. Nevertheless I'm left wondering if running levels though your control wouldn't be quicker and - at least - equally effective.
That’s exactly it.
You float the zenith observations to and from the traverse hubs in the legs that are braced.
it sounds like more effort than it is from a field perspective. It is significantly faster adding common points to your traverse vs adding a level run. No real comparison IME but this should be more obvious once I get a video out. You also get all the other advantages of a braced traverse.
I find it hard to believe it takes less time to set up these prisms than it takes to run levels. How many prisms am I going to need to do this? Do I have to buy a bunch or will I have to spend time moving the ones I have because I don't have enough? The more I imagine the steps needed, the better levels look.
I find it hard to believe it takes less time to set up these prisms than it takes to run levels. How many prisms am I going to need to do this? Do I have to buy a bunch or will I have to spend time moving the ones I have because I don't have enough? The more I imagine the steps needed, the better levels look.
This traverse method wont be faster or more accurate than a level run on it's own but we want horizontal positions too. Adding common points will be faster (IMO) than running a traverse + adding a level run after.
And the level run will be more accurate. But this method can be done with one person among other benefits. And when you start working in terrain with a lot of vertical relief, trig levelling starts to become faster on it's own than a level run but "trig levelling" depending on how you want to define that term, isn't really what Im describing here... again depending on your definition of the field procedure of trig levelling.
I more so think of this as 3D traverse with post processing to mimic the advantages of trig levelling methods as describe by Jesse's paper "Electronic total stations are levels too".
I was running 4 prisms. Two balls prisms with mag nests and screw on adapters that fit in a little box I 3D printed (about 6"x 2" x 2") one or two prism and mini tripods and my pole/bipod. Everything fits inside of my vest or can be carried so it's very transportable.
On this traverse I setup my TS on a hub, set my backsight mini (or pole if there are site line/refraction considerations) screw in a ball prism nest on a utility pole about halfway between my setup and BS, walk past my instrument, add another ball prism then walk to my FS and either use another mini tripod or my pole. The BS, FS and setup are all standard so the only thing unique is the common points. In this case I used the ball prisms that work on anything I can screw into or ferrous material that the magnetic nests can attach to or is situation where these dont exist, I'll set a mini tripod and prism. If I was using full tripod/tribrach/prism setups this would not be nearly as efficient.
It took me about 15 seconds to set a ball prism on a pole and then of course I need to walk back to it to turn it once I bump my total station, and then again to remove it once I sight it. If you have two people & get a rhythm down you can really zoom through a traverse.
The method described is *probably* more accurate than doing measure-ups alone, but the question in my mind is whether or not that increment of accuracy is worth the extra effort required.
I do a lot of pre-design topo surveys of intensively-developed sites, and I generally work in areas with very little vertical relief (gutter slopes are often 0.005, for example). I've been doing these exclusively with a robotic total station for years, and haven't had any complaints from the design or construction teams about vertical accuracy.
Measure-up procedure can also matter. Although I use a tape to measure HI (and a standard graduated pole for the HT), I measure from the ground point to a particular flat spot on the alidade so that I don't have to bend the tape in order to reach the index mark on the side of the gun. I know from careful measurements where that flat spot is with respect to both horizontal and vertical axes, and I have a function programmed into the HP-48 emulator on my phone that converts the measured distance to a vertical HI. The result is close to, but slightly better than, the old "measure to the index mark and cut 0.01 foot" approach.
We ran a ton of traverses with a total station ignoring a measure up that using GPS requires. Just do your best to balance your shots to be somewhat close to equal to minimize errors. Roll on. Be careful to keep the shots such that you are clearly observing the center of the crosshairs. Just because you can see the prism a mile away does not ensure you are sighted on what you think you are seeing.
The method described is *probably* more accurate than doing measure-ups alone, but the question in my mind is whether or not that increment of accuracy is worth the extra effort required.
I do a lot of pre-design topo surveys of intensively-developed sites, and I generally work in areas with very little vertical relief (gutter slopes are often 0.005, for example). I've been doing these exclusively with a robotic total station for years, and haven't had any complaints from the design or construction teams about vertical accuracy.
Measure-up procedure can also matter. Although I use a tape to measure HI (and a standard graduated pole for the HT), I measure from the ground point to a particular flat spot on the alidade so that I don't have to bend the tape in order to reach the index mark on the side of the gun. I know from careful measurements where that flat spot is with respect to both horizontal and vertical axes, and I have a function programmed into the HP-48 emulator on my phone that converts the measured distance to a vertical HI. The result is close to, but slightly better than, the old "measure to the index mark and cut 0.01 foot" approach.
Yea so that is the question in my mind. Is the juice worth the squeeze.
If you're using a fixed height rod (or adjustable height with good repeatable vertically) I think the difference will be small. With my Trimble gun I can measure the slant height to the bottom notch and Access automatically converts the slant height into a vertical one, adding the vertical offset to the trunnion axis. I like to think I can measure HI to 1-2mm is most cases. If someone is measuring HT to the side of a prism on a tribrach or eyeing out the center I think there is more room for error there.
Mathematically speaking I can't see a valid counter argument to IF its more accurate, unless Im missing something which is very possible. We're essentially comparing the accuracy of the Hi/Ht measurement vs the vertical centering error of the common point. But the question of whether it's worth it or not is absolutely one that can be debated.
Bracing each leg also allows for a real time error check in the field and if something slips by (a miscentered or mislevelled prism or instrument tangent to the BS that doesn't show up in your HD check) you have the ability to salvage that setup through the common point in post processing.
I should note the common points had very little effect on the horizontal closure of the traverse. But... if you set those CP's in a place where they can be seen from other traverse hubs in the network separated by a significant geometry things would look different. Because you don't need to occupy your CPs you can set them up high above obstructions in places where they may be visible from across your network. I think there is little debate at what kind of effect diagonal lines/cross ties/an overdetermined network and good triangulation can have on a control network when processed in a LSA. You're minimizing the opportunity for small angular error to be amplified into large positional discrepancies.
What distances were you shooting? What is the average HI height and Target Heights of your main traverse legs? Trig leveling can be very good. I would imagine Jesse learned a lot of his stuff from the late Charlie Glover. He had a great system for trig leveling that had proved beyond what most could do on a daily bases. Charlie worked for NGS. Great man. The reason I ask about your average height of instrument and targets as that slope distance to true height is proportional to the height you set up. Aka. That short guy like me has an increased error of true vs the actual measured height to the scope on a total station vs someone at 6 ft plus. It’s a triangle. Trimble has remedied this with the bottom of notch. Leica with the vertical laser measure up through the plummet. Using the Balls prisms which I assume you are talking about SMR’s. Technology has come so far. But one thing I would state is. If you take the best level and run in one direction and come back and can set up exactly in the same spots the. Run randomly outside of that same line say a loop you will have different answers. The manic in levels and vertical height is not only the methods but also in realizing the gravity in which you level to has to be accounted for as gravity is not the same in every exact location. Same with traversing along a mountain range it doesn’t matter how well your direct and revers or your mean angle residuals are. Gravity is pulling or pushing you period. Jesse is an outstanding individual and extremely intelligent. He is a great guy. I wish I had half or a quarter of his experience and knowledge. One thing is to remember that I have had to learn since coming back to the private sector side is what is acceptable and what is realistic in what we need to achieve on a daily bases. I did not have all that luxury when I was doing geodesic work. It had to be right the I’s dotted the T’s crossed on every set up every time and the math had to be perfect in order to claim a certain accuracy period. Every variable had to be accounted for. Gravity deflection of the vertical etc etc. in every day practice these things do not matter much where I use to sweat a mm now a tenth or so is actually not going to make me break out the Tums. lol. Do not get me wrong I over the last several years still have adopted and found a sweet spot for field procedures that are cost effective and accurate and precise enough than most perform in daily duties. If and when I can achieve my license I use to say when someone follows me they would be like dang I am all over his stuff. Now I am more about hey this guy has the right corner and didn’t cause an overlap or gap. He was a good surveyor. Nice work by the way. Not a bad study at all. Good stuff. Keep up the learning and keep posting as these things make us all better.
I am no mathematician but if we are adding and subtracting are we not canceling some of this error ?
We always ran trig levels on everything, whether you needed it or not, you just never know. On some projects levels were required and trig elevations were not accepted. On each one of those , we were well within any error budgets and proved time and time again that trig leveling was good.
If you really need that level of accuracy, just use a level on your tripod heads at each setup
I really like how Shae thinks outside the box and tries new methods, then drills down into the results.
We had been using a Leica height hook to get direct height measurements (we still do for static GPS), we'd photograph the tape to check for transcription errors, but measuring occupation height is time consuming and has no error uncertainty budget in least squares, yet we found that measuring it more than once, it could still vary by a mm or more, especially if there's a breeze that causes the tape to bend. Initially I was thinking about those Kern tripods with the 4th middle leg. Then you think about those old tribraches with four levelling screws, where the height doesn't change...
So we stopped occupying points, we still perform a traverse, with backsight and foresights, use fixed mini prisms as tie points, similar to what Shae is doing along with some ground points on mini tripods at fixed heights, then we'd measure height differences between tripods and common ground points with the level, instead of measuring occupation height, then process it all through least squares. Not so sure about our tribrach adapter contact area though. No levelling of the level is required as the tribrach is already level. Then we'd use a fixed occupation height for our total station, above the level occupation.
There's always a small difference between screws and nails, prism rod fixed height and the level rod / staff. I have thought about designing a small diameter spring-loaded tip that protrudes from a flat face, so fixed prism rod height matches the staff and can still centre properly. As the tip wore, you could clean it up on the bench grinder without affecting height as it's only for centring.
Trig. Levelling & Traversing
If you are using forced centring tribrachs with the three tripod method of traversing then essentially you are determining height differences between tribrachs. The measurement from the Target/Inst. down to the station marker is in effect an eccentric measurement.
For instance the elevation of the back station and fore station will be correct if the Targ/Inst is measured down to the station correctly but if the occupied station has been measured incorrectly only that particular Stn. Elevation will be wrong.
If the traverse is carried out independently of any other observations the short time between BS and FS observations will ensure more accurate Trig. Heighting as the dH is increased for inclinations and decreased for depressions. The most accurate way of Trig. levelling is by using simultaneously reciprocal observations from two instruments. This is because of the compensating error cancelling out the environmental effects. This of course is impractical for most operations but rapid traversing will improve results.
In horizontal positioning in traversing incorrect centring over a particular station does not likewise have a knock-on effect on the forward station. The eccentricity is confined to the mis-centred station because of the forced tribrach centring. It is always helpful if the target and instrument height axes are at the same height above the tribrach cup as you can directly compare dH back &firward during the course of the work.
To guard against faulty Inst/Target heights measure the height down in metres and feet. As mentioned elsewhere devices for achieving more accurate measurement are available from the manufacturers.