Looking at the error elipses on a traverse run through Starnet, it seems clear that the farther you go...the more angles you turn, the larger the potential error (as indicated by the size of the elipses). This makes sense, because the most likely position of the next point depends, in part on knowing where the previous point is.
Therefore, if this is true, does it make sense to divide up traverses into smaller chunks, starting from the same point? 
In this simplified scenario, would the results using least squares be any better traversing from 1 to 2 to 3, then 1 to 4 to 3, as opposed to just running 1 to 2 to 3 and back to 4?
Hello rfc,
Short answer: no.
Looks like you are doing something wrong/unexpected. If 1 is a fixed station why is there an error ellipse on it in the first traverse but not the second? You're obviously not comparing apples with apples; the traverses mustn't contain the same observations if this is happening. I'm assuming you are talking about two closed figures as you're descriptions do not make this clear.
rfc, post: 330986, member: 8882 wrote: Looking at the error elipses on a traverse run through Starnet, it seems clear that the farther you go...the more angles you turn, the larger the potential error (as indicated by the size of the elipses). This makes sense, because the most likely position of the next point depends, in part on knowing where the previous point is.
Therefore, if this is true, does it make sense to divide up traverses into smaller chunks, starting from the same point?
The error ellipse at 5 is for an unnamed point 5. In LS when you make 5 = 1 that error ellipse disappears and the ellipse at 2, 3 & 4 get readjusted. You do say which point you first occupied, 1 or 2 and at which point and what observations where made. I am assuming from the left sketch: you occupied 1, then:
BS X, @ 1, FS 2
BS 1, @ 2, FS 3
BS 2, @ 3, FS 4
BS 3, @ 4, FS 5
You merely have closing coordinates, but not a closed traverse.
To fully complete a traverse worthy of LS adjustment you need to do one of the following:
BS 4, @ 1, FS 2
or
BS 4, @ 1, FS X
Redundant redundancy is what is required.
Paul in PA
I hesitate to respond as I am not clear what you are trying to say. Your diagrams do not help. Probably my problem.
Nonetheless, the statement you make to the effect that one can obtain better results with fewer results is directly contradictory to the purpose of least squares.
First of all, no least squares solution is possible with only the minimum number of observation made. A problem with zero degrees of freedom will yield one solution. Your second scenario implies that to me.
Secondly, one critical element in determining good results via the method of least squares is the correct determination of observation weights. Appropriate weighting based on instrument specifications and observation procedures can be challenging.
Third, making a series of small networks is not really what you want if you are trying to get the best fit of points over a large area. While it is possible to get very precise results over small areas, collecting them into a larger network can lead to a mess. Look up Helmet blocking and read Dr Milbert's report on the NAD 83 (2007) adjustment.
While I am not familiar with StarNet, I assume it includes an option to enter pseudo-observations and a priori weights in order to optimize your network. In other words, these tools allow you to plan how you will observe your network in order to achieve your intended accuracy. Making too many observations is expensive; making too few will increase the likelihood that your survey will not meet standards or be robust enough to find problems.
I hope I have not too badly interpreted your posting.
Cheers,
DMM
Conrad, post: 331019, member: 6642 wrote: Hello rfc,
Short answer: no.
Looks like you are doing something wrong/unexpected. If 1 is a fixed station why is there an error ellipse on it in the first traverse but not the second? You're obviously not comparing apples with apples; the traverses mustn't contain the same observations if this is happening. I'm assuming you are talking about two closed figures as you're descriptions do not make this clear.
Yes, both closed figures, and yes, understood that there wouldn't be an error ellipse on station 1 if it's fixed.
Paul in PA, post: 331020, member: 236 wrote: The error ellipse at 5 is for an unnamed point 5. In LS when you make 5 = 1 that error ellipse disappears and the ellipse at 2, 3 & 4 get readjusted. You do say which point you first occupied, 1 or 2 and at which point and what observations where made. I am assuming from the left sketch: you occupied 1, then:
BS X, @ 1, FS 2
BS 1, @ 2, FS 3
BS 2, @ 3, FS 4
BS 3, @ 4, FS 5
You merely have closing coordinates, but not a closed traverse.To fully complete a traverse worthy of LS adjustment you need to do one of the following:
BS 4, @ 1, FS 2
or
BS 4, @ 1, FS XRedundant redundancy is what is required.
Paul in PA
As usual, you answered the question I didn't ask properly. I see that the choice of "x" for the back sight has muddied my question, and that either back sighting 4 @ 1 and then fore sighting 2 or X would provide some redundancy. I see now that the question was whether it's better to return to the POB from the distant point, allowing adjustment along the way (out and back), vs. starting at the POB and getting to the distant point using multiple paths.
I guess what I'm asking is that, if you have fixed your OP and BS, and want to adjust a point at the far end of a traverse, are you better off "getting there" with fewer, rather than more, stops along the way. I think the answer to that is "fewer". If so, is it better to redundantly shoot that path multiple times, or choose an alternate path of the same number of points?
Holding 1, backsighting X is one way to get a fixed azimuth.
Holding 1 and holding azimuth to 2 is a second.
In either case you need to return to 1 and backsighting 4 turn to X or 2 to get redundant observations. If you do not do that, LS will do you no good.
Minimum, number of observations are not worthy of adjustment, redundant observations are.
Paul in PA
A regular traverse is kinda useless in LS, as it will give you nothing the compass rule does not. The results will be exactly the same as the compass rule.
If you shot cross ties from each station to each other station, or set up a random place in the middle and took a direction set to each station, then you'd have some redundancy to chew on.
Use the "pre-analysis" function in starnet and you can test all the data types with some seed data. LS will set you free. Traverse is for dinosaurs.
Make a figure that closes, fix a few coordinates, type in a bunch of garbage measurements and then run it. Starnet will correct your garbage measurements, now cut & paste them back in and you have something close. Unfix everything and play with it. Put in coordinates and measurement weights that represent your instruments, see what that looks like. When I am retracing old plats I use weights like, 0.1' centering error (plumb bob on a windy day), distance constant error, 0.1', distance proportional error, 200ppm (1 in 5000) , similar with angles, half a minute, sometimes even a minute. Tighten or loosen the assumptions so that you are landing between the upper and lower bounds of the chi square test results. It's a good way to reverse engineer the shoe size of the footprints you are following before you hit the field. Helps to know what size shovel to bring along.
Oh right and: Fixed points. No such thing. Every point has an error ellipse. It just might not be published. If you are using GPS, especially RTK, to get your "fixed points", rather than setting up on one and backsighting another you get a much more precise initial position sitting the middle and doing a direction set to 3 or 4 or 5 points.
There are places in LS to use fixed points. Columbus has a neat brute force algorithm for selecting which points to fix, based on the factorial number of possible fixed points and how well the network of observations fits the points as it holds every combination in turn. With starnet I quit holding any actual field data or GPS coordinate as fixed years ago.
Different thing when using starnet to run out a deed and see how it closes or if it has typos. There I use the "fixed" ("!" delimiter) quite often, usually to hold a point to dangle everything else off of so that starnet will converge at all, or to hold a 90 degree angle from the PC to the radius point and again from the PT back to the radius point when traversing the "straight" components of a curve -- how I learned to plot it in old school CAD before the nice curve tools, and how I get parts of a curve into starnet 6.0 that only knows about straight lines.
My usual workflow is to "draw" the deeds in starnet grammar, hold a rough GPS or published geodetic point, then take the GPS for a hike and start to dig stuff up. As I get actual field data, I "unfix" things I was assuming to get going on the recon and substitute actual field measurements. As we pin things down we add the total station and level data to the starnet file. At the end of the day I have a starnet file with all the research data, record measurements and recon calcs sitting there commented out and left for the chain-of-evidence, or sitting there with no weight ("*" delimiter), plus all the field measurements and GPS and everything we need to be on the datum du jour and deliver the client's favorite flavor.
rfc, post: 331043, member: 8882 wrote: As usual, you answered the question I didn't ask properly. I see that the choice of "x" for the back sight has muddied my question, and that either back sighting 4 @ 1 and then fore sighting 2 or X would provide some redundancy. I see now that the question was whether it's better to return to the POB from the distant point, allowing adjustment along the way (out and back), vs. starting at the POB and getting to the distant point using multiple paths.
I guess what I'm asking is that, if you have fixed your OP and BS, and want to adjust a point at the far end of a traverse, are you better off "getting there" with fewer, rather than more, stops along the way. I think the answer to that is "fewer". If so, is it better to redundantly shoot that path multiple times, or choose an alternate path of the same number of points?
There is an old saying that a total work of fiction is a closed legal description; I heard that years ago when I started and it stuck with me ever since. Back in the day and even up to a few years ago there were surveyors who returned the actual measurments they took when they surveyed. Of course the figure wouldn't close but to them it was honest. Then surveys began to be adjusted, and when I was doing them traverses were adjusted using the compass rule (something you should learn, it's not all that hard and it is hands on).
Then programs came out where LS was available and those became the thing to do, most all survey programs have them intergrated now, and there is almost no time spent using them compared to the old days. They give you many options, but what you are doing and what many of us do is closing a very simple traverse, and if its weighted evenly when LS adjusted it will basically give you the same numbers as a compass rule adjustment. The point being is that these simple traverses with modern equipment should have almost no adjustment, you should close extremely tightly. Not just the coordinates but the sum of the interior angles should meet a very tight standard.
If not, then adjustments are a work of fiction as the old timers would argue.
I've seen LS adjustments applied to all sorts of data, but without tight networks those kinds of adjustments are just playing around.
Frankly until I have the traverse where I want it, I'm not going to apply any type of adjustment.
Breaking it up into smaller traverses would improve the precision, but not in the way you are saying. measuring from 1 to 2, 1 to 4 and 1 to 3, then doing every measurement from every setup (2 to 1, 2 to 3, 2 to 4....etc). Of course seeing between all of these points would be an issue. But the point is you want as much redundancy as you can get.
BTW...the then/than difference is a common misunderstanding
In theory you're certainly correct, but in practice I doubt it will make much difference. Ultimately your want there to be a minimal amount of change between measured angles and distances and adjusted angles and distances. With contemporary instruments you normally get unadjusted results that are far better than needed, so I doubt that method of adjustment or method of measuring a traverse would make much difference in terms of project requirements. However, if you really do need to get better results, i.e. less change between measured and adjusted values, far greater differences will be noticed by cross ties and making something of a spider web of connections rather than the change effected by breaking up a loop traverse into two parts. This can be simulated in Starnet before doing any field work.
Tom Adams, post: 331099, member: 7285 wrote:
BTW...the then/than difference is a common misunderstanding
Sir Tom: Just out of curiosity, was the reference to "then/than" directed at MOI? I did, in fact use both words in a single post, but pretty sure I used them properly. I know that if I were to use "than" more than "then", then there might be some that would then call me on the excessive use of "than", but, to my knowledge, that's not the case.:-D
rfc, post: 331101, member: 8882 wrote:
Sir Tom: Just out of curiosity, was the reference to "then/than" directed at MOI? I did, in fact use both words in a single post, but pretty sure I used them properly. I know that if I were to use "than" more than "then", then there might be some that would then call me on the excessive use of "than", but, to my knowledge, that's not the case.:-D
You're right. I directed it @ you, and you did use it correctly. I misread it the first time and shouldn't have put in that reference. (you asked if it would be better to do [a] then ; and I thought you meant to ask would it be better to do [a] than .) My bad. :-$
Regardless doing half-way one direction then halfway the other direction does not improve your precision. Redundancy is the key to getting a more certain solution. I think you get it. All these smart guys gave you better and more information than me.
