Wikipedia: Resection (Free Stationing)

I don't like the use of the word "bearing" when it should say "angle." We turn angles and compute bearings.

Bearing is correct. In the Free Station method I use in SMI, the two known points have calculated known coordinates and therefore a known bearing and distance. 2PFS assumes them correct and calculates a bearing and distance to Point A, calculates a bearing to Point B and holds it. The precision error it reports is the difference in the calced Points A to B less the observed A to B divided by the former. Even a 1/200 precision can get the job done and error in 1' in 200'. That is usually close enough to get you on the deed system and close enough to find other points. It is seldom necessary to adjust any further in the field. There are times when the error shows you one of the assumed points is not what you think it is so you look further and find it. SMI assumes Point A has a more precise position than point B. Strength of triangles has nothing to do with your point selection.

Only once did I find in doing a 2PFS on a recent project that I was not happy with the Precision. Since a third known point was available I did a second 2PFS and was not quite able to immediately determine which point was off so I meaned the 2 sets of 2PFS point coordinates and everything was within my error budget. If I had not been happy I would have done a third combination and meaned all 3.

From what I see I do not think SMI uses an LS solution just a best fit of bearing, distance, bearing.

Paul in PA

I think the article is excellent - although I do agree with foggyidea that the bearings are not known until the position of the instrument is calculated.
You do a good job to explain the different types of resection.

After a LSA free station is performed "the errors" are shown. I have found there to be misunderstanding about this. What is shown is generally the standard deviation of the residual errors as a whole, OR, the individual residual errors.

Maybe the "Design of the Backsight Point Configuration" section could do with a diagram or two showing good and bad configurations.
Your analysis that the stations should surround the working area is spot on.

Well done

I also use SMI

The coords of the first entry will be held and the result will rotate to the direction of the second entry.

I always stake to other points to see if the results hold are good enough for control.

Depending upon the accuracy needed, I usually resect using the results of many points and average the unknown position.

Still it is best to not set control any farther than either control shot taken for resection without traversing onward to a closing point.

A Harris, post: 357054, member: 81 wrote: I also use SMI

The coords of the first entry will be held and the result will rotate to the direction of the second entry.

I always stake to other points to see if the results hold are good enough for control.

Depending upon the accuracy needed, I usually resect using the results of many points and average the unknown position.

Still it is best to not set control any farther than either control shot taken for resection without traversing onward to a closing point.

used to call this a "swing".
not really comparable to a multi point free-station/resection solved by LSA.
although for the two point scenario it should give the same answer if the errors are small.

for all those north of the equatorial line we do refer to bearings as bearings here.
I'm not sure if I've ever used 'angles' other than to refer to 'included angles', derived from observing bearings. Yes the assumed or uncorrected ones before any adjustments.
It's our convention here so Darwipli as an Aussie is also writing as an Aussie. (I guess that to be the case)
We also refer to a bearing Datum which in most cases is MGA (Mapping Grid of Australia)- all if cadastral surveys.

On a more related matter, one of the most simple of calculations is an observation to a distant known point (Trig on a mountain - bearing only) and another to a very close-by known point but observing bearing (included angle) and distance.
Then its basic maths to work out the position of instrument.
I could never fathom why Field Genius didn't offer such a simple procedure.

This is called an eccentric station setup in Trimble Access. Don't need to do anything special just 1 angle and distance observation and 1 angles only observation (in the resection routine).

When you are doing a backsight or other station setup you need to measure at least 1 horizontal angle to set the orientation. After this the horizontal angle read on the instrument may be the same as the bearing depending on how you're working.