The ongoing Saga of "How accurate is my ancient Topcon Total Station?", a seemingly simple question, yes?
Not when Kent gets his hands on it. Nosiree.
Kent said near the end of Chapter Two:
>"If you add four, very sharp marks at minimum distances from the instrument (in other words, the targets of the test range consist of four targets about 8 ft. away at nominally 0, 90, 180, and 270 from the instrument and five more distant ones as previously described) and
>- take directions to them in the round of directions in each set, and
>- measure approximate distances to all points (+/-0.5 ft. is perfect),
>you can enter the directions in Star*Net to solve the standard error of a direction to the more distant targets allowing for the small differences in centering. In this procedure, if you are actually computing the centering errors for each setup, the more distant targets could be as close as 20 ft. as long as they were perfectly stable between sets. While one is at that, it would be easy enough to add extra setups with directions to the close targets to actually determine the standard error of instrument centering at the same time. Ten setups with directions to the close targets should be plenty.
>The solution via Star*Net is the value of the standard error of a direction that gives a standard error of unit weight in the residuals and can be easily arrived at by trial and error."
And in Chapter 3, he refined the process as follows:
>The near targets enable the correction for small centering errors at each setup. One thing to keep in mind is that all of the directions need to be measured in one session if you are using targets of questionable long-term stability such as the 1x2 stakes with applied targets. It's imperative, particularly at shorter ranges that the targets not move even by a whisker from setup to setup.
>Their purpose is to allow the computation of the instrument center for each setup in relation to the position of the instrument at the first setup. This is partly why the test has to be done at one time, not spread out over several days.
>You need to rotate the circle, and with your instrument that means physically rotating the tribrach that the instrument is attached to, and then recentering the instrument after rotation as well as you can. The inner circle of targets will allow the correction for any remaining centering errors.
I thought this endeavor was intended to provide insight to INSTRUMENT ERRORS, not "operational" setup (centering) errors.
>The instrument errors are partially dependent upon which part of the circle the directions are taken on. So, to eliminate the errors from that, the circle must be physically rotated so that the measurements are taken over quite different parts of it. This is easy to do in geodetic-grade instruments which have circles that can be rotated without disturbing the centering of the instrument."
So I completed the task...on a day hotter'n blazes (for Vermont in September...pushing 85 degrees!) It took 3 hours. Here's the setup (all the creature comforts of home...I got tired of getting kicked off the soccer field by kids who wanted to play soccer.
So now I have all the Face Left and Right observations meaned, and put into Starnet, but can't crunch with the demo version.
Here's a link to the file:
-- https://www.dropbox.com/s/werrbuauq62yjsd/TS%20Station%20Kent%20Test%20II.xlsx?dl=0
The second worksheet of the file should have all the observations as Kent recommended in Starnet.
If anyone has the time (or inclination) to take a look, I'd much appreciate it.
I did get a code that lets me activate Starnet Pro for 30 days or something, but haven't been able to make it work yet.
> Here's a link to the file:
> -- https://www.dropbox.com/s/werrbuauq62yjsd/TS%20Station%20Kent%20Test%20II.xlsx?dl=0
I'm unable to make that link work.
Why not just post the ascii text of the Star*Net DAT file here via cut-and-paste technology?
Okay, I got the link to work. What were the nominal distances from the instrument to the various targets? Only need those +/-0.10 ft. or so.
Obs. Face Left Face Right FR Reduced Mean
01A1 00°00'00" ######### 00°00'10" 00°00'05"
01A2 59°51'50" ######### 59°52'10" 59°52'00"
01A3 119°49'50" ######### 119°50'30" 119°50'20"
01A4 179°47'10" ######### 179°47'30" 179°47'20"
01A5 238°54'40" 58°55'00" 238°55'00" 238°54'50"
01A6 292°18'10" ######### 292°18'10" 292°18'10"
01V1 06°09'20" ######### 06°09'00" 06°09'10"
01V2 93°42'40" ######### 93°42'50" 93°42'45"
01V3 186°31'10" 06°32'00" 186°32'00" 186°31'25"
01V4 273°23'30" 93°23'40" 273°23'40" 273°23'35"
02A1 00°00'00" ######### 00°00'10" 00°00'05"
02A2 59°52'00" ######### 59°52'00" 59°52'00"
02A3 119°50'20" ######### 119°50'40" 119°50'30"
02A4 179°48'00" ######### 179°48'00" 179°48'00"
02A5 238°55'10" 58°55'20" 238°55'20" 238°55'15"
02A6 292°18'20" ######### 292°18'40" 292°18'30"
02A1 00°00'00" ######### 00°00'10" 00°00'05"
02V1 06°08'00" ######### 06°08'10" 06°09'05"
02V2 93°42'20" ######### 93°42'40" 93°42'30"
02V3 186°33'10" 06°33'00" 186°33'00" 186°33'05"
02V4 273°23'50" 93°24'00" 273°24'00" 273°23'55"
03A1 00°00'00" ######### 00°00'10" 00°00'05"
03A2 59°52'00" ######### 59°52'00" 59°52'00"
03A3 119°50'20" ######### 119°50'20" 119°50'20"
03A4 179°47'20" ######### 179°47'00" 179°47'20"
03A5 238°54'40" 58°55'00" 238°55'00" 238°54'50"
03A6 292°18'00" ######### 292°18'20" 292°18'10"
03V1 06°08'20" ######### 06°08'40" 06°08'30"
03V2 93°42'20" ######### 93°42'40" 93°42'30"
03V3 186°31'40" 06°32'20" 186°32'20" 186°33'00"
03V4 273°23'20" 93°23'30" 273°23'30" 273°23'25"
04A1 00°00'00" ######### 00°00'20" 00°00'05"
04A2 59°52'10" ######### 59°52'10" 59°52'00"
04A3 119°50'20" ######### 119°50'30" 119°50'20"
04A4 179°47'40" ######### 179°47'50" 179°47'20"
04A5 238°55'00" 58°55'20" 238°55'20" 238°55'10"
04A6 292°18'30" ######### 292°18'40" 292°18'35"
04V1 06°08'30" ######### 06°08'40" 06°08'35"
04V2 93°42'10" ######### 93°42'30" 93°42'20"
04V3 186°32'10" 06°32'40" 186°32'40" 186°31'25"
04V4 273°23'40" 93°23'50" 273°23'50" 273°23'45"
05A1 00°00'00" ######### 00°00'20" 00°00'10"
05A2 59°52'00" ######### 59°52'10" 59°52'05"
05A3 119°50'10" ######### 119°50'40" 119°50'25"
05A4 179°47'30" ######### 179°48'00" 179°47'45"
05A5 238°54'50" 58°55'20" 238°55'20" 238°55'05"
05A6 292°18'10" ######### 292°18'30" 292°18'20"
05V1 06°08'30" ######### 06°08'30" 06°08'30"
05V2 93°42'10" ######### 93°42'40" 93°42'25"
05V3 186°32'20" 06°33'30" 186°33'30" 186°33'55"
05V4 273°23'30" 93°24'00" 273°24'00" 273°23'45"
This is what the Star*Net input file would look like for a 2D adjustment. The "DM" lines need approximate (+/-0.10 ft. is perfect) horizontal distances to the targets appearing on them to enable the computation of coordinates good enough for the adjustment to give meaningful answers as to standard errors in directions.
[pre]
C 01 1000.000 1000.000 ! !
B 01-A1 0-00-00 !
# Set 1 - Inst @ 01
DB 01
DM A1 0-00-05
DM A2 59-52-00
DM A3 119-50-20
DM A4 179-47-20
DM A5 238-54-50
DM A6 292-18-10
DM V1 6-09-10
DM V2 93-42-45
DM V3 186-31-25
DM V4 273-23-35
DE
# Set 2 - Inst @ 02
DB 02
DN A1 0-00-05
DN A2 59-52-00
DN A3 119-50-30
DN A4 179-48-00
DN A5 238-55-15
DN A6 292-18-30
DN V1 6-09-05
DN V2 93-42-30
DN V3 186-33-05
DN V4 273-23-55
DE
# Set 3 - Inst @ 03
DB 03
DN A1 0-00-05
DN A2 59-52-00
DN A3 119-50-20
DN A4 179-47-20
DN A5 238-54-50
DN A6 292-18-10
DN V1 6-08-30
DN V2 93-42-30
DN V3 186-33-00
DN V4 273-23-25
DE
# Set 4 - Inst @ 04
DB 04
DN A1 0-00-05
DN A2 59-52-00
DN A3 119-50-20
DN A4 179-47-20
DN A5 238-55-10
DN A6 292-18-35
DN V1 6-08-35
DN V2 93-42-20
DN V3 186-31-25
DN V4 273-23-45
DE
# Set 5 - Inst @ 05
DB 05
DN A1 0-00-10
DN A2 59-52-05
DN A3 119-50-25
DN A4 179-47-45
DN A5 238-55-05
DN A6 292-18-20
DN V1 6-08-30
DN V2 93-42-25
DN V3 186-33-55
DN V4 273-23-45
DE
[/pre]
> This is what the Star*Net input file would look like for a 2D adjustment. The "DM" lines need approximate (+/-0.10 ft. is perfect) horizontal distances to the targets appearing on them to enable the computation of coordinates good enough for the adjustment to give meaningful answers as to standard errors in directions.
>
The "A" Targets were 35 feet, with the exception of A6, which was 34.5; the "V" targets were 10'
> This is what the Star*Net input file would look like for a 2D adjustment.
> [pre]
>
> # Set 3 - Inst @ 03
> DB 03
> DN A1 0-00-05
> DN A2 59-52-00
> DN A3 119-50-20
> DN A4 179-47-20 Should be 179-47-10
> DN A5 238-54-50
> DN A6 292-18-10
> DN V1 6-08-30
> DN V2 93-42-30
> DN V3 186-33-00
> DN V4 273-23-25
> DE
>
> # Set 4 - Inst @ 04
> DB 04
> DN A1 0-00-05 Should be 00-00-10
> DN A2 59-52-00 Should be 59-52-10
> DN A3 119-50-20 Should be 119-50-25
> DN A4 179-47-20 Should be 179-47-45
> DN A5 238-55-10
> DN A6 292-18-35
> DN V1 6-08-35
> DN V2 93-42-20
> DN V3 186-31-25
> DN V4 273-23-45
> DE
>
> [/pre]
Already found mistakes in my own data. ARGH! Gotta get me a data collector!
This is the output from Star*Net's blunder detection:
[pre]
Differences from Observed Directions (DMS)
From To Direction Difference
Set 1
01 A1 0-00-09.83 0-00-04.83
01 A2 59-52-03.28 0-00-03.28
01 A3 119-50-12.41 -0-00-07.59
01 A4 179-47-15.08 -0-00-04.92
01 A5 238-54-43.49 -0-00-06.51
01 A6 292-18-12.88 0-00-02.88
01 V1 6-09-24.85 0-00-14.85
01 V2 93-42-31.84 -0-00-13.16
01 V3 186-31-45.52 0-00-20.52
01 V4 273-23-20.83 -0-00-14.17
Set 2
02 A1 0-00-14.47 0-00-09.47
02 A2 59-52-09.73 0-00-09.73
02 A3 119-50-33.44 0-00-03.44
02 A4 179-47-48.89 -0-00-11.11
02 A5 238-55-15.66 0-00-00.66
02 A6 292-18-32.41 0-00-02.41
02 V1 6-08-50.94 -0-00-14.06
02 V2 93-42-32.35 0-00-02.35
02 V3 186-32-58.02 -0-00-06.98
02 V4 273-23-59.08 0-00-04.08
Set 3
03 A1 359-59-54.82 -0-00-10.18
03 A2 59-51-55.08 -0-00-04.92
03 A3 119-50-20.96 0-00-00.96
03 A4 179-47-33.57 0-00-23.57
03 A5 238-54-55.39 0-00-05.39
03 A6 292-18-09.83 -0-00-00.17
03 V1 6-08-27.64 -0-00-02.36
03 V2 93-42-31.20 0-00-01.20
03 V3 186-32-46.21 -0-00-13.79
03 V4 273-23-25.29 0-00-00.29
Set 4
04 A1 0-00-13.50 0-00-03.50
04 A2 59-52-05.83 -0-00-04.17
04 A3 119-50-22.87 -0-00-02.13
04 A4 179-47-34.60 -0-00-10.40
04 A5 238-55-04.21 -0-00-05.79
04 A6 292-18-26.93 -0-00-08.07
04 V1 6-09-06.66 0-00-31.66
04 V2 93-42-24.74 0-00-04.74
04 V3 186-32-27.03 0-01-02.03
04 V4 273-23-51.29 0-00-06.29
Set 5
05 A1 0-00-02.37 -0-00-07.63
05 A2 59-52-01.09 -0-00-03.91
05 A3 119-50-30.32 0-00-05.32
05 A4 179-47-47.85 0-00-02.85
05 A5 238-55-11.25 0-00-06.25
05 A6 292-18-22.95 0-00-02.95
05 V1 6-08-25.42 -0-00-04.58
05 V2 93-42-29.87 0-00-04.87
05 V3 186-33-10.35 -0-00-44.65
05 V4 273-23-48.51 0-00-03.51
Largest Difference from Observed Direction
04 V3 186-32-27.03 0-01-02.03
[/pre]
The inner targets appear to be somewhat problematic. The likely causes are either that the targets weren't perfectly sharp and in good contrast or observer fatigue. The direction from 04 to V3 definitely appears to be a blunder.
I got a 10 day trial with the Pro program. Clock is ticking!
Only way I could get it to work was to change all the DB lines to 01...get a "station not defined" error otherwise.
What I posted above was just the directions, without the distances to the targets since you hadn't provided them yet. This what the Star*Net input file looks like fully fleshed out.
[pre]
C 01 1000.000 1000.000 ! !
C 02 1000.000 1000.000 * *
C 03 1000.000 1000.000 * *
C 04 1000.000 1000.000 * *
C 05 1000.000 1000.000 * *
B 01-A1 0-00-00 !
# Set 1
DB 01
DM A1 0-00-05 35 & !
DM A2 59-52-00 35 & !
DM A3 119-50-20 35 & !
DM A4 179-47-20 35 & !
DM A5 238-54-50 35 & !
DM A6 292-18-10 34.5 & !
DM V1 6-09-10 10 & !
DM V2 93-42-45 10 & !
DM V3 186-31-25 10 & !
DM V4 273-23-35 10 & !
DE
# Set 2
DB 02
DN A1 0-00-05
DN A2 59-52-00
DN A3 119-50-30
DN A4 179-48-00
DN A5 238-55-15
DN A6 292-18-30
DN V1 6-09-05
DN V2 93-42-30
DN V3 186-33-05
DN V4 273-23-55
DE
# Set 3
DB 03
DN A1 0-00-05
DN A2 59-52-00
DN A3 119-50-20
DN A4 179-47-10
DN A5 238-54-50
DN A6 292-18-10
DN V1 6-08-30
DN V2 93-42-30
DN V3 186-33-00
DN V4 273-23-25
DE
# Set 4
DB 04
DN A1 0-00-10
DN A2 59-52-10
DN A3 119-50-25
DN A4 179-47-45
DN A5 238-55-10
DN A6 292-18-35
DN V1 6-08-35
DN V2 93-42-20
DN V3 186-31-25
DN V4 273-23-45
DE
# Set 5
DB 05
DN A1 0-00-10
DN A2 59-52-05
DN A3 119-50-25
DN A4 179-47-45
DN A5 238-55-05
DN A6 292-18-20
DN V1 6-08-30
DN V2 93-42-25
DN V3 186-33-55
DN V4 273-23-45
DE
[/pre]
Without knowing more about Target V3, I just eliminated it from the adjustment. These are the coordinates of the instrument at the four setups from which the standard error of instrument centering can be computed:
[pre]
01 1000.0000 1000.0000
02 999.9990 1000.0012
03 999.9998 1000.0012
04 999.9990 1000.0018
05 999.9992 1000.0020
----------- -----------
Std Error 0.0005 0.0008
[/pre]
Those give a pooled estimate of the standard error of instrument centering of:
+/-0.00066 ft. = +/-0.20mm, which is the value that several other posters, myself included, have obtained with instruments with rotatable optical plummets in our own tests of instrument centering.
In Star*Net, a standard error of instrument centering of +/-0.001 ft. would not be problematic for most cases.
These are the adjusted directions to the targets after V3 is removed from the sets:
[pre]
Adjusted Direction Observations (DMS)
From To Direction Residual StdErr StdRes
Set 1
01 A1 0-00-09.82 0-00-04.82 9.00 0.5
01 A2 59-52-05.27 0-00-05.27 9.00 0.6
01 A3 119-50-18.96 -0-00-01.04 9.00 0.1
01 A4 179-47-24.17 0-00-04.17 9.00 0.5
01 A5 238-54-50.64 0-00-00.64 9.00 0.1
01 A6 292-18-15.95 0-00-05.95 9.00 0.7
01 V1 6-09-08.35 -0-00-01.65 9.00 0.2
01 V2 93-42-36.36 -0-00-08.64 9.00 1.0
01 V4 273-23-25.48 -0-00-09.52 9.00 1.1
Set 2
02 A1 0-00-16.20 0-00-11.20 9.00 1.2
02 A2 59-52-10.10 0-00-10.10 9.00 1.1
02 A3 119-50-30.72 0-00-00.72 9.00 0.1
02 A4 179-47-44.46 -0-00-15.54 9.00 1.7
02 A5 238-55-12.54 -0-00-02.46 9.00 0.3
02 A6 292-18-32.06 0-00-02.06 9.00 0.2
02 V1 6-08-55.28 -0-00-09.72 9.00 1.1
02 V2 93-42-30.99 0-00-00.99 9.00 0.1
02 V4 273-23-57.66 0-00-02.66 9.00 0.3
Set 3
03 A1 359-59-56.98 -0-00-08.02 9.00 0.9
03 A2 59-51-55.04 -0-00-04.96 9.00 0.6
03 A3 119-50-15.95 -0-00-04.05 9.00 0.5
03 A4 179-47-25.79 0-00-15.79 9.00 1.8
03 A5 238-54-49.73 -0-00-00.27 9.00 0.0
03 A6 292-18-08.62 -0-00-01.38 9.00 0.2
03 V1 6-08-37.14 0-00-07.14 9.00 0.8
03 V2 93-42-28.38 -0-00-01.62 9.00 0.2
03 V4 273-23-22.37 -0-00-02.63 9.00 0.3
Set 4
04 A1 0-00-07.74 -0-00-02.26 9.00 0.3
04 A2 59-52-03.30 -0-00-06.70 9.00 0.7
04 A3 119-50-27.66 0-00-02.66 9.00 0.3
04 A4 179-47-43.47 -0-00-01.53 9.00 0.2
04 A5 238-55-09.95 -0-00-00.05 9.00 0.0
04 A6 292-18-26.11 -0-00-08.89 9.00 1.0
04 V1 6-08-37.47 0-00-02.47 9.00 0.3
04 V2 93-42-26.31 0-00-06.31 9.00 0.7
04 V4 273-23-52.98 0-00-07.98 9.00 0.9
Set 5
05 A1 0-00-04.26 -0-00-05.74 9.00 0.6
05 A2 59-52-01.29 -0-00-03.71 9.00 0.4
05 A3 119-50-26.71 0-00-01.71 9.00 0.2
05 A4 179-47-42.11 -0-00-02.89 9.00 0.3
05 A5 238-55-07.14 0-00-02.14 9.00 0.2
05 A6 292-18-22.26 0-00-02.26 9.00 0.3
05 V1 6-08-31.77 0-00-01.77 9.00 0.2
05 V2 93-42-27.95 0-00-02.95 9.00 0.3
05 V4 273-23-46.51 0-00-01.51 9.00 0.2
[/pre]
The test data you provided indicates that a direction taken as the mean of Face Left and Face Right with your Topcon total station has a standard error of +/-9".
This is demonstrated from the summary of the above residuals given by Star*Net when the directions are adjusted using a standard error of +/-9" for all directions:
[pre]
Adjustment Statistical Summary
==============================
Convergence Iterations = 3
Number of Stations = 14
Number of Observations = 55
Number of Unknowns = 31
Number of Redundant Obs = 24
Observation Count Sum Squares Error
of StdRes Factor
Directions 45 19.784 1.004
Distances 9 0.000 0.000
Az/Bearings 1 0.000 0.000
Total 55 19.784 0.908
The Chi-Square Test at 5.00% Level Passed
Lower/Upper Bounds (0.719/1.281)
[/pre]
More Errors
> This is the output from Star*Net's blunder detection:
>
> [pre]
> 04 V1 6-09-06.66 0-00-31.66
> 04 V3 186-32-27.03 0-01-02.03
>
> Set 5
> 05 V3 186-33-10.35 -0-00-44.65
>
> Largest Difference from Observed Direction
>
> 04 V3 186-32-27.03 0-01-02.03
> [/pre]
>
> The inner targets appear to be somewhat problematic. The likely causes are either that the targets weren't perfectly sharp and in good contrast or observer fatigue. The direction from 04 to V3 definitely appears to be a blunder.
I found some discrepancies between your Starnet file and my spreadsheet and yet another discrepancy between my spreadsheet and my field notes.
It looks like these discrepancies could account for the blunders:
04 V1 is 06-08-35.
04 V3 is 186-32-25
05 V3 is 186-32-40
One thing is becoming clear to me though: Every transfer of data from one place to another...field book to Excel; Excel to Starnet, etc. is an opportunity for error!
I'll put these in and run Blunder Detect again.
Update: Ran Blunder detect again and again, using "Largest Difference from observed Direction" as a guide to track down more errors, and found at least 4 more--mainly in calculating the means.
Now I'm down to the largest observed difference being 13.44 seconds (01 V4).
I never really appreciated how useful Blunder Detect can be!
Thanks!
With all the corrections previously noted, here is the new data file.
Now maybe we can get to the real issue....how accurate is my TS?
C 01 1000.000 1000.000 ! !
C 02 1000.000 1000.000 * *
C 03 1000.000 1000.000 * *
C 04 1000.000 1000.000 * *
C 05 1000.000 1000.000 * *
B 01-A1 0-00-00 !
# Set 1
DB 01
DM A1 0-00-05 35 & !
DM A2 59-52-00 35 & !
DM A3 119-50-20 35 & !
DM A4 179-47-20 35 & !
DM A5 238-54-50 35 & !
DM A6 292-18-10 34.5 & !
DM V1 6-09-10 10 & !
DM V2 93-42-45 10 & !
DM V3 186-31-25 10 & !
DM V4 273-23-35 10 & !
DE
# Set 2
DB 02
DN A1 0-00-05
DN A2 59-52-00
DN A3 119-50-30
DN A4 179-48-00
DN A5 238-55-15
DN A6 292-18-30
DN V1 6-08-05
DN V2 93-42-30
DN V3 186-33-05
DN V4 273-23-55
DE
# Set 3
DB 03
DN A1 0-00-05
DN A2 59-52-00
DN A3 119-50-20
DN A4 179-47-10
DN A5 238-54-50
DN A6 292-18-10
DN V1 6-08-30
DN V2 93-42-30
DN V3 186-32-00
DN V4 273-23-25
DE
# Set 4
DB 04
DN A1 0-00-10
DN A2 59-52-10
DN A3 119-50-25
DN A4 179-47-45
DN A5 238-55-10
DN A6 292-18-35
DN V1 6-08-35
DN V2 93-42-20
DN V3 186-32-25
DN V4 273-23-45
DE
# Set 5
DB 05
DN A1 0-00-10
DN A2 59-52-05
DN A3 119-50-25
DN A4 179-47-45
DN A5 238-55-05
DN A6 292-18-20
DN V1 6-08-30
DN V2 93-42-25
DN V3 186-32-40
DN V4 273-23-45
DE
If I find one more error, I'm hitting the Home Equity Loan account for a Data Collector:pissed:
> With all the corrections previously noted, here is the new data file.
> If I find one more error, I'm hitting the Home Equity Loan account for a Data Collector:pissed:
Uh... Found three more.
Set 1 A3 is 119-50-10
Set 1 V3 is 186-31-35
Set 3 A3 is 119-50-10
ARGH!
With every error found, the Error Factor goes down. What does it mean if the Chi-Square Lower Bound is exceeded?
C 01 1000.000 1000.000 ! !
C 02 1000.000 1000.000 * *
C 03 1000.000 1000.000 * *
C 04 1000.000 1000.000 * *
C 05 1000.000 1000.000 * *
B 01-A1 0-00-00 !
# Set 1
DB 01
DM A1 0-00-05 35 & !
DM A2 59-52-00 35 & !
DM A3 119-50-10 35 & !
DM A4 179-47-20 35 & !
DM A5 238-54-50 35 & !
DM A6 292-18-10 34.5 & !
DM V1 6-09-10 10 & !
DM V2 93-42-45 10 & !
DM V3 186-31-35 10 & !
DM V4 273-23-35 10 & !
DE
# Set 2
DB 02
DN A1 0-00-05
DN A2 59-52-00
DN A3 119-50-30
DN A4 179-48-00
DN A5 238-55-15
DN A6 292-18-30
DN V1 6-08-05
DN V2 93-42-30
DN V3 186-33-05
DN V4 273-23-55
DE
# Set 3
DB 03
DN A1 0-00-05
DN A2 59-52-00
DN A3 119-50-10
DN A4 179-47-10
DN A5 238-54-50
DN A6 292-18-10
DN V1 6-08-30
DN V2 93-42-30
DN V3 186-32-00
DN V4 273-23-25
DE
# Set 4
DB 04
DN A1 0-00-10
DN A2 59-52-10
DN A3 119-50-25
DN A4 179-47-45
DN A5 238-55-10
DN A6 292-18-35
DN V1 6-08-35
DN V2 93-42-20
DN V3 186-32-25
DN V4 273-23-45
DE
# Set 5
DB 05
DN A1 0-00-10
DN A2 59-52-05
DN A3 119-50-25
DN A4 179-47-45
DN A5 238-55-05
DN A6 292-18-20
DN V1 6-08-30
DN V2 93-42-25
DN V3 186-32-40
DN V4 273-23-45
DE
" What does it mean if the Chi-Square Lower Bound is exceeded?"
It means your survey was too good, i.e., the tolerance parameters may be set too high or perhaps compensating errors resulted in a super-tight survey. Probably other factors would cause this but these were the two from the top of my head.
I've seen this occur more and more with the improvements in total station precision and accuracy.
TS Direction Standard Error = +/ 6"
Running the corrected input file you provide gives the following coordinates for the five setups from which the standard error of centering can be calculated.
[pre]
Adjusted Coordinates (FeetUS)
=============================
Station N E
01 1000.0000 1000.0000
02 999.9989 1000.0036
03 999.9998 1000.0013
04 999.9990 1000.0019
05 999.9992 1000.0024
[/pre]
The standard error of a direction taken as the mean of Face Left and Face Right that would be the best estimate from the corrected input file is 6" (to the nearest second).
[pre]
Adjusted Direction Observations (DMS)
From To Direction Residual StdErr StdRes
Set 1
01 A1 0-00-12.52 0-00-07.52 6.00 1.3
01 A2 59-52-06.25 0-00-06.25 6.00 1.0
01 A3 119-50-12.43 0-00-02.43 6.00 0.4
01 A4 179-47-19.87 -0-00-00.13 6.00 0.0
01 A5 238-54-48.00 -0-00-02.00 6.00 0.3
01 A6 292-18-16.47 0-00-06.47 6.00 1.1
01 V1 6-09-07.73 -0-00-02.27 6.00 0.4
01 V2 93-42-34.84 -0-00-10.16 6.00 1.7
01 V3 186-31-36.58 0-00-01.58 6.00 0.3
01 V4 273-23-25.32 -0-00-09.68 6.00 1.6
Set 2
02 A1 0-00-04.46 -0-00-00.54 6.00 0.1
02 A2 59-52-03.23 0-00-03.23 6.00 0.5
02 A3 119-50-30.59 0-00-00.59 6.00 0.1
02 A4 179-47-54.19 -0-00-05.81 6.00 1.0
02 A5 238-55-17.55 0-00-02.55 6.00 0.4
02 A6 292-18-27.44 -0-00-02.56 6.00 0.4
02 V1 6-08-04.71 -0-00-00.29 6.00 0.0
02 V2 93-42-30.50 0-00-00.50 6.00 0.1
02 V3 186-33-05.99 0-00-00.99 6.00 0.2
02 V4 273-23-56.36 0-00-01.36 6.00 0.2
Set 3
03 A1 359-59-59.53 -0-00-05.47 6.00 0.9
03 A2 59-51-56.15 -0-00-03.85 6.00 0.6
03 A3 119-50-10.19 0-00-00.19 6.00 0.0
03 A4 179-47-22.61 0-00-12.61 6.00 2.1
03 A5 238-54-47.96 -0-00-02.04 6.00 0.3
03 A6 292-18-09.43 -0-00-00.57 6.00 0.1
03 V1 6-08-34.79 0-00-04.79 6.00 0.8
03 V2 93-42-27.36 -0-00-02.64 6.00 0.4
03 V3 186-31-59.29 -0-00-00.71 6.00 0.1
03 V4 273-23-22.71 -0-00-02.29 6.00 0.4
Set 4
04 A1 0-00-11.19 0-00-01.19 6.00 0.2
04 A2 59-52-05.50 -0-00-04.50 6.00 0.7
04 A3 119-50-22.78 -0-00-02.22 6.00 0.4
04 A4 179-47-40.76 -0-00-04.24 6.00 0.7
04 A5 238-55-08.44 -0-00-01.56 6.00 0.3
04 A6 292-18-27.36 -0-00-07.64 6.00 1.3
04 V1 6-08-36.69 0-00-01.69 6.00 0.3
04 V2 93-42-27.14 0-00-07.14 6.00 1.2
04 V3 186-32-27.31 0-00-02.31 6.00 0.4
04 V4 273-23-52.82 0-00-07.82 6.00 1.3
Set 5
05 A1 0-00-07.30 -0-00-02.70 6.00 0.4
05 A2 59-52-03.88 -0-00-01.12 6.00 0.2
05 A3 119-50-24.02 -0-00-00.98 6.00 0.2
05 A4 179-47-42.58 -0-00-02.42 6.00 0.4
05 A5 238-55-08.05 0-00-03.05 6.00 0.5
05 A6 292-18-24.31 0-00-04.31 6.00 0.7
05 V1 6-08-26.08 -0-00-03.92 6.00 0.7
05 V2 93-42-30.16 0-00-05.16 6.00 0.9
05 V3 186-32-35.83 -0-00-04.17 6.00 0.7
05 V4 273-23-47.79 0-00-02.79 6.00 0.5
[/pre]
The calculation of the standard error of a direction in Star*Net with test directions of this sort simply consists of varying the standard error of a direction in the "Project Options" tab until the error factor for directions in the statistical summary is nominally 1.00.
Here is the statistical summary from the above adjustment.
[pre]
Adjustment Statistical Summary
==============================
Convergence Iterations = 3
Number of Stations = 15
Number of Observations = 61
Number of Unknowns = 33
Number of Redundant Obs = 28
Observation Count Sum Squares Error
of StdRes Factor
Directions 50 27.583 1.096
Distances 10 0.000 0.000
Az/Bearings 1 0.000 0.000
Total 61 27.583 0.993
The Chi-Square Test at 5.00% Level Passed
Lower/Upper Bounds (0.739/1.260)
[/pre]
TS Direction Standard Error = +/ 6"
>
> The standard error of a direction taken as the mean of Face Left and Face Right that would be the best estimate from the corrected input file is 6" (to the nearest second).
>
Would I be able to assume that, under these ideal conditions, the instrument/operator combo is performing at or better than the published specifications of the instrument? And, by extrapolation, if I took as much time and care in the field, I could expect to get close to this precision?
>
> The calculation of the standard error of a direction in Star*Net with test directions of this sort simply consists of varying the standard error of a direction in the "Project Options" tab until the error factor for directions in the statistical summary is nominally 1.00.
> 
If I understand correctly, you're talking about the "Fixed Std Err: Angular" field, currently at 1.00010e-000, would be adjusted up or down, but typically set at 6.60000e+000?
It looks like engineering notation, but I've tried changing it and readjusted the network but the error factor does not change.
TS Direction Standard Error = +/ 6"
> The calculation of the standard error of a direction in Star*Net with test directions of this sort simply consists of varying the standard error of a direction in the "Project Options" tab until the error factor for directions in the statistical summary is nominally 1.00.
And here is the demonstration of how the error factor of directions changes in the above adjustment with different a priori values of the standard error of a direction (mean of Face Left and Face Right) assigned to observations in the adjustment.
[pre]
s.e. = 6.2"
Statistical Summary
Observation Count Error Factor
Directions 50 1.061
Distances 10 0.000
Az/Bearings 1 0.000
Total 61 0.961
s.e. = 6.4"
Statistical Summary
Observation Count Error Factor
Directions 50 1.028
Distances 10 0.000
Az/Bearings 1 0.000
Total 61 0.930
s.e. = 6.6"
Statistical Summary
Observation Count Error Factor
Directions 50 0.997
Distances 10 0.000
Az/Bearings 1 0.000
Total 61 0.902
s.e. = 6.8"
Statistical Summary
Observation Count Error Factor
Directions 50 0.967
Distances 10 0.000
Az/Bearings 1 0.000
Total 61 0.876
s.e. = 7.0"
Statistical Summary
Observation Count Error Factor
Directions 50 0.940
Distances 10 0.000
Az/Bearings 1 0.000
Total 61 0.851
[/pre]
So, actually the best estimate of the standard error from the above test measurements is closer to +/-6.6". That means that the standard error of an angle taken as the mean of Face Left and Face Right with your total station would be estimated as:
SQRT(2) x 6.6" = 9.3" = 9"
TS Direction Standard Error = +/ 6"
> Would I be able to assume that, under these ideal conditions, the instrument/operator combo is performing at or better than the published specifications of the instrument? And, by extrapolation, if I took as much time and care in the field, I could expect to get close to this precision?
Actually, it would be reasonable to expect that angles measured with that instrument to sharp, well-defined targets with the instrument very carefully levelled have standard errors of SQRT(2) x 6.6" = 9.3" (= 9" for practical purposes)
That nominal accuracy will be degraded by random errors in target centering, which must also be evaluated and specified in the adjustment.
> > The calculation of the standard error of a direction in Star*Net with test directions of this sort simply consists of varying the standard error of a direction in the "Project Options" tab until the error factor for directions in the statistical summary is nominally 1.00.
> >
>
>
> If I understand correctly, you're talking about the "Fixed Std Err: Angular" field, currently at 1.00010e-000, would be adjusted up or down, but typically set at 6.00000e+000?
No that isn't the correct tab. There should be one in which the standard errors of angles, directions, distances, centering, etc. are assigned.
Plug in a standard error of 6.6" for the standard error of a direction and rerun the adjustment. The error factor for directions should be nominally 1.00.
TS Direction Standard Error = +/ 6"
> > The calculation of the standard error of a direction in Star*Net with test directions of this sort simply consists of varying the standard error of a direction in the "Project Options" tab until the error factor for directions in the statistical summary is nominally 1.00.
Ok. Got it! But my numbers aren't coming up the same. I'm still down at .470 Error Factor with a standard error for directions of 6.6". I'm still doing something wrong.
When you say:
Do you mean to go back into the data table and replace all of the assumed coordinates with the adjusted coordinates?
