Total Station - Angle quality estimate.

Not Enough Info

Is it the same observer every time?

What is the sighting precision of that operator, a separate test that needs to be done prior to testing instrument accuracy?

That are the targets used for these tests?

What are the atmospheric conditions, sunlight etc. during these tests?

What is the position of the sun relative to the observation target points?

What are the manufacturer specs for each instrument?

Paul in PA

LS FOR TOTAL STATION A

Instrument Standard Error Settings

Project Default Instrument
Distances (Constant) : 1.000000 FeetUS
Distances (PPM) : 0.000000
Angles : 6.999000 Seconds
Directions : 1.000000 Seconds
Azimuths & Bearings : 1.000000 Seconds
Centering Error Instrument : 0.000000 FeetUS
Centering Error Target : 0.000000 FeetUS

Summary of Unadjusted Input Observations
========================================

Number of Entered Stations (FeetUS) = 3

Fixed Stations N E Description
B 5000.0000 1000.0000
A 5100.0000 1000.0000

Free Stations N E Description
C 5092.3657 1032.3221

Number of Azimuth/Bearing Observations (DMS) = 1

From To Bearing StdErr
B A N00-00-00.00E 1.00

Adjustment Statistical Summary
==============================

Iterations = 4

Number of Stations = 3

Number of Observations = 61
Number of Unknowns = 2
Number of Redundant Obs = 59

Observation Count Sum Squares Error
of StdRes Factor
Angles 54 59.212 1.065
Distances 6 0.000 0.000
Az/Bearings 1 0.000 0.000

Total 61 59.212 1.002

The Chi-Square Test at 5.00% Level Passed
Lower/Upper Bounds (0.820/1.180)

Adjusted Coordinates (FeetUS)
=============================

Station N E Description
B 5000.0000 1000.0000
A 5100.0000 1000.0000
C 5092.3675 1038.3177

Adjusted Observations and Residuals
===================================

Adjusted Angle Observations (DMS)

From At To Angle Residual StdErr StdRes File:Line
A B C 22-31-50.25 -0-00-08.85 7.00 1.3 1:6
A B C 22-31-50.25 -0-00-09.65 7.00 1.4 1:7
A B C 22-31-50.25 -0-00-03.65 7.00 0.5 1:8
A B C 22-31-50.25 -0-00-03.55 7.00 0.5 1:9
A B C 22-31-50.25 -0-00-07.15 7.00 1.0 1:10
A B C 22-31-50.25 -0-00-06.75 7.00 1.0 1:11
A B C 22-31-50.25 -0-00-10.65 7.00 1.5 1:13
A B C 22-31-50.25 -0-00-10.75 7.00 1.5 1:14
A B C 22-31-50.25 -0-00-07.55 7.00 1.1 1:15
A B C 22-31-50.25 -0-00-08.45 7.00 1.2 1:16
A B C 22-31-50.25 -0-00-12.55 7.00 1.8 1:17
A B C 22-31-50.25 -0-00-13.15 7.00 1.9 1:18
A B C 22-31-50.25 -0-00-06.75 7.00 1.0 1:20
A B C 22-31-50.25 -0-00-06.75 7.00 1.0 1:21
A B C 22-31-50.25 -0-00-02.85 7.00 0.4 1:22
A B C 22-31-50.25 -0-00-02.65 7.00 0.4 1:23
A B C 22-31-50.25 -0-00-05.85 7.00 0.8 1:24
A B C 22-31-50.25 -0-00-05.65 7.00 0.8 1:25
A B C 22-31-50.25 0-00-00.05 7.00 0.0 1:27
A B C 22-31-50.25 -0-00-00.85 7.00 0.1 1:28
A B C 22-31-50.25 -0-00-00.85 7.00 0.1 1:29
A B C 22-31-50.25 -0-00-00.25 7.00 0.0 1:30
A B C 22-31-50.25 -0-00-05.15 7.00 0.7 1:31
A B C 22-31-50.25 -0-00-05.05 7.00 0.7 1:32
A B C 22-31-50.25 -0-00-03.95 7.00 0.6 1:34
A B C 22-31-50.25 -0-00-04.45 7.00 0.6 1:35
A B C 22-31-50.25 0-00-00.15 7.00 0.0 1:36
A B C 22-31-50.25 0-00-00.15 7.00 0.0 1:37
A B C 22-31-50.25 -0-00-04.05 7.00 0.6 1:38
A B C 22-31-50.25 -0-00-04.95 7.00 0.7 1:39
A B C 22-31-50.25 0-00-00.65 7.00 0.1 1:41
A B C 22-31-50.25 0-00-00.35 7.00 0.0 1:42
A B C 22-31-50.25 0-00-05.45 7.00 0.8 1:43
A B C 22-31-50.25 0-00-05.55 7.00 0.8 1:44
A B C 22-31-50.25 0-00-05.45 7.00 0.8 1:45
A B C 22-31-50.25 0-00-05.75 7.00 0.8 1:46
A B C 22-31-50.25 0-00-01.35 7.00 0.2 1:48
A B C 22-31-50.25 0-00-01.55 7.00 0.2 1:49
A B C 22-31-50.25 0-00-04.65 7.00 0.7 1:50
A B C 22-31-50.25 0-00-04.25 7.00 0.6 1:51
A B C 22-31-50.25 -0-00-00.45 7.00 0.1 1:52
A B C 22-31-50.25 -0-00-00.55 7.00 0.1 1:53
A B C 22-31-50.25 0-00-13.45 7.00 1.9 1:55
A B C 22-31-50.25 0-00-13.65 7.00 1.9 1:56
A B C 22-31-50.25 0-00-11.05 7.00 1.6 1:57
A B C 22-31-50.25 0-00-10.65 7.00 1.5 1:58
A B C 22-31-50.25 0-00-08.65 7.00 1.2 1:59
A B C 22-31-50.25 0-00-08.25 7.00 1.2 1:60
A B C 22-31-50.25 0-00-10.15 7.00 1.4 1:62
A B C 22-31-50.25 0-00-10.45 7.00 1.5 1:63
A B C 22-31-50.25 0-00-14.05 7.00 2.0 1:64
A B C 22-31-50.25 0-00-13.65 7.00 1.9 1:65
A B C 22-31-50.25 0-00-07.25 7.00 1.0 1:66
A B C 22-31-50.25 0-00-07.35 7.00 1.0 1:67

Adjusted Azimuth/Bearing Observations (DMS)

From To Bearing Residual StdErr StdRes File:Line
B A N00-00-00.00E 0-00-00.00 1.00 0.0 1:4

Adjusted Bearings (DMS) and Horizontal Distances (FeetUS)
=========================================================
(Relative Confidence of Bearing is in Seconds)

From To Bearing Distance 95% RelConfidence
Brg Dist PPM
A B S00-00-00.00E 100.0000 0.00 0.0000 0.0114
B C N22-31-50.25E 100.0000 2.33 0.9993 9992.8846

Error Propagation
=================

Station Coordinate Standard Deviations (FeetUS)

Station N E
B 0.000000 0.000000
A 0.000000 0.000000
C 0.377089 0.156432

Station Coordinate Error Ellipses (FeetUS)
Confidence Region = 95%

Station Semi-Major Semi-Minor Azimuth of
Axis Axis Major Axis
B 0.000000 0.000000 0-00
A 0.000000 0.000000 0-00
C 0.999288 0.001130 22-32

Relative Error Ellipses (FeetUS)
Confidence Region = 95%

Stations Semi-Major Semi-Minor Azimuth of
From To Axis Axis Major Axis
A B 0.000000 0.000000 0-00
B C 0.999288 0.001130 22-32

Elapsed Time = 00:00:00

LS FOR TOTAL STATION B

Instrument Standard Error Settings

Project Default Instrument
Distances (Constant) : 1.000000 FeetUS
Distances (PPM) : 0.000000
Angles : 6.999000 Seconds
Directions : 1.000000 Seconds
Azimuths & Bearings : 1.000000 Seconds
Centering Error Instrument : 0.000000 FeetUS
Centering Error Target : 0.000000 FeetUS

Summary of Unadjusted Input Observations
========================================

Number of Entered Stations (FeetUS) = 3

Fixed Stations N E Description
B 5000.0000 1000.0000
A 5100.0000 1000.0000

Unused Stations
C
Number of Azimuth/Bearing Observations (DMS) = 1

From To Bearing StdErr
B A N00-00-00.00E 1.00

Adjustment Statistical Summary
==============================

Iterations = 2

Number of Stations = 3

Number of Observations = 61
Number of Unknowns = 2
Number of Redundant Obs = 59

Observation Count Sum Squares Error
of StdRes Factor
Angles 54 54.209 1.019
Distances 6 0.000 0.000
Az/Bearings 1 0.000 0.000

Total 61 54.209 0.959

The Chi-Square Test at 5.00% Level Passed
Lower/Upper Bounds (0.820/1.180)

Adjusted Coordinates (FeetUS)
=============================

Station N E Description
B 5000.0000 1000.0000
A 5100.0000 1000.0000
C1 5092.3675 1038.3177

Adjusted Observations and Residuals
===================================

Adjusted Angle Observations (DMS)

From At To Angle Residual StdErr StdRes File:Line
A B C1 22-31-50.25 -0-00-06.55 7.00 0.9 1:73
A B C1 22-31-50.25 -0-00-07.35 7.00 1.1 1:74
A B C1 22-31-50.25 -0-00-06.55 7.00 0.9 1:75
A B C1 22-31-50.25 -0-00-06.45 7.00 0.9 1:76
A B C1 22-31-50.25 -0-00-06.55 7.00 0.9 1:77
A B C1 22-31-50.25 -0-00-06.15 7.00 0.9 1:78
A B C1 22-31-50.25 -0-00-11.25 7.00 1.6 1:81
A B C1 22-31-50.25 -0-00-09.75 7.00 1.4 1:82
A B C1 22-31-50.25 -0-00-11.35 7.00 1.6 1:83
A B C1 22-31-50.25 -0-00-10.75 7.00 1.5 1:84
A B C1 22-31-50.25 -0-00-09.65 7.00 1.4 1:85
A B C1 22-31-50.25 -0-00-10.25 7.00 1.5 1:86
A B C1 22-31-50.25 -0-00-04.45 7.00 0.6 1:88
A B C1 22-31-50.25 -0-00-04.55 7.00 0.7 1:89
A B C1 22-31-50.25 -0-00-05.75 7.00 0.8 1:90
A B C1 22-31-50.25 -0-00-05.55 7.00 0.8 1:91
A B C1 22-31-50.25 -0-00-05.25 7.00 0.8 1:92
A B C1 22-31-50.25 -0-00-05.05 7.00 0.7 1:93
A B C1 22-31-50.25 -0-00-01.65 7.00 0.2 1:95
A B C1 22-31-50.25 -0-00-02.55 7.00 0.4 1:96
A B C1 22-31-50.25 -0-00-02.25 7.00 0.3 1:97
A B C1 22-31-50.25 -0-00-01.65 7.00 0.2 1:98
A B C1 22-31-50.25 -0-00-02.05 7.00 0.3 1:99
A B C1 22-31-50.25 -0-00-02.05 7.00 0.3 1:100
A B C1 22-31-50.25 -0-00-02.55 7.00 0.4 1:102
A B C1 22-31-50.25 -0-00-02.95 7.00 0.4 1:103
A B C1 22-31-50.25 -0-00-02.95 7.00 0.4 1:104
A B C1 22-31-50.25 -0-00-02.95 7.00 0.4 1:105
A B C1 22-31-50.25 -0-00-02.45 7.00 0.4 1:106
A B C1 22-31-50.25 -0-00-03.25 7.00 0.5 1:107
A B C1 22-31-50.25 0-00-03.75 7.00 0.5 1:109
A B C1 22-31-50.25 0-00-03.35 7.00 0.5 1:110
A B C1 22-31-50.25 0-00-03.75 7.00 0.5 1:111
A B C1 22-31-50.25 0-00-03.95 7.00 0.6 1:112
A B C1 22-31-50.25 0-00-03.95 7.00 0.6 1:113
A B C1 22-31-50.25 0-00-04.35 7.00 0.6 1:114
A B C1 22-31-50.25 0-00-01.85 7.00 0.3 1:116
A B C1 22-31-50.25 0-00-01.95 7.00 0.3 1:117
A B C1 22-31-50.25 0-00-01.75 7.00 0.2 1:118
A B C1 22-31-50.25 0-00-01.35 7.00 0.2 1:119
A B C1 22-31-50.25 0-00-01.95 7.00 0.3 1:120
A B C1 22-31-50.25 0-00-01.85 7.00 0.3 1:121
A B C1 22-31-50.25 0-00-11.05 7.00 1.6 1:123
A B C1 22-31-50.25 0-00-11.25 7.00 1.6 1:124
A B C1 22-31-50.25 0-00-10.65 7.00 1.5 1:125
A B C1 22-31-50.25 0-00-10.25 7.00 1.5 1:126
A B C1 22-31-50.25 0-00-11.55 7.00 1.6 1:127
A B C1 22-31-50.25 0-00-11.05 7.00 1.6 1:128
A B C1 22-31-50.25 0-00-10.55 7.00 1.5 1:130
A B C1 22-31-50.25 0-00-10.95 7.00 1.6 1:131
A B C1 22-31-50.25 0-00-11.25 7.00 1.6 1:132
A B C1 22-31-50.25 0-00-10.85 7.00 1.5 1:133
A B C1 22-31-50.25 0-00-09.65 7.00 1.4 1:134
A B C1 22-31-50.25 0-00-09.85 7.00 1.4 1:135

Adjusted Distance Observations (FeetUS)

From To Distance Residual StdErr StdRes File:Line
B C1 100.0000 0.0000 1.0000 0.0 1:73
B C1 100.0000 0.0000 1.0000 0.0 1:74
B C1 100.0000 0.0000 1.0000 0.0 1:75
B C1 100.0000 0.0000 1.0000 0.0 1:76
B C1 100.0000 0.0000 1.0000 0.0 1:77
B C1 100.0000 0.0000 1.0000 0.0 1:78

Adjusted Azimuth/Bearing Observations (DMS)

From To Bearing Residual StdErr StdRes File:Line
B A N00-00-00.00E 0-00-00.00 1.00 0.0 1:4

Adjusted Bearings (DMS) and Horizontal Distances (FeetUS)
=========================================================
(Relative Confidence of Bearing is in Seconds)

From To Bearing Distance 95% RelConfidence
Brg Dist PPM
A B S00-00-00.00E 100.0000 0.00 0.0000 0.0114
B C1 N22-31-50.25E 100.0000 2.33 0.9993 9992.8846

Error Propagation
=================

Station Coordinate Standard Deviations (FeetUS)

Station N E
B 0.000000 0.000000
A 0.000000 0.000000
C1 0.377089 0.156432

Station Coordinate Error Ellipses (FeetUS)
Confidence Region = 95%

Station Semi-Major Semi-Minor Azimuth of
Axis Axis Major Axis
B 0.000000 0.000000 0-00
A 0.000000 0.000000 0-00
C1 0.999288 0.001130 22-32

Relative Error Ellipses (FeetUS)
Confidence Region = 95%

Stations Semi-Major Semi-Minor Azimuth of
From To Axis Axis Major Axis
A B 0.000000 0.000000 0-00
B C1 0.999288 0.001130 22-32

Elapsed Time = 00:00:00

ERROR FACTOR OF 1

THE ADJUSTMENTS ARE NOT REALISTIC BECAUSE THERE IS NO ACCOUNTING FOR CENTERING ERRORS. The standard instrument error used for total station A was 6.999". The instrument standard error used for total station B was 6.70. This leads me to form the opinion that total station B is slightly more precise that total station A. Assume the true value of the angle is 23-32-00, then the total station that returns that value or a value very close to that value is the more accurate instrument.

> Consider some angles from total station A and total station B. An angle here being direction STN2 minus direction STN1. Each total station reads the same angle 6 times. Then the same two total stations read a (slightly) different angle another 6 times each. In each case the 'true' angle is not known. We stop at 9 groups of 6 angles. Can you estimate the angular accuracy of each total station? Is this test a test of precision or accuracy? How much 'better' is total station B than total station A?

The way that I tackled the problem was to estimate the standard error of a direction from the scatter of repeat directions to each target.

That gave the following apparent standard errors:

TS-A = +/-2.6"

TS-B = +/-0.5"

To save computational labor, I ran both sets of directions through Star*Net using the following input file:

[pre]

C 100 1000 1000 ! !
C 1 2000 1000 ! !
D 100-2 1000 !
D 100-3 1000 !
D 100-4 1000 !
D 100-5 1000 !
D 100-6 1000 !
D 100-7 1000 !
D 100-8 1000 !
D 100-9 1000 !

.DATA ON
# TS A
.INSTRUMENT TS-A
DB 100
DN 1 022-31-59.1
DN 1 022-31-59.9
DN 1 022-31-53.9
DN 1 022-31-53.8
DN 1 022-31-57.4
DN 1 022-31-57.0

DN 2 022-32-00.9
DN 2 022-32-01.0
DN 2 022-31-57.8
DN 2 022-31-58.7
DN 2 022-32-02.8
DN 2 022-32-03.4

DN 3 022-31-57.0
DN 3 022-31-57.0
DN 3 022-31-53.1
DN 3 022-31-52.9
DN 3 022-31-56.1
DN 3 022-31-55.9

DN 4 022-31-50.2
DN 4 022-31-51.1
DN 4 022-31-51.1
DN 4 022-31-50.5
DN 4 022-31-55.4
DN 4 022-31-55.3

DN 5 022-31-54.2
DN 5 022-31-54.7
DN 5 022-31-50.1
DN 5 022-31-50.1
DN 5 022-31-54.3
DN 5 022-31-55.2

DN 6 022-31-49.6
DN 6 022-31-49.9
DN 6 022-31-44.8
DN 6 022-31-44.7
DN 6 022-31-44.8
DN 6 022-31-44.5

DN 7 022-31-48.9
DN 7 022-31-48.7
DN 7 022-31-45.6
DN 7 022-31-46.0
DN 7 022-31-50.7
DN 7 022-31-50.8

DN 8 022-31-36.8
DN 8 022-31-36.6
DN 8 022-31-39.2
DN 8 022-31-39.6
DN 8 022-31-41.6
DN 8 022-31-42.0

DN 9 022-31-40.1
DN 9 022-31-39.8
DN 9 022-31-36.2
DN 9 022-31-36.6
DN 9 022-31-43.0
DN 9 022-31-42.9
DE

.DATA ON
#TS B
.INSTRUMENT TS-B
DB 100
DN 1 022-31-56.8
DN 1 022-31-57.6
DN 1 022-31-56.8
DN 1 022-31-56.7
DN 1 022-31-56.8
DN 1 022-31-56.4

DN 2 022-32-01.5
DN 2 022-32-01.6
DN 2 022-32-00.0
DN 2 022-32-01.0
DN 2 022-31-59.9
DN 2 022-32-00.5

DN 3 022-31-54.7
DN 3 022-31-54.8
DN 3 022-31-56.0
DN 3 022-31-55.8
DN 3 022-31-55.5
DN 3 022-31-55.3

DN 4 022-31-51.9
DN 4 022-31-52.8
DN 4 022-31-52.5
DN 4 022-31-51.9
DN 4 022-31-52.3
DN 4 022-31-52.3

DN 5 022-31-52.8
DN 5 022-31-53.2
DN 5 022-31-53.2
DN 5 022-31-53.2
DN 5 022-31-52.7
DN 5 022-31-53.5

DN 6 022-31-46.5
DN 6 022-31-46.9
DN 6 022-31-46.5
DN 6 022-31-46.3
DN 6 022-31-46.3
DN 6 022-31-45.9

DN 7 022-31-48.4
DN 7 022-31-48.3
DN 7 022-31-48.5
DN 7 022-31-48.9
DN 7 022-31-48.3
DN 7 022-31-48.4

DN 8 022-31-39.2
DN 8 022-31-39.0
DN 8 022-31-39.6
DN 8 022-31-40.0
DN 8 022-31-38.7
DN 8 022-31-39.2

DN 9 022-31-39.7
DN 9 022-31-39.3
DN 9 022-31-39.0
DN 9 022-31-39.4
DN 9 022-31-40.6
DN 9 022-31-40.4
DE
[/pre]

If a Star*Net user wants to duplicate the calculation, just copy the above input file and run the adjustment for just the directions observed with TS-A by changing the

".DATA ON" line at the end of that set to ".DATA OFF"

Add the "#" comment label to the ".INSTRUMENT TS-A" and ".INSTRUMENT TS-B" inline commands. Those will be used after the standard errors of both instruments are separately estimated.

That will turn off all of the input file that follows and the directions from the set measured with TS-B won't be used in the adjustment.

Run the adjustment as 2D.

Set instrument and target centering errors to 0.000000

Chose a trial value for the standard error of a direction and run the adjustment until the error factor for directions is 1.00.

That is the best estimate of the standard error of a direction from just the TS-A observations provided.

Then, turn off the TS-A part of the input file by changing the inline commands so that the TS-A observations follow a ".DATA OFF" and are in turn followed by a ".DATA ON" before the TS-B observations.

So, having separately estimated the standard errors of a direction taken with TS-A and TS-B, you can apply those standard errors to both sets of observations and adjustment together.

The joint adjustment suggests from the Chi Square test that the standard errors of both TS-A and TS-B should be reduced by a factor of about 0.92, which gives the following estimated standard errors of directions taken with the two instruments.

TS-A = +/-2.46"

TS-B = +/-0.46"

If you want to work the problem longhand, you'd separately calculate the apparent standard error of the directions to each target and combine those nine values

[pre]
DB 100
DN1 022-31-59.1
DN1 022-31-59.9
DN1 022-31-53.9
DN1 022-31-53.8
DN1 022-31-57.4
DN1 022-31-57.0
------
56.85 = mean
2.56 = s

DN2 022-32-00.9
DN2 022-32-01.0
DN2 022-31-57.8
DN2 022-31-58.7
DN2 022-32-02.8
DN2 022-32-03.4
------
60.77 = mean
2.20 = s

DN3 022-31-57.0
DN3 022-31-57.0
DN3 022-31-53.1
DN3 022-31-52.9
DN3 022-31-56.1
DN3 022-31-55.9
------
55.33 = mean
1.86 = s

DN4 022-31-50.2
DN4 022-31-51.1
DN4 022-31-51.1
DN4 022-31-50.5
DN4 022-31-55.4
DN4 022-31-55.3
------
52.27 = mean
2.41 = s

DN5 022-31-54.2
DN5 022-31-54.7
DN5 022-31-50.1
DN5 022-31-50.1
DN5 022-31-54.3
DN5 022-31-55.2
------
53.10 = mean
2.35 = s

DN6 022-31-49.6
DN6 022-31-49.9
DN6 022-31-44.8
DN6 022-31-44.7
DN6 022-31-44.8
DN6 022-31-44.5
------
46.38 = mean
2.61 = s

DN7 022-31-48.9
DN7 022-31-48.7
DN7 022-31-45.6
DN7 022-31-46.0
DN7 022-31-50.7
DN7 022-31-50.8
------
48.45 = mean
2.23 = s

DN8 022-31-36.8
DN8 022-31-36.6
DN8 022-31-39.2
DN8 022-31-39.6
DN8 022-31-41.6
DN8 022-31-42.0
------
39.30 = mean
2.29 = s

DN9 022-31-40.1
DN9 022-31-39.8
DN9 022-31-36.2
DN9 022-31-36.6
DN9 022-31-43.0
DN9 022-31-42.9
-----
39.77 = mean
2.94 = s
[/pre]

So the pooled estimate of the standard error of a direction taken with TS-A is:

SQRT [ (2.56^2 + 2.20^2 + 1.86^2 + 2.41^2 + 2.35^2 + 2.61^2 + 2.23^2 + 2.29^2 + 2.94^2) / 9 ] = 2.40”

And working the apparent standard error of a direction taken with TS-B is done longhand as follows:

[pre]

#TS B

DB 100
DN 1 022-31-56.8
DN 1 022-31-57.6
DN 1 022-31-56.8
DN 1 022-31-56.7
DN 1 022-31-56.8
DN 1 022-31-56.4
-----
56.85 = mean
0.40 = s

DN 2 022-32-01.5
DN 2 022-32-01.6
DN 2 022-32-00.0
DN 2 022-32-01.0
DN 2 022-31-59.9
DN 2 022-32-00.5
-----
60.75 = mean
0.73 = s

DN 3 022-31-54.7
DN 3 022-31-54.8
DN 3 022-31-56.0
DN 3 022-31-55.8
DN 3 022-31-55.5
DN 3 022-31-55.3
-----
55.35 = mean
0.52 = s

DN 4 022-31-51.9
DN 4 022-31-52.8
DN 4 022-31-52.5
DN 4 022-31-51.9
DN 4 022-31-52.3
DN 4 022-31-52.3
-----
52.28 = mean
0.35 = s

DN 5 022-31-52.8
DN 5 022-31-53.2
DN 5 022-31-53.2
DN 5 022-31-53.2
DN 5 022-31-52.7
DN 5 022-31-53.5
-----
53.10 = mean
0.30 = s

DN 6 022-31-46.5
DN 6 022-31-46.9
DN 6 022-31-46.5
DN 6 022-31-46.3
DN 6 022-31-46.3
DN 6 022-31-45.9
-----
46.40 = mean
0.33 = s

DN 7 022-31-48.4
DN 7 022-31-48.3
DN 7 022-31-48.5
DN 7 022-31-48.9
DN 7 022-31-48.3
DN 7 022-31-48.4
-----
48.47 = mean
0.22 = s

DN 8 022-31-39.2
DN 8 022-31-39.0
DN 8 022-31-39.6
DN 8 022-31-40.0
DN 8 022-31-38.7
DN 8 022-31-39.2
-----
39.28 = mean
0.46 = s

DN 9 022-31-39.7
DN 9 022-31-39.3
DN 9 022-31-39.0
DN 9 022-31-39.4
DN 9 022-31-40.6
DN 9 022-31-40.4
-----
39.73 = mean
0.64 = s
[/pre]

Pooled estimate of the standard error of a direction from the above observations is then:

[pre]
SQRT [ (0.40^2 + 0.73^2 + 0.52^2 + 0.35^2 + 0.30^2 + 0.33^2 + 0.22^2 + 0.46^2 + 0.64^2) / 9 ] = 0.46”
[/pre]

Running the adjustment in Star*Net of both sets of directions, those of TS-A and TS-B, together with the standard errors derived above:

TS-A s.e. = 2.40"

TS-B s.e. = 0.46"

Gives the following statistical summary:

[pre]

Statistical Summary
Observation Count Error Factor
Directions 108 1.000
Distances 8 0.000
Total 116 0.965

Chi-Square Test at 5.00% Level Passed
Lower/Upper Bounds (0.860/1.140)

Performing Error Propagation ...
Writing Output Files ...

Network Processing Completed
Elapsed Time = 00:00:00
[/pre]

The Error Factor of Directions being exactly 1.000 indicates that there is nothing about the adjustment to indicate that the values of 2.40" and 0.46" are inconsistent with the residuals when the directions from TS-A and TS-B are adjusted together.

In other words, from the limited data provided, standard errors of 2.40" and 0.46" are not shown to be wrong.

okay what am I missing.

Conrad calls these ANGLES. The way I set up the file the adjusted result is for ONE POINT position. I tried to process Kent's dat file and I wind up with 10 positions for point no. 1. How would one set up the dat file to derive a single position? I get an error message when I enter the same station name follow DN.

okay what am I missing.

> Conrad calls these ANGLES. The way I set up the file the adjusted result is for ONE POINT position. I tried to process Kent's dat file and I wind up with 10 positions for point no. 1. How would one set up the dat file to derive a single position?

You're right, they are NOT directions. They are the differences between directions and so should be adjusted as "A" lines or a mix of "A" and "M" lines.

Sorry 'bout that.

LS FOR TOTAL STATION B

> Instrument Standard Error Settings
>
> Project Default Instrument
> Distances (Constant) : 1.000000 FeetUS
> Distances (PPM) : 0.000000
> Angles : 6.999000 Seconds
> Directions : 1.000000 Seconds
> Azimuths & Bearings : 1.000000 Seconds
> Centering Error Instrument : 0.000000 FeetUS
> Centering Error Target : 0.000000 FeetUS
>
Why are you using 6.99 seconds as the standard error for angles?
I thought that if your standard errors for directions was one second, the standard error for angles would be about 1.5 times that for directions, a resul of the square root of the sum of the squares of two directions, no?

okay what am I missing.

Here's the Star*Net file revised to input the angles and the differences in directions that they are, not directions.

[pre]

C 100 1000 1000 ! !
C 101 2000 1000 ! !
D 100-1 1000 !
D 100-2 1000 !
D 100-3 1000 !
D 100-4 1000 !
D 100-5 1000 !
D 100-6 1000 !
D 100-7 1000 !
D 100-8 1000 !
D 100-9 1000 !

# TS A

.DATA ON
.INSTRUMENT TS-A

M 101-100-1 022-31-59.1 1000 & !
A 101-100-1 022-31-59.9
A 101-100-1 022-31-53.9
A 101-100-1 022-31-53.8
A 101-100-1 022-31-57.4
A 101-100-1 022-31-57.0

M 101-100-2 022-32-00.9 1000 & !
A 101-100-2 022-32-01.0
A 101-100-2 022-31-57.8
A 101-100-2 022-31-58.7
A 101-100-2 022-32-02.8
A 101-100-2 022-32-03.4

M 101-100-3 022-31-57.0 1000 & !
A 101-100-3 022-31-57.0
A 101-100-3 022-31-53.1
A 101-100-3 022-31-52.9
A 101-100-3 022-31-56.1
A 101-100-3 022-31-55.9

M 101-100-4 022-31-50.2 1000 & !
A 101-100-4 022-31-51.1
A 101-100-4 022-31-51.1
A 101-100-4 022-31-50.5
A 101-100-4 022-31-55.4
A 101-100-4 022-31-55.3

M 101-100-5 022-31-54.2 1000 & !
A 101-100-5 022-31-54.7
A 101-100-5 022-31-50.1
A 101-100-5 022-31-50.1
A 101-100-5 022-31-54.3
A 101-100-5 022-31-55.2

M 101-100-6 022-31-49.6 1000 & !
A 101-100-6 022-31-49.9
A 101-100-6 022-31-44.8
A 101-100-6 022-31-44.7
A 101-100-6 022-31-44.8
A 101-100-6 022-31-44.5

M 101-100-7 022-31-48.9 1000 & !
A 101-100-7 022-31-48.7
A 101-100-7 022-31-45.6
A 101-100-7 022-31-46.0
A 101-100-7 022-31-50.7
A 101-100-7 022-31-50.8

M 101-100-8 022-31-36.8 1000 & !
A 101-100-8 022-31-36.6
A 101-100-8 022-31-39.2
A 101-100-8 022-31-39.6
A 101-100-8 022-31-41.6
A 101-100-8 022-31-42.0

M 101-100-9 022-31-40.1 1000 & !
A 101-100-9 022-31-39.8
A 101-100-9 022-31-36.2
A 101-100-9 022-31-36.6
A 101-100-9 022-31-43.0
A 101-100-9 022-31-42.9

.DATA ON
#TS B
.INSTRUMENT TS-B
M 101-100-1 022-31-56.8 1000 & !
A 101-100-1 022-31-57.6
A 101-100-1 022-31-56.8
A 101-100-1 022-31-56.7
A 101-100-1 022-31-56.8
A 101-100-1 022-31-56.4

M 101-100-2 022-32-01.5 1000 & !
A 101-100-2 022-32-01.6
A 101-100-2 022-32-00.0
A 101-100-2 022-32-01.0
A 101-100-2 022-31-59.9
A 101-100-2 022-32-00.5

M 101-100-3 022-31-54.7 1000 & !
A 101-100-3 022-31-54.8
A 101-100-3 022-31-56.0
A 101-100-3 022-31-55.8
A 101-100-3 022-31-55.5
A 101-100-3 022-31-55.3

M 101-100-4 022-31-51.9 1000 & !
A 101-100-4 022-31-52.8
A 101-100-4 022-31-52.5
A 101-100-4 022-31-51.9
A 101-100-4 022-31-52.3
A 101-100-4 022-31-52.3

M 101-100-5 022-31-52.8 1000 & !
A 101-100-5 022-31-53.2
A 101-100-5 022-31-53.2
A 101-100-5 022-31-53.2
A 101-100-5 022-31-52.7
A 101-100-5 022-31-53.5

M 101-100-6 022-31-46.5 1000 & !
A 101-100-6 022-31-46.9
A 101-100-6 022-31-46.5
A 101-100-6 022-31-46.3
A 101-100-6 022-31-46.3
A 101-100-6 022-31-45.9

M 101-100-7 022-31-48.4 1000 & !
A 101-100-7 022-31-48.3
A 101-100-7 022-31-48.5
A 101-100-7 022-31-48.9
A 101-100-7 022-31-48.3
A 101-100-7 022-31-48.4

M 101-100-8 022-31-39.2 1000 & !
A 101-100-8 022-31-39.0
A 101-100-8 022-31-39.6
A 101-100-8 022-31-40.0
A 101-100-8 022-31-38.7
A 101-100-8 022-31-39.2

M 101-100-9 022-31-39.7 1000 & !
A 101-100-9 022-31-39.3
A 101-100-9 022-31-39.0
A 101-100-9 022-31-39.4
A 101-100-9 022-31-40.6
A 101-100-9 022-31-40.4

[/pre]

Why 6.999".

Project Library Instrument TS-A
Note: n/a
Distances (Constant) : 1.000000 FeetUS
Distances (PPM) : 0.000000
Angles : 1.000000 Seconds
Directions : 6.999000 Seconds
Azimuths & Bearings : 1.000000 Seconds
Centering Error Instrument : 0.000000 FeetUS
Centering Error Target : 0.000000 FeetUS

6.999" was arrived at by trial and error
I went back and re-ran the project using Kent's dat file with some edits
When I use 6.999" I get the following result

Observation Count Sum Squares Error
of StdRes Factor
Directions 54 52.022 1.028
Distances 2 0.000 0.000
Az/Bearings 1 0.000 0.000

Total 57 52.022 1.000

The Chi-Square Test at 5.00% Level Passed
Lower/Upper Bounds (0.808/1.191)

I kept getting the following error message

ERROR [Line: 82] All Directions in Current Direction Set are to Same Station
DE

Processing Terminated Due to Errors.

The error message goes away when I change one of the directions to point no. 2. Basically I have run the adjustment using the input data as angles and as directions and I get essentially the same number for the error

edits to Kent's dat file

I thought the objective was to use the angular data in order to arrive at a single adjusted position. Kent's dat file used the 54 directions to adjust 9 points and therefore he was able to produce an adjustment that passed the Chi test. I was unable to produce the same result using the same error estimate when attempting to use the 54 directions to the SAME POINT.

.DATA ON
C 100 1000 1000 ! !
C 1 2000 1000

B 100-1 n00-00-00e
D 100-1 1000 !
D 100-2 1000 !
#D 100-3 1000 !
#D 100-4 1000 !
#D 100-5 1000 !
#D 100-6 1000 !
#D 100-7 1000 !
#D 100-8 1000 !
#D 100-9 1000 !

.DATA on
# TS A
.INSTRUMENT TS-A
DB 100
DN 1 022-31-56.8
DN 1 022-31-57.6
DN 1 022-31-56.8
DN 1 022-31-56.7
DN 1 022-31-56.8
DN 1 022-31-56.4

DN 1 022-32-01.5
DN 1 022-32-01.6
DN 1 022-32-00.0
DN 1 022-32-01.0
DN 1 022-31-59.9
DN 2 022-32-00.5 #edited to remove error message ERROR [Line: 82] All Directions in Current Direction Set are to Same Station
DE

DN 1 022-31-54.7
DN 1 022-31-54.8
DN 1 022-31-56.0
DN 1 022-31-55.8
DN 1 022-31-55.5
DN 1 022-31-55.3

DN 1 022-31-51.9
DN 1 022-31-52.8
DN 1 022-31-52.5
DN 1 022-31-51.9
DN 1 022-31-52.3
DN 1 022-31-52.3

DN 1 022-31-52.8
DN 1 022-31-53.2
DN 1 022-31-53.2
DN 1 022-31-53.2
DN 1 022-31-52.7
DN 1 022-31-53.5

DN 1 022-31-46.5
DN 1 022-31-46.9
DN 1 022-31-46.5
DN 1 022-31-46.3
DN 1 022-31-46.3
DN 1 022-31-45.9

DN 1 022-31-48.4
DN 1 022-31-48.3
DN 1 022-31-48.5
DN 1 022-31-48.9
DN 1 022-31-48.3
DN 1 022-31-48.4

DN 1 022-31-39.2
DN 1 022-31-39.0
DN 1 022-31-39.6
DN 1 022-31-40.0
DN 1 022-31-38.7
DN 1 022-31-39.2

DN 1 022-31-39.7
DN 1 022-31-39.3
DN 1 022-31-39.0
DN 1 022-31-39.4
DN 1 022-31-40.6
DN 1 022-31-40.4
DE

.DATA OFF

edits to Kent's dat file

> I thought the objective was to use the angular data in order to arrive at a single adjusted position. Kent's dat file used the 54 directions to adjust 9 points and therefore he was able to produce an adjustment that passed the Chi test. I was unable to produce the same result using the same error estimate when attempting to use the 54 directions to the SAME POINT.

Ah! Mystery solved!

Not Enough Info

Hello Paul,

>Is it the same observer every time?
>What is the sighting precision of that operator, a separate test that needs to be done prior to testing instrument accuracy?
>That are the targets used for these tests?
>What are the atmospheric conditions, sunlight etc. during these tests?
>What is the position of the sun relative to the observation target points?
>What are the manufacturer specs for each instrument?

For your calculations assume:
Yes.
0.3"
Prisms.
Conditions perfect.
Overcast.
Don't care; we're trying to work out our own.

edits to Kent's dat file

Hello DANEMINCE and Kent,

Sorry if I wasn't clear enough. There are 9 different stations occupied.

I ended up with the angle stdev for instrument A at 2.40" and instrument B at 0.46". I used a different formula than Kent for the pooled variance, but in the case of variances drawn from equal population sizes I don't think it makes any difference.