Chi-Square Exceeding Upper bounds Starnet
Hi All,
I have a traverse and I am attempting to do a LSA on it with starnet. However, I am not sure why it is failing the chi-sq test.
I determined a local grid and fixed coordinates for 2 points. Angles and distances were measured with a total station.
Can anyone advise?
Here is my data:
# local Grid
C E 5 48 !!
C D 5 75.977 !!
# Without crosshairs
TB B
T A 25-18-42.5 51.099
T E 155-53-30.5 27.977
T D 86-11-7 37.639
T C 66-54-40.5 34.91025
T B 205-42-26.5 40.961
TE A
# With crosshairs
M B-A-E 256-32-45.6 22.4735
M C-B-A 13-52-47 73.986
- 27 Replies
I haven’t tried the traverse, but if doesn’t have some obvious blunder in it, then anyone who wants to address the Chi-Square issue needs to know what standard errors you have given the program for angles, distances, instrument centering, and target centering.
One apparent problem is that you have fixed both coordinates of points D and E but then give traverse measurements through them. Try freeing one of those four coordinate values.
.
Passes easily for me with the following standard errors:
Project Default Instrument
Distances (Constant) : 0.005000 FeetInt
Distances (PPM) : 2.000000
Angles : 3.000000 Seconds
Directions : 3.000000 Seconds
Azimuths & Bearings : 3.000000 Seconds
Centering Error Instrument : 0.003000 FeetInt
Centering Error Target : 0.010000 FeetInt
I took an Error Analysis Class.
The instructor said he doesn’t even care if it passes Chi Square or not. I got the vapors, they had to give me smelling salts.
If it exceeds the lower bound, I don’t worry about it. If it exceeds the upper bound then I look for my stupid mistake I can’t see for the life of me even though it is staring right at me.
People who deal with social stats usually don’t care about the chi square result. When you actually have to make things work it needs to pass…
MicroSurvey STAR*NET-PRO Version 6.0.43
Copyright 1988-2011 MicroSurvey Software Inc.
Run Date: Thu Dec 13 2018 12:45:24Summary of Files Used and Option Settings
=========================================Project Folder and Data Files
Project Name RPLS-TEST
Project Folder C:OLD DATA DRIVECAL FIRE PROJECTSRPLS-TEST
Data File List 1. RPLS-test.datProject Option Settings
STAR*NET Run Mode : Adjust with Error Propagation
Type of Adjustment : 2D
Project Units : FeetUS; DMS
Coordinate System : LOCAL
Default Project Elevation : 0.0000 FeetUS
Apply Average Scale Factor : 1.0000000000
Input/Output Coordinate Order : North-East
Angle Data Station Order : At-From-To
Distance/Vertical Data Type : Slope/Zenith
Convergence Limit; Max Iterations : 0.010000; 10
Default Coefficient of Refraction : 0.070000
Earth Radius : 6372000.00 Meters
Create Coordinate File : Yes
Create Ground Scale Coordinate File : No
Create Dump File : NoInstrument Standard Error Settings
Project Default Instrument
Distances (Constant) : 0.010000 FeetUS
Distances (PPM) : 1.000000
Angles : 4.000000 Seconds
Directions : 3.000000 Seconds
Azimuths & Bearings : 4.000000 Seconds
Centering Error Instrument : 0.005000 FeetUS
Centering Error Target : 0.005000 FeetUSSummary of Unadjusted Input Observations
========================================Number of Entered Stations (FeetUS) = 2
Fixed Stations N E Description
E 5.0000 48.0000Free Stations N E Description
D 5.0000 75.9770Number of Angle Observations (DMS) = 7
At From To Angle StdErr
A B E 25-18-42.50 34.33
E A D 155-53-30.50 70.05
D E C 86-11-07.00 64.04
C D B 66-54-40.50 51.27
B C A 205-42-26.50 66.09
B A E 256-32-45.60 77.61
C B A 13-52-47.00 36.75Number of Distance Observations (FeetUS) = 7
From To Distance StdErr
A E 51.0990 0.0123
E D 27.9770 0.0123
D C 37.6390 0.0123
C B 34.9102 0.0123
B A 40.9610 0.0123
B E 22.4735 0.0123
C A 73.9860 0.0123Number of Azimuth/Bearing Observations (DMS) = 1
From To Bearing StdErr
E D N90-00-00.00E FIXEDAdjustment Statistical Summary
==============================Iterations = 2
Number of Stations = 5
Number of Observations = 15
Number of Unknowns = 8
Number of Redundant Obs = 7Observation Count Sum Squares Error
of StdRes Factor
Angles 7 2.796 0.925
Distances 7 3.292 1.004
Az/Bearings 1 0.000 0.000Total 15 6.088 0.933
The Chi-Square Test at 5.00% Level Passed
Lower/Upper Bounds (0.491/1.512)Adjusted Station Information
============================Coordinate Changes from Entered Provisionals (FeetUS)
Station dN dE
E -0.0000 -0.0000
D -0.0000 -0.0127Adjusted Coordinates (FeetUS)
Station N E Description
E 5.0000 48.0000
D 5.0000 75.9643
B 26.7377 42.3125
A 25.8722 1.3612
C 42.5447 73.4524Adjusted Observations and Residuals
===================================Adjusted Angle Observations (DMS)
At From To Angle Residual StdErr StdRes
A B E 25-19-14.53 0-00-32.03 34.33 0.9
E A D 155-53-24.54 -0-00-05.96 70.05 0.1
D E C 86-10-20.39 -0-00-46.61 64.04 0.7
C D B 66-54-53.40 0-00-12.90 51.27 0.3
B C A 205-42-07.15 -0-00-19.35 66.09 0.3
B A E 256-32-55.19 0-00-09.59 77.61 0.1
C B A 13-53-27.67 0-00-40.67 36.75 1.1Adjusted Distance Observations (FeetUS)
From To Distance Residual StdErr StdRes
A E 51.0962 -0.0028 0.0123 0.2
E D 27.9643 -0.0127 0.0123 1.0
D C 37.6286 -0.0104 0.0123 0.8
C B 34.9220 0.0118 0.0123 1.0
B A 40.9605 -0.0005 0.0123 0.0
B E 22.4695 -0.0040 0.0123 0.3
C A 73.9940 0.0080 0.0123 0.6Adjusted Azimuth/Bearing Observations (DMS)
From To Bearing Residual StdErr StdRes
E D N90-00-00.00E 0-00-00.00 FIXED 0.0Adjusted Bearings (DMS) and Horizontal Distances (FeetUS)
=========================================================
(Relative Confidence of Bearing is in Seconds)From To Bearing Distance 95% RelConfidence
Brg Dist PPM
A B N88-47-20.93E 40.9605 127.37 0.0196 478.5187
A C N76-58-41.46E 73.9940 115.49 0.0214 289.0120
A E S65-53-24.54E 51.0962 132.40 0.0208 407.0983
B C N63-05-13.79E 34.9220 121.19 0.0203 580.1120
B E S14-39-43.87E 22.4695 179.74 0.0158 704.7071
C D S03-49-39.61E 37.6286 117.68 0.0218 578.9600
D E S90-00-00.00W 27.9643 0.00 0.0226 806.4779Traverse Closures of Unadjusted Observations
============================================
(Beginning and Ending on Adjusted Stations)TRAVERSE 1
Error Angular = 27.00 Sec, 5 Angles, 5.40 Sec/Angle
Error Linear = 0.0260 N, 0.0302 E
Horiz Precision = 0.0398 Error in 192.5863, 1:4837, 206.75 PPMFrom To Unadj Bearing Unadj Dist
A B N88-47-20.93E BS
A E S65-54-01.97E 51.0990
E D N89-59-23.13E 27.9770
D C N03-49-35.27W 37.6390
C B S63-04-59.83W 34.9102
B A S88-47-20.93W 40.9610Error Propagation
=================Station Coordinate Standard Deviations (FeetUS)
Station N E
E 0.000000 0.000000
D 0.000000 0.009214
B 0.006361 0.008085
A 0.013092 0.008965
C 0.008651 0.011315Station Coordinate Error Ellipses (FeetUS)
Confidence Region = 95%Station Semi-Major Semi-Minor Azimuth of
Axis Axis Major Axis
E 0.000000 0.000000 0-00
D 0.022553 0.000000 90-00
B 0.019792 0.015569 89-00
A 0.032942 0.020574 17-16
C 0.029082 0.019230 113-59Relative Error Ellipses (FeetUS)
Confidence Region = 95%Stations Semi-Major Semi-Minor Azimuth of
From To Axis Axis Major Axis
A B 0.025299 0.019592 176-44
A C 0.041441 0.021363 165-25
A E 0.032942 0.020574 17-16
B C 0.020740 0.020033 118-54
B E 0.019792 0.015569 89-00
C D 0.025773 0.016471 132-10
D E 0.022553 0.000000 90-00Elapsed Time = 00:00:00
I changed the input a little bit:
# local Grid
C E 5 48 !!
B E-D N90-00-00.00E !C D 5 75.977 **
# Without crosshairs
TB B
T A 25-18-42.5 51.099
T E 155-53-30.5 27.977
T D 86-11-7 37.639
T C 66-54-40.5 34.91025
T B 205-42-26.5 40.961
TE A
# With crosshairs
M B-A-E 256-32-45.6 22.4735
M C-B-A 13-52-47 73.986
-Break————————————————————–Break-
It exceeds the upper bound with zero on the centering errors:
Network Adjustment with Error Propagation
Loading Network Data …
Checking Network Data …Performing Network Adjustment …
Iteration # 1
Iteration # 2
Iteration # 3
Solution Has Converged in 3 IterationsStatistical Summary
Observation Count Error Factor
Angles 7 2.964
Distances 7 3.579
Az/Bearings 1 0.000
Total 15 3.175Warning: Chi-Square Exceeded Upper Bound
Lower/Upper Bounds (0.491/1.512)Performing Error Propagation …
Writing Output Files …Network Processing Completed
Elapsed Time = 00:00:00On the other hand if I put in 1.00 centering errors it exceeds the lower bound:
Network Adjustment with Error Propagation
Loading Network Data …
Checking Network Data …Performing Network Adjustment …
Iteration # 1
Solution Has Converged in 1 IterationsStatistical Summary
Observation Count Error Factor
Angles 7 0.007
Distances 7 0.005
Az/Bearings 1 0.000
Total 15 0.006Warning: Chi-Square Exceeded Lower Bound
Lower/Upper Bounds (0.491/1.512)Performing Error Propagation …
Writing Output Files …Network Processing Completed
Elapsed Time = 00:00:00
I took an Error Analysis Class.
The instructor said he doesn’t even care if it passes Chi Square or not. I got the vapors, they had to give me smelling salts.
If it exceeds the lower bound, I don’t worry about it. If it exceeds the upper bound then I look for my stupid mistake I can’t see for the life of me even though it is staring right at me.
I agree with your instructor. Look at the residuals. If there is a blunder it will normally show up there. If the residuals look good, who cares what a subjective “goodness of fit” statistical test says. YMMV
If it exceeds the lower bound, I don’t worry about it. If it exceeds the upper bound then I look for my stupid mistake I can’t see for the life of me even though it is staring right at me.
I don’t like to have a statement about exceeding bounds one way or the other. I figure that some day some lawyer might latch onto that lower bounds fail without appreciating it’s true meaning. So I’ll dial down the centering errors until I get a pass. Generally that does it.
Centering errors=0.005:
A,25.87217,1.36119,
B,26.73774,42.31254,
C,42.54465,73.45237,
D,5.00000,75.96429,
E,5.00000,48.00000,Centering errors=0.00
A,25.86142,1.38409,
B,26.72045,42.31934,
C,42.53696,73.48722,
D,5.00000,75.99093,
E,5.00000,48.00000,Centering errors=1.00:
A,25.87513,1.36207,
B,26.74096,42.31441,
C,42.54891,73.44917,
D,5.00000,75.96836,
E,5.00000,48.00000,If it exceeds the lower bound, I don’t worry about it. If it exceeds the upper bound then I look for my stupid mistake I can’t see for the life of me even though it is staring right at me.
I don’t like to have a statement about exceeding bounds one way or the other. I figure that some day some lawyer might latch onto that lower bounds fail without appreciating it’s true meaning. So I’ll dial down the centering errors until I get a pass. Generally that does it.
Not to be contrarian, but if one decides to manipulate the a priori error estimates to get the chi-square statistic within the “bounds” why not go all the way in so that the statistic = 1.0000000?
Folks much wiser than I have told me enough times that my analysis of the LSA results should be concentrated on the residuals and whether they are reasonable. If one is interested in a mathematically robust method to detect outliers, I suggest the tau-test statistic. Dr. Alan J. Pope authored the NOAA Technical Report NOS 65 NGS1, “The Statistics of Residuals and the Detection of Outliers” in May 1976. It dealt with the detection of outliers in conventional triangulation networks when he worked at the NGS. The report includes an appendix with Pope’s algorithm chiseled in FORTRAN IV (for the other old pharts here)!
Failure of Chi square tells me there is likely a problem with my estimates or procedure. While it may be true that a particular dataset is just fine without passing, sound practice dictates that I figure out why. Not all problems manifest consistently…
Not to be contrarian, but if one decides to manipulate the a priori error estimates to get the chi-square statistic within the “bounds” why not go all the way in so that the statistic = 1.0000000?
Because that would be greedy.
Failure of Chi square tells me there is likely a problem with my estimates or procedure. While it may be true that a particular dataset is just fine without passing, sound practice dictates that I figure out why. Not all problems manifest consistently…
If you are talking about conventional traversing, I agree. I imagine that you have a better than fair idea of the a priori error estimates.
In my defense, I cannot remember the last time one of my surveys was done solely with terrestrial instruments. Being old and solo, the bulk of my work is done with GPS with minor conventional traverses when I’m below timberline. I’m also prone to shoot two or more intervisible control stations and combine with the GPS observations in an LSA. The chi-square test usually has a tantrum whenever I combine terrestrial measurements and GPS observations, which is why I concentrate on the residuals.
I agree that the residuals are what is truly important, and that the Chi-square is akin to a dashboard idiot light.
The chi-square test usually has a tantrum whenever I combine terrestrial measurements and GPS observations, which is why I concentrate on the residuals.
That suggests to me that you’re using unrealistic standard errors. Baseline processors are notoriously optimistic, and I usually have to scale the GNSS errors by 1.5 or 2.0 to get them to play nicely with my total station work.
Being “below the tree line” most of the time I combine GPS and terrestrial routinely. If your error estimates are realistic you should have no trouble with the adjustment. Generally I use the specifications on the data sheets for the instruments employed and mess with the centering errors. Only rarely do I dial up the GPS error factor to 1.5 or so, that being necessary when the observing conditions are obviously sketchy.
Gene,
I ran starnet for about 12 years, most of that combining data. If I were solo I wouldn’t bat an eye because I would know if the field crew was doing bonehead stuff. The statistical tests are a handy way to support or refute what the notes say and it can tell you how the equipment is being treated..
A general question to Jim and Norman: If you don’t scale the GPS, do the residuals significantly change?
Gene is right about large GNSS networks with a small conventional tie off in a corner, it can make the statistics look funny. If the GNSS and conventional are roughly equal sizes then the issue doesn’t appear as much.
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