Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph...
Transcript of Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph...
![Page 1: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/1.jpg)
1/10/19
1
Errors Analysis in SurveyingJoseph Paiva
Saratoga SpringsJanuary 2019
Objectives• Something about errors and mistakes• Something about types and sources of errors• Standard deviation and its relevance to us• Use statistics to design surveying procedures• Analyzing what we do• Applying the results of the analysis
© 2019 J.V.R. Paiva 21/10/19
![Page 2: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/2.jpg)
1/10/19
2
Errors• Difference between a measurement and the true
value• ! = #$%& − ()*$• Therefore ()*$ = #$%& − !• Errors can be positive or negative depending on
whether the true value is larger or smaller than the measured value
© 2019 J.V.R. Paiva 31/10/19
It Makes The Difference• Surveying is a tough business• Especially when competitors are constantly
undercutting each other decreasing the value of a survey
• This “competition” also moves status of asurvey map or plat toward being meaningless
© 2019 J.V.R. Paiva 41/10/19
![Page 3: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/3.jpg)
1/10/19
3
Instead• Avoid “me too” work• Be proud of what you deliver when you
perform a survey• Actually describe it piece by piece• TALK to your clients, business groups, service
groups, etc.© 2019 J.V.R. Paiva 51/10/19
But…• That means talking about your work as if you
are an expert• But without obfuscation or talking down
© 2019 J.V.R. Paiva 61/10/19
![Page 4: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/4.jpg)
1/10/19
4
When It Comes to Errors• Know the language• Know the math• Know the statistics• If we can’t explain the technical aspects of
what we do, why would anyone want to pay good money for it? [and think it was worth it]
© 2019 J.V.R. Paiva 71/10/19
Definitions [1]• Error: difference between a measurement and
true value• So positive error means the measurement is
larger than the true value• BUT! How do we know what the true value is?
© 2019 J.V.R. Paiva 81/10/19
![Page 5: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/5.jpg)
1/10/19
5
Definitions [2]• Mean is the average• Usually considered more reliable than a single
measurement• Redundancy is one of the hallmarks of good
surveying measurement• Independent measurements is another© 2019 J.V.R. Paiva 91/10/19
Definitions [3]• Residual is the difference between a measurement
and the mean• ! = #$%& − ()• Where ! is residual• () is the mean• If we have n measurements, then we will have n
residuals© 2019 J.V.R. Paiva 101/10/19
![Page 6: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/6.jpg)
1/10/19
6
Error Sources• Nature (natural errors) – from the
environment• Technology (instrumental errors)• Humans (personal errors) – usually cause of
randomness in how something is sighted, aligned, marked, etc.
Definitions [4]
© 2019 J.V.R. Paiva 111/10/19
Error Types• Systematic– Usually varies as a function of the measurement,
but not always linear as in curvature of the Earth• Random– Varies in sign and magnitude with every
measurement– Large random errors occur rarely
Definitions [5]
© 2019 J.V.R. Paiva 121/10/19
![Page 7: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/7.jpg)
1/10/19
7
Mistakes• Also known as blunders• Usually caused by lack of care or attention in
the measurement process by humans• There are cases of technology defects that
appear as blunders in measurements
Definitions [6]
© 2019 J.V.R. Paiva 131/10/19
If We Are Going To Be Precise…• Do not interchange error and mistake• Do not call typing errors errors; they are
mistakes• Do not call errors in sports errors; mistakes!• When you write something down incorrectly,
that’s not an error MISTAKE!© 2019 J.V.R. Paiva 141/10/19
![Page 8: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/8.jpg)
1/10/19
8
Bias in Measurements• Your car odometer reads 10.1 miles when you
have truly gone 10.0 miles• Error or mistake?• Systematic or Random?• Source?
© 2019 J.V.R. Paiva 151/10/19
Bias in Measurements• Your EDM measurements are consistently ~0.1
ft long regardless of how long the measurement is
• Error or mistake?• Systematic or Random?• Source?© 2019 J.V.R. Paiva 161/10/19
![Page 9: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/9.jpg)
1/10/19
9
Bias in Measurements• You initialize your RTK system, then conduct a
survey• You check into two known monuments and each is
1.2 ft N and 3.4 ft W of your record• Error or mistake?• Systematic or Random?• Source?
© 2019 J.V.R. Paiva 171/10/19
Bias in Measurements• You are following a surveyor• You set up at a monument on map, sight along
block and turn 90°16’30” to find a corner that’s at a record distance of 567.00 ft
• You find the monument, but miss it for distance by -0.06 ft and for angle by 0.04 ft to the right
© 2019 J.V.R. Paiva 181/10/19
![Page 10: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/10.jpg)
1/10/19
10
What Do You Do?• Call existing monument good?• Set your own monument?• Something else?• [The monuments on the subdivision plat were
set in …]
© 2019 J.V.R. Paiva 191/10/19
How Well• Can you define a direction?• A distance?• A position?• An elevation?
© 2019 J.V.R. Paiva 201/10/19
![Page 11: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/11.jpg)
1/10/19
11
What Is The [Un]Certainty• In your measurements?• Why should you care?• Does anybody care?
© 2019 J.V.R. Paiva 211/10/19
The Average• Can be a better value than any single
measurement• But only if you’ve removed systematic errors
and the blunders have been prevented or eliminated
© 2019 J.V.R. Paiva 221/10/19
![Page 12: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/12.jpg)
1/10/19
12
Accuracy• A statement of how close a measurement or
value is to the true value• A reflection of the results of measurements
and analysisOUTCOMES
© 2019 J.V.R. Paiva 231/10/19
Precision• A statement of repeatability, fineness of
measuring technology, care taken in the measurements
• A reflection of the methods used in the measurement
PROCESSES
© 2019 J.V.R. Paiva 241/10/19
![Page 13: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/13.jpg)
1/10/19
13
The Shooting Analogy
© 2019 J.V.R. Paiva 25
Precise or accurate?
1/10/19
Errors• Understand them (how they are caused, when
they are caused, the magnitude?)• Eliminate as many as possible through
modeling, procedures, instrumentation, software, and in post-processing
• Watch out for blunders! (operations and data analysis)
26© 2019 J.V.R. Paiva 1/10/19
![Page 14: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/14.jpg)
1/10/19
14
Continuing About the Mean• When systematic errors in the measurements
have been �handled� as best as possiblethrough procedures and calculations, the mean is the best estimate of the true value
• �Best as possible� varies depending on the intended use of the survey data by the �user�
27© 2019 J.V.R. Paiva 1/10/19
Standard Normal Distribution•Can be understood through process of plotting a histogram
28
http://upload.wikimedia.org/wikipedia/commons/thumb/7/74/Normal_Distribution_PDF.svg/350px-Normal_Distribution_PDF.svg.png© 2019 J.V.R. Paiva
1/10/19
![Page 15: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/15.jpg)
1/10/19
15
Random Error Example•Angle measured 50 times•Calculate mean, residuals and standard deviation• Let’s say we calculate that s = �7�• Standard deviation theory: examine individual
measurements, 68% will be within 7 seconds of the mean•Also, if you make one more measurement, there is a 68%
probability that it will be within 7� of the mean
29© 2019 J.V.R. Paiva
1/10/19
Histogram Plot
30
- 0 +
Magnitude of Class IntervalsNum
ber o
f mea
sure
men
ts in
cla
ss in
terv
al
• Sort by sign and interval; determine class interval; plot bar graph
• Join tops of bars; approximates standard normal (Gauss) curve
• As measurements are increased and class intervals decreased, ideal shape can be observed
© 2019 J.V.R. Paiva 1/10/19
![Page 16: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/16.jpg)
1/10/19
16
Understanding Probability
31
http://www.usmle-forums.com/images/added/attachments/inpost/bellcurve.gif
© 2019 J.V.R. Paiva 1/10/19
Confidence Levels (area under curve)
• 68.2% for s• 95.4% for 2s• 99.7% for 3s• 50% for 0.645s
Areaundercurve
s coefficient
0.80 1.28155
0.90 1.64485
0.95 1.95996
0.98 2.32635
0.99 2.57583
0.995 2.80703
0.998 3.09023
0.999 3.29052
1/10/19 32© 2019 J.V.R. Paiva
![Page 17: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/17.jpg)
1/10/19
17
Thus…• Measurement has three parts– The quantity measured– The uncertainty– The confidence level– E.g. 118°42’12”�2.1” std dev (68% conf)– E.g. 23,478.65 m ±0.324 m @ 95% confidence
1/10/19 33© 2019 J.V.R. Paiva
Simple s Calculation
1/10/19 34
No. MeasurementResi-dual
Resi-dual2
1 27�43’ 55” 2 42 27�43’ 55” 2 43 27�43’ 50” -3 94 27�43’ 52” -1 15 27�44’ 00” 7 496 27�43’ 49” -4 167 27�43’ 54” 1 18 27�43’ 56” 3 99 27�43’ 46” -7 49
10 27�43’ 51” -2 4Mean = 27� 43’ 53”
Sum of n2 = 146
n-1 = 9
146/9 = 16.2
Sq. rt. of 16.2 = �4�
! = ± Σ%&' − 1
© 2019 J.V.R. Paiva
![Page 18: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/18.jpg)
1/10/19
18
• The standard deviation of the 50 measurements in our �thought�experiment is �7�
• But what is the standard deviation of the mean?
• Logical that mean should be more certain than an individual measurement
The Strength of the Mean
1/10/19 35
!" = !$
!" = 750 ≅ 1”
© 2019 J.V.R. Paiva
“Designing” Procedures
1/10/19© 2019 J.V.R. Paiva 36
!"#$%& =!()#*+#,-
.
. = !()#*+#,-!"#$%&
/
Eq. A
Eq. B
• Tot Sta accuracy ±5”• Specs req ±4” @ 95% conf• Requirement at 68% conf is ±2”• Substitute into eq. B to solve for n
. = 52
/= 2.5/ = 6.25
• n = 6, 7, 8?
![Page 19: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/19.jpg)
1/10/19
19
Combining Random Errors
371/10/19
!"#$%&#" = !() + !)) + !+) + ⋯+ !-)
!"#$%&#" = !.%-/0# 1
© 2019 J.V.R. Paiva
How Much is the Error (e.g. prism pole)?• Typical level vial sensitivity can vary on prism
poles from 10 to 60 minutes• The level spec refers to the angle change to
move the position of the bubble 2 mm• If 30 minutes, and the bubble is 2 mm out-of-
center…• Prism on top of 6 ft pole is out of plumb 0.05 ft
1/10/19 38© 2019 J.V.R. Paiva
![Page 20: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/20.jpg)
1/10/19
20
Calculating Prism Pole Error
1/10/19 39
e
ht
a
! = #$%&' (ℎ(*+ℎ#
( = ℎ(*+ℎ#× tan != 61#× tan 30′= 0.052 1#
© 2019 J.V.R. Paiva
Level Vial Centering/Adjustment
1/10/19 40© 2019 J.V.R. Paiva
![Page 21: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/21.jpg)
1/10/19
21
Angle-Distance Relationships
1/10/19 41
dangle
ddist
A
B
dangle = ddist (if angles and distances have same uncertainty)
© 2019 J.V.R. Paiva
Expanded View
1/10/19© 2019 J.V.R. Paiva 42
![Page 22: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/22.jpg)
1/10/19
22
Angle-Distance Relationships
1/10/19 43
a
dist
ddist
! = tan&' ()*+,-./0
tan ! = 1234./.56
© 2019 J.V.R. Paiva
Angle-Distance Relationships
• When measuring angles and distances, what is the limiting factor?
• Remember a chain is only as strong as its weakest link
1/10/19 44© 2019 J.V.R. Paiva
![Page 23: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/23.jpg)
1/10/19
23
Angle–Distance Relationships / 2
• If you are required to perform a survey with a relative accuracy of 1:50,000 what should the accuracy of the angles be? [�4�]
• If you can measure angles �3�, what should the relative accuracy of the distances be to be comparable in accuracy? [1/70,000]
1/10/19 45© 2019 J.V.R. Paiva
Conditions Causing 0.01 ft error in 100 ft(calibrated steel tape/band)
Tape Length 0.01 Temperature 15o F Tension (pull) 5.4 lbsSag 7.5” at centerAlignment 1.4 ft at one end or 7.5” at centerTape Not Level 1.4 ft diff in elevationPlumbing 0.01Marking 0.01Interpolation 0.01
461/10/19© 2019 J.V.R. Paiva
![Page 24: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/24.jpg)
1/10/19
24
Possible Errors Using Common ProceduresStandard 100 ft measurement with calibrated tape
Source Error (ft.) Error2 \
Tape Length Known 0.000000Temp (10o F error) 0.006 0.000036Tension (5 lb error) 0.009 0.000081Alignment (0.05 ft) 0.000 0.000000Tape Not Level (0.5 ft) 0.001 0.000001Plumbing 0.005 0.000025Marking 0.001 0.000001Interpolation 0.001 0.000001SUM 0.023 0.000145
47
Sq Rt of Sum of Errors2 = 0.012 ft
1:8,000 OR 120 PPM
1/10/19© 2019 J.V.R. Paiva
1/10/19© 2019 J.V.R. Paiva 48
Possible Errors Using Common ProceduresCalibrated EDM (100 ft; accuracy 3 mm + 3 PPM)
Source Error (ft.) Error2
Length Known 0.000000Temp (10o F error) 5 PPM = 0.0005 0.00000025Pressure (1/2” Hg) 5 PPM = 0.0005 0.00000025Centering with pole 0.03 0.0009Centering w/O.P. 0.005 0.000025Mfr’s error constant 0.003 0.000009Mfr’s error scale 3 PPM = 0.0003 0.00000009SUM 0.0393 0.000093459
0.0306 ft
1: 3,000 OR 306 PPM
![Page 25: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/25.jpg)
1/10/19
25
1/10/19© 2019 J.V.R. Paiva 49
Possible Errors Using Common ProceduresCalibrated EDM (5,000 ft; accuracy 3 mm + 3 PPM)
Source Error (ft.) Error2
Length Known 0.000000Temp (10o F error) 5 PPM = 0.025 0.000625Pressure (1” Hg) 5 PPM = 0.025 0.000625Centering w/O.P. 0.005 0.000025Centering w/O.P. 0.005 0.000025Mfr’s error constant 0.003 0.000009Mfr’s error scale 3 PPM = 0.015 0.000225SUM 0.078 0.001534
0.03917 ft
1: 127,000 OR 8 PPM
Possible Errors Using Common ProceduresRTK GPS (pole w/bipod) 2,500 ft baseline (acc. 1 cm + 2 PPM)
501/10/19© 2019 J.V.R. Paiva
Source Error (ft.) Error2
Length Known 0.000000Tropospheric delays 0.0025 m = 0.008 0.000067Centering w/O.P. 0.005 0.000025Centering w/bubble 0.005 0.000025Mfr’s error constant 0.01 m = 0.03281 0.001076Mfr’s error scale 2 PPM = 0.005 0.000025SUM 0.05581 0.001218
0.0349 ft
1:72,000 OR 14 PPM
![Page 26: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/26.jpg)
1/10/19
26
Typical Total Station Error
• ±3 arc seconds AND
• ±(2 mm + 2 PPM)
511/10/19© 2019 J.V.R. Paiva
Actually A Statement Of Precision • Becomes a statement of accuracy only if• Blunders have been eliminated and,• Systematic errors have been removed
521/10/19© 2019 J.V.R. Paiva
![Page 27: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/27.jpg)
1/10/19
27
Example• Measure a traverse four times or ten times• Average the “precision” computed by dividing the
closure error by the perimeter• Let’s say the total error in the traverse averaged
out to 0.20 m and the total traverse length was 10,000 m
• Then precision is 1:50,000
531/10/19© 2019 J.V.R. Paiva
BUT• Let’s say PPM correction for temperature and
pressure (combined) as used is set to +45• But it really should have been set to -5 PPM• So, considering distances alone, they are all in
error by 1,000,000/50 = 1:20,000• This is 2.5 cm per 500 m traverse side (0.082 ft per
1,600 ft)
541/10/19© 2019 J.V.R. Paiva
![Page 28: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/28.jpg)
1/10/19
28
So…• No matter how well the precision comes out
(in this case 1:50,000)• The accuracy can’t be better that 1:20,000• In fact it will be worse, as we have not
evaluated angle errors yet [plus, what other error sources have not yet been accounted for?]
551/10/19© 2019 J.V.R. Paiva
Typical RTK Error• ±(1 to 2 cm + 1 to 2 PPM)• Again determined from repeated
measurements• Value is standard deviation with assumption
that blunders and systematic errors have been eliminated
561/10/19© 2019 J.V.R. Paiva
![Page 29: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/29.jpg)
1/10/19
29
Bad News For RTK-Determinations• When you use RTK-derived positions to inverse
the distance, what’s the uncertainty & confidence level?
• Answer: 1.4 cm (0.043 ft) one sigma, double if two sigma
1/10/19© 2019 J.V.R. Paiva 57
If line is 400 ft, precision is 1:9,000 at 68% confidence and 1:4,500 at 95% confidence
Worst Case• If we use 0.086 ft (95% conf.) for radius of
circle and L = 200 ft• Potential error in bearing is ≈ 89 arc seconds• Angle uncertainty of ±89” is equivalent to
1:2,300 or 430 PPM
1/10/19© 2019 J.V.R. Paiva 58
![Page 30: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/30.jpg)
1/10/19
30
When You Determine Survey “Accuracy”
• Most of the time you are only determining precision
• UNLESS…. • What?
591/10/19© 2019 J.V.R. Paiva
Least Squares Adjustments• What do you put in for angle/distance uncertainty?• What do you put in for position and/or line
uncertainty?• How do you make allowances for number of sets
(rounds) measured?• How do you account for number of epochs,
satellites, observation time, DOP, etc.?
601/10/19© 2019 J.V.R. Paiva
![Page 31: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/31.jpg)
1/10/19
31
What Do Manufacturers Account For?• Not your leveling error• Not your centering error• If using prism/antenna pole, not its straightness• Not centering and leveling error of target if TS• Not temp and pressure PPM error• Not iono and tropo error• Etc.
611/10/19© 2019 J.V.R. Paiva
What Will You Account For?Good Luck!
1/10/19© 2019 J.V.R. Paiva 62
![Page 32: Errors Analysis in Surveying2019 - cdn.ymaws.com · 1/10/19 1 Errors Analysis in Surveying Joseph Paiva Saratoga Springs January 2019 Objectives •Something about errors and mistakes](https://reader034.fdocuments.net/reader034/viewer/2022051808/6009f1b33c3d53499f230185/html5/thumbnails/32.jpg)
www.geo-learn.com
AboutseminarpresenterJosephV.R.Paiva
Dr. Joseph V.R. Paiva, is principal and CEO of GeoLearn, LLC (www.geo-learn.com), an online provider of professional and technician education since February 2014. He also works as a consultant to lawyers, surveyors and engineers, and international developers, manufacturers and distributors of instrumentation and other geomatics tools, as well being a writer and speaker. One of his previous roles was COO at Gatewing NV, a Belgian manufacturer of unmanned aerial systems (UAS) for surveying and mapping during 2010-2012. Trimble acquired Gatewing in 2012. Because of this interest in drones, Joe is an FAA-licensed Remote Pilot.
Selected previous positions Joe has held includes: managing director of Spatial Data Research, Inc., a GIS data collection, compilation and software development company; senior scientist and technical advisor for Land Survey research & development, VP of the Land Survey group, and director of business development for the Engineering and Construction Division of Trimble; vice president and a founder of Sokkia Technology, Inc., guiding development of GPS- and software-based products for surveying, mapping, measurement and positioning. Other positions include senior technical management positions in The Lietz Co. and Sokkia Co. Ltd., assistant professor of civil engineering at the University of Missouri-Columbia, and partner in a surveying/civil engineering consulting firm.
Joe has continued his interest in teaching by serving as an adjunct instructor of online credit and non-credit courses at the State Technical College of Missouri, Texas A&M University-Corpus Christi and the Missouri University of Science and Technology. His key contributions in the development field are: design of software flow for the SDR2 and SDR20 series of Electronic Field Books, project manager and software design of the SDR33, and software interface design for the Trimble TTS500 total station.
He is a Registered Professional Engineer and Professional Land Surveyor, was an NSPS representative to ABET serving as a program evaluator, where he previously served as team chair, and commissioner, and has more than 30 years experience working in civil engineering, surveying and mapping. Joe writes for POB, The Empire State Surveyor and many other publications and has been a past contributor of columns to Civil Engineering News. He has published dozens of articles and papers and has presented over 150 seminars, workshops, papers, and talks in panel discussions, including authoring the positioning component of the Surveying Body of Knowledge published in Surveying and Land Information Science. Joe has B.S., M.S. and PhD degrees in Civil Engineering from the University of Missouri-Columbia. Joe’s current volunteer professional responsibilities include president of the Surveying and Geomatics Educators Society (SaGES) and various ad hoc and organized committees of NSPS, the Missouri Society of Professional Surveyors and other groups.
GeoLearn is the online learning portal provider for the Missouri Society of Professional Surveyors, the Kansas Society of Land Surveyors, the New York State Association of Professional Land Surveyors, The Texas Society of Professional Surveyors, The Pennsylvania Society of Land Surveyors, the Wisconsin Society of Land Surveyors, Arizona Professional Land Surveyors, the Oklahoma Society of Land Surveyors and the Geographic and Land Information Society. More organizations are set to partner with GeoLearn soon. Dr. Paiva can be reached at [email protected] or on Skype at joseph_paiva.
Jan 2019