nysapls conference 2015 · ©2010 j.v.r. paiva 1 1 joseph v.r. paiva, phd, ps, pe nysapls...

©2010 J.V.R. Paiva 1

1

Joseph V.R. Paiva, PhD, PS, PE

NYSAPLS

Conference 2015

• Poor quality results because even though

precision is high, accuracy may be lower than

desired

• Laypeople with science backgrounds will know if

subjects of errors and statistics are misunderstood

• Casts less than flattering light on the profession

• Costs!! (Rework, head scratching, nail biting, etc.)

2

• Know what/why you’re surveying

• Determine quality of results needed from client, situation and your own analysis

• Actively design work and post-survey analysis around pre-defined (expected) results

3


• Errors: types and sources in general

• Total station measurements

• GPS measurements

• Some ideas on how to model errors and improve accuracy

• Operational and organizational tips

[We’re only spending ½ a day on this!]

4

• Present in all measurements in surveying

• Thus no measurement is “TRUE” except by accident

• Error = Measurement True Value

• Correction = Error

5

• Not error

• Blunder

• Preventable with care, through processes and

standards

6


• Surveyors are measurement experts

• Goal is “true” measurements

• All measurements susceptible to error

• Therefore,

True measurement = observation + correction

Correction = opposite sign of combined errors from all sources

7

Understand them (how are they caused,

when are they caused, what is the

magnitude?)

Eliminate as many as possible (or as much

as needed) through modeling, procedures,

instrumentation, software, and in post-

processing

Watch out for blunders! (operations and data

analysis, develop your blunder sniffing skills)

8

• Personal (you, your crew—i.e. contributed by personnel)

• Natural (the environment)

• Instrumental (GPS, total station, optical plummet, prism pole, tape, etc., etc.—i.e. everything in your surveying system except for personnel)

9


• Systematic (Bias)

Can be determined if you know enough about instrumentation and environment

Can be eliminated thru calcs or procedures

• Random

Unpredictable as to sign and magnitude

Tend to be small

In the long run roughly equal positive and negative errors, thus tend to cancel out somewhat

10

• Fineness of measurement, repeatability,

reflection of the tools

• Emphasis on the methods

11

• Nearness of a measurement to the true value

• Emphasis on the results

12


• Not synonymous

• You don’t automatically get one with the other

• Surveyor must strive for both

• Possible to do well in one and horribly in the other

• Possible to accidentally do well in one

13

14

Precise

…and accurate

Precise

Accurate

…but is it precise?

Less precise

…but accurate

15

Random error ( is small)

Random error ( is large)

Systematic error

(or bias)

Unbia

sed

Bia

sed


1. Small

2. Unpredictable as to size

3. Unpredictable as to sign

4. Close to equal positive and negative errors

5. Tend to cancel out—but some remains!

16

• Residual = Measurement – Mean =

• Error = Measurement – True Value

• Be aware of the difference

• They are not the same, but often residuals are analyzed to understand how errors behave

17

is Greek letter, pronounced

“nu”, often called “vee” because

it looks like the English letter

• When a quantity is measured several times (with equal care), the mean will always be more reliable than any single one of those measurements

• The mean is the true value only when

o all systematic errors have been eliminated and

o sufficient measurements have been taken to average out random errors

18


• When systematic errors in the measurements have been “handled” as best as possible through 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”

19

• Can be understood through process of plotting a histogram

20

• Angle measured 50 times

• Calculate mean, residuals and standard deviation

• Let’s say we calculate that = ±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

21


22

- 0 +

Magnitude of Class IntervalsNu

mb

er

of

me

asu

rem

en

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

23

24

•Tall versus squat = high precision versus low precision

•Thus standard deviation is low on left curve and high on right curve


• Measure of precision

• Covers 68% of area under the curve

• Other ratios of give specific areas

corresponding to confidence levels

25

26

-E95 = -2 E95 = 2

• 68.2% for

• 95.4% for 2

• 99.7% for 3

• 50% for 0.645

Area

under

curve

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

27

©2010 J.V.R. Paiva 10

• Measurement has three parts

o The quantity measured

o The uncertainty

o The confidence level

o E.g. 118°42’12”±2.1” standard deviation

o E.g. 23,478.65 m ±0.324 m @ 95% confidence

28

1

2

n

• is the residual of each measurement (measurement – mean),

• 2 is the sum of the squares of the residuals,

• n is the number of measurements,

• is also referred to as “Root Mean Square Error”(“RMSE” and sometimes simply “RMS”).

29

30

No. Measurement Resi-

dual

Resi-

dual2

1 27°43’55” 2 4

2 27°43’55” 2 4

3 27°43’50” -3 9

4 27°43’52” -1 1

5 27°44’00” 7 49

6 27°43’49” -4 16

7 27°43’54” 1 1

8 27°43’56” 3 9

9 27°43’46” -7 49

10 27°43’51” -2 4

Mean = 27°43’53”

1

2

n

Sum of 2 = 146

n-1 = 9

146/9 = 16.2

Sq. rt. of 16.2 = ±4”

©2010 J.V.R. Paiva 11

• 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

150

7m

31

nm

• For all the previous calcs use the basic equation

for the standard deviation of the mean

nm

32

• Sum

• Sum when uncertainty

for each measurement

is equal

22

3

2

2

2

1 ... nsum

neachsum

33

©2010 J.V.R. Paiva 12

• Dissimilar uncertainties

• Four distances are measured end-to-end by four different survey crews

• The distances are:

o 4328.74 ft ±0.09

o 9843.56 ft ±0.27

o 3412.94 ft ±0.14

o 3585.02 ft ±0.11

• What is the most probable value of the total distance and its uncertainty?

34

• Most probable value is the sum of those four end-to-end distances: 21,170.26 ft

• Uncertainty is square root of the sum of the squares of the individual uncertainties

ftsum 336.011.14.27.09. 2222

35

• A survey crew measures several distances end-to-end. The uncertainty in each of those measurements is ±0.23 ft standard deviation.

• What is the total uncertainty in a string of 20 measurements?

36

©2010 J.V.R. Paiva 13

• As the uncertainty in each measurement is the same, the simplified equation can be used.

• The uncertainty is going to be the square root of the number of measurements multiplied by the uncertainty in one measurement

ftsum 03.12023.0

37

• Total independence not always possible

• But try to be as “independent as possible”

• i.e. make EDM measurement, turn away from prism, return and measure again

• In traverse measure “forward” and “back”

38

• If you are measuring two vectors from one point

with two GNSS receivers, break down the set up

between measurements

39

B

A

10

0

©2010 J.V.R. Paiva 14

• If angle rating is per DIN or ISO,

• multiply value by 2 …

• to get standard deviation of angle measured with this instrument in F1 and F2

40

• Instrument spec is ±3”

• This is uncertainty for each pointing

• Each angle has two pointings (directions)

• Thus angle uncertainty is ±32=±4.2”

41

• If each angle is measured 1DR (i.e. twice), angle uncertainty is ±4.2”

• If each angle is measured 2DR (i.e. four times)

• Angle uncertainty is ±4.2/2=±3”

• If angle is measured 1D, angle uncertainty is ±4.2 2=±6”

42

©2010 J.V.R. Paiva 15

43

•Rigorous field process

•Easy to make mistakes

•Long and tedious

•Evaluate scale and constant errors

•Standard deviation

•Use of Calibration Base Lines

NOAA Technical Memorandum

NOS NGS-10

•Computation using “CALIBRAT”

44

A B C

AB + BC should equal AC

If error exists (e), then

it will be in each of the

measurements, thus

AB + BC – AC = e

45

Accuracy 100 Ft. 1100Ft. 2200 Ft. 3300 Ft.

(2mm+2ppm) 2.1mm=0.007ft 2.7mm=0.009ft 3.3mm=0.011ft 4mm=0.013ft.









©2010 J.V.R. Paiva 16

• 1/1,000,000 (!)

• No different than precision ratios

• With temperature, 10°C = 10 PPM

• With pressure, 1” Hg = 10 PPM

• Did you know 1.1” Hg change 1000+ ft?

46

• 1 PPM = 1:1,000,000

• 10 PPM = 1:100,000

• 100 PPM = 1:10,000

• 5 PPM = ?

• 20 PPM = ?

• 80 PPM = ?

• 125 PPM = ?

47

• If EDM is rated at 3mm + 3 PPM, what is error in a 50 ft shot?

• What is the precision ratio?

• Answer:

• First convert both to distances

• 3mm = 0.003m = 0.01 ft

• 3*(3/1,000,000)*50 ft = 0.0005 ft (negligible)

• Thus precision is 0.01/50 = 1:5,000 (!)

48

©2010 J.V.R. Paiva 17

• What is PPM impact?

• Rule of thumb:• 10 PPM per 10°C 20°F

• 10 PPM per 1.1 inch of mercury (Hg)

• The OTHER rule: use local pressure (i.e. no radio station temperature and pressure, especially pressure!)

49

• Temp is measured in the shade, approx 6 ft off the ground

• Where the line of sight passes is critical!

• If barometer is used, calibrate periodically

• If using weather station data:

o Know elev of weather sta

o Know your elev

o Correct at the rate of approx 1.1” Hg per 1000 ft

50

• Error in 100 ft with 20 PPM of error is 0.002 ft

• …in 1000 ft, error is = 0.02

• What is the equivalent precision ratio?

• Answer: 1/50,000

51

©2010 J.V.R. Paiva 18

52Project Area0 miles 5 10 15

53

A

B

C

1

2

Reflections off buildings, trees, ground, water, fences, etc.

54

Direct Signal

Reflected Signal

©2010 J.V.R. Paiva 19

55

Local Topography

Geoid

Ellipsoid

Mass Deficiency

Mass Excess

56

Topographic Surface

Geoid

Ellipsoid

H h

N

H = h + N

e = Deflection of the vertical

e

H = Ellipsoid Height

h = Orthometric Height

N = Geoid Undulation

• Just as important as the “big two” components of the system

• Chain is only as strong as its weakest link

• Don’t forget anything!

• Be constantly evaluating

• Most important accessory: humans

57

©2010 J.V.R. Paiva 20

• Fit

• Cleanliness

• Check threads (grit, smoothness, lubrication)

• Moisture issues

• Vibration and shock issues

58

• If not rotatable, watch out!

• Know how to check

• Know how to adjust

• Errors in excess of 0.1 ft per setup not uncommon

59

60

©2010 J.V.R. Paiva 21

• Easily forgotten

• Easily fixed

• Match the tripod to the job

• Be aware of the weak points: hinges, clamps,

shoes, head

61

• Straightness

• Sensitivity of circular bubble vial

• Degree of adjustment of circular vial

62

• Typical level vial sensitivity can vary on prism poles from 5 minutes to 60 minutes

• If 30 minutes, 2 mm out-of-center…

prism on top of 6 ft pole is out of plumb 0.05 ft

• How to calculate?

63

©2010 J.V.R. Paiva 22

64

height

e1tan

ftftheighte 052.0'30tan6tan

e

ht

65

Tape Length 0.01

Temperature 15o F

Tension (pull) 5.4 lbs

Sag 7.5” at center

Alignment 1.4 ft at one end or 7.5” at center

Tape Not Level 1.4 ft diff in elevation

Plumbing 0.01

Marking 0.01

Interpolation 0.01

66

©2010 J.V.R. Paiva 23

100 ft

Source Error (ft.) Error2

Tape Length Known 0.000000

Temp (10o F error) 0.006 0.000036

Tension (5 lb error) 0.009 0.000081

Alignment (0.05 ft) 0.000 0.000000

Tape Not Level (0.5 ft) 0.001 0.000001

Plumbing 0.005 0.000025

Marking 0.001 0.000001

Interpolation 0.001 0.000001

SUM 0.023 0.000145

Sq Rt of Sum of Errors2 = 0.012 ft

1: 8,000 OR 120 PPM67

100


Length Known 0.000000

Temp (10o F error) 5 PPM = 0.0005 0.00000025

Pressure (1” Hg) 5 PPM = 0.0005 0.00000025

Centering with pole 0.03 0.0009

Centering w/O.P. 0.005 0.000025

Mfr’s error constant 0.003 0.000009

Mfr’s error scale 3 PPM = 0.0003 0.00000009

SUM 0.0393 0.000093459


1: 3,000 OR 306 PPM

68

(5,000



Temp (10o F error) 5 PPM = 0.025 0.000625

Pressure (1” Hg) 5 PPM = 0.025 0.000625

Centering w/O.P. 0.005 0.000025

Centering w/O.P. 0.005 0.000025

Mfr’s error constant 0.003 0.000009


SUM 0.078 0.001534


1: 127,000 OR 8 PPM

69

©2010 J.V.R. Paiva 24

2,500 ft



Tropospheric delays0.0025 m = 0.008 ft 0.000067

Centering w/O.P. 0.005 0.000025

Centering w/O.P. 0.005 0.000025

Mfr’s error constant 0.01 m = 0.03281 0.001076


SUM 0.05581 0.001218

Sq Rt of Errors2 = 0.0349 ft

1:72,000 OR 14 PPM

70

71

22

3

2

2

2

1 ... nderived

72

nsinglederived

About seminar presenter Joseph V.R. Paiva Dr. Joseph V.R. Paiva, is principal and CEO at GeoLearn, LLC (www.geo-learn.com) which is an online provider of professional and technical education since February 2014. He continues to serve as a consultant in the field of geomatics and general business, particularly to lawyers, surveyors and engineers, and international developers, manufacturers and distributors of instrumentation and other geomatics tools. One of Joe’s previous roles was COO at Gatewing NV, a Belgian manufacturer of unmanned aerial systems (UAS) for surveying and mapping during 2010-2011. He also is a writer in many magazines and journals and has been on the “seminar circuit,” delivering continuing education to geospatial professionals, as well as technician and exam preparation courses. Joe was previously 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. He has continued his interest in teaching by serving as an adjunct instructor of online credit and non-credit courses at Texas A&M-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, SDR20 series and SDR33 Electronic Field Books and software interface 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. He writes for POB and The Empire State Surveyor magazines, occasionally contributes to other publications and has been a past contributor of columns to Civil Engineering News. GeoLearn is the online learning portal provider of the Missouri Society of Professional Surveyors and the Geographic and Land Information Society. To access these sites, find the links to their portals at these organizations’ websites. More organizations are set to partner with GeoLearn in 2015. Dr. Paiva can be reached at joepaiva@geo-‐learn.com or on Skype at joseph_paiva.

www.GeoLearn.com

Jan2015

nysapls conference 2015 · ©2010 j.v.r. paiva 1 1 joseph v.r. paiva, phd, ps, pe nysapls...

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