GPS Derived Heights: A Height Modernization Primer

1
GPS Derived Heights A Height ModernizationPrime
r
Marquette, Michigan.January 24, 2006 Flint,
Michigan..January 26, 2006

• Renee Shields
• National Geodetic Survey
• National Oceanic and Atmospheric Administration

2
Height Modernization is
the ability to compute accurate orthometric
(sea level) heights using GPS technology
the establishment of accurate, reliable heights
using GPS technology in conjunction with
traditional leveling, gravity, and modern remote
sensing information.
3
How to achieve accurate GPS heights

• 1) What types of heights are involved?
• Orthometric heights
• Ellipsoid heights
• Geoid heights
• 2) How are these heights defined and related?
• 3) How accurately can these heights be determined?

4
What is a GEODETIC DATUM?

• Geodetic Datum
• A set of constants specifying the coordinate
  system used for geodetic control, i.e., for
  calculating coordinates of points on the Earth
• above together with the coordinate system and
  the set of all points and lines whose
  coordinates, lengths, and directions have been
  determined by measurement or calculation.
• Definitions from the Geodetic Glossary,
  September 1986

5
Not To Be Confused With

• Ellipsoid
• A closed surface, whose planar sections are
  either ellipsoids or circles.
• Mathematical figure which helps define a
  Reference Frame
• Clarke 1866, GRS80
• Reference Frame
• A coordinate system associated with a physical
  system.
• NSRS, ITRF
• Definitions from the Geodetic Glossary,
  September 1986

6
Horizontal Control Datum?

• Horizontal Control Datum
• A Geodetic Datum specifying the coordinate
  system in which horizontal control points are
  located.
• Defined by 8 Constants
• 3 specify the location of the origin of the
  coordinate system.
• 3 specify the orientation of the coordinate
  system.
• 2 specify the dimensions of the reference
  ellipsoid.
• NAD 27, NAD 83
• Definition
  from the Geodetic Glossary, September 1986

7
Comparison of Horizontal Datum Elements

• 
  NAD 27 NAD 83
• ELLIPSOID CLARKE 1866 GRS80
• a 6,378,206.4 m
  a 6,378,137. M
• 1/f 294.9786982
  1/f 298.257222101
• DATUM POINT Triangulation
  Station
  NONE
• MEADES RANCH, KANSAS EARTH MASS
  CENTER
• ADJUSTMENT 25k
  STATIONS 250k STATIONS
• Several Hundred Base Lines
  Appox. 30k EDMI Base Lines
• Several Hundred Astro Azimuths
  5k Astro Azimuths
• 
  Doppler Point Positions
• 
  VLBI Vectors
• BEST FITTING North
  America
  World-Wide

8
NAD 27 and NAD 83
9
Vertical Control Datum?

• Vertical Control Datum
• A Geodetic Datum specifying the system in which
  vertical control points are located.
• A set of fundamental elevations to which other
  elevations are referred
• NGVD 29, NAVD 88 Orthometric, Sea Level
• Others Cairo, Local Tidal
• Definitions from the Geodetic Glossary,
  September 1986

10
Orthometric HeightsComparison of Vertical Datum
Elements

• 
  NGVD 29 NAVD 88
• DATUM DEFINITION 26 TIDE GAUGES
  FATHERS POINT/RIMOUSKI
• IN THE
  U.S. CANADA QUEBEC,
  CANADA
• BENCH MARKS 100,000
  450,000
• LEVELING (Km)
  102,724
  1,001,500
• GEOID FITTING Distorted to Fit
  MSL Gauges Best Continental
  Model

11
NGVD 29 and NAVD 88
12
Conventional Leveling
ROD 1
BM 100
INSTR
BM
13
Ellipsoid, Geoid, and Orthometric Heights
H Orthometric Height (NAVD 88)
h Ellipsoidal Height (NAD 83)
H h - N
N Geoid Height (GEOID 03)

TOPOGRAPHIC SURFACE
H
A
B
14
Gravity measurements help answer two big
questions
How high above sea level am I? (FEMA, USACE,
Surveying and Mapping)
How large are near-shore hydrodynamic
processes? (Coast Survey, CSC, CZM)
Earths Surface
Orthometric Ht From Leveling
Geoid
Coast
Ocean Surface
Ellipsoid
Geoid Height From Gravity
Ellipsoid Ht From GPS
From Satellite Altimetry
15
What is the GEOID?

• The equipotential surface of the Earths gravity
  field which best fits, in the least squares
  sense, mean sea level.
• Cant see the surface or measure it directly.
• Can be modeled from gravity data.
• Definition from the Geodetic Glossary,
  September 1986

16
In Search of the Geoid
Courtesy of Natural Resources Canada
www.geod.nrcan.gc.ca/index_e/geodesy_e/geoid03_e.h
tml
17
High Resolution Geoid ModelsG99SSS (Scientific
Model)

• Earth Gravity Model of 1996 (EGM96)
• 2.6 million terrestrial, ship-borne, and
  altimetric gravity measurements
• 30 arc second Digital Elevation Data
• 3 arc second DEM for the Northwest USA
• Decimated from 1 arc second NGSDEM99
• Computed on 1 x 1 arc minute grid spacing
• GRS-80 ellipsoid centered at ITRF97 origin

18
High Resolution Geoid ModelsUSGG2003 (Scientific
Model)

• 2.6 million terrestrial, ship, and altimetric
  gravity measurements
• offshore altimetry from GSFC.001 instead of KMS98
• 30 arc second Digital Elevation Data
• 3 arc second DEM for the Northwest USA
• Decimated from 1 arc second NGSDEM99
• Earth Gravity Model of 1996 (EGM96)
• Computed on 1 x 1 arc minute grid spacing
• GRS-80 ellipsoid centered at ITRF00 origin

19
Gravity Coverage for GEOID03
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High Resolution Geoid ModelsGEOID03 (vs. Geoid99)

• Begin with USGG2003 model
• 14,185 NAD83 GPS heights on NAVD88 leveled
  benchmarks (vs. 6169)
• Determine national bias and trend relative to
  GPS/BMs
• Create grid to model local (state-wide) remaining
  differences
• ITRF00/NAD83 transformation (vs. ITRF97)
• Compute and remove conversion surface from
  USGG2003

22
High Resolution Geoid ModelsGEOID03 (vs. Geoid99)

• Relative to non-geocentric GRS-80 ellipsoid
• 2.7 cm RMS nationally when compared to BM data
  (vs. 4.6 cm)
• RMS ? 50 improvement over GEOID99 (Geoid96 to 99
  was 16)

23
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GPS on Bench Marks in Michigan
25
Composite Geoids
Earths Surface
Ellipsoid
Composite Geoid
0.271 M in Traverse City 1999 model
0.308 M in Traverse City 2003 model
Gravity Geoid

• Gravity Geoid systematic misfit with benchmarks
• Composite Geoid biased to fit local benchmarks

26
Sample Datasheet

• National Geodetic Survey, Retrieval
  Date DECEMBER 28, 2005
• PL0314
  
• PL0314 DESIGNATION - V 27
• PL0314 PID - PL0314
• PL0314 STATE/COUNTY- MI/GRAND TRAVERSE
• PL0314 USGS QUAD -
• PL0314
• PL0314 CURRENT SURVEY
  CONTROL
• PL0314 _________________________________________
  __________________________
• PL0314 NAD 83(1994)- 44 39 02.41202(N) 085
  46 04.27942(W) ADJUSTED
• PL0314 NAVD 88 - 257.838 (meters)
  845.92 (feet) ADJUSTED
• PL0314 _________________________________________
  __________________________
• PL0314 X - 335,419.145 (meters)
  COMP
• PL0314 Y - -4,532,722.532 (meters)
  COMP
• PL0314 Z - 4,459,971.520 (meters)
  COMP
• PL0314 LAPLACE CORR- 5.18 (seconds)
  DEFLEC99
• PL0314 ELLIP HEIGHT- 223.17 (meters)
  (07/17/02) GPS OBS
• PL0314 GEOID HEIGHT- -34.68 (meters)
  GEOID03

27
Sample Datasheet

• PL0314
• PL0314 HORZ ORDER - FIRST
• PL0314 VERT ORDER - FIRST CLASS II
• PL0314 ELLP ORDER - FOURTH CLASS I
• PL0314
• PL0314.The horizontal coordinates were
  established by GPS observations
• PL0314.and adjusted by the National Geodetic
  Survey in February 1997.
• PL0314
• PL0314.The orthometric height was determined by
  differential leveling
• PL0314.and adjusted by the National Geodetic
  Survey in June 1991.
• PL0314
• PL0314.The X, Y, and Z were computed from the
  position and the ellipsoidal ht.
• PL0314
• PL0314.The Laplace correction was computed from
  DEFLEC99 derived deflections.
• PL0314
• PL0314.The ellipsoidal height was determined by
  GPS observations
• PL0314.and is referenced to NAD 83.
• PL0314
• PL0314.The geoid height was determined by
  GEOID03.

28
Sample Datasheet

• PL0314
• PL0314.The modeled gravity was interpolated from
  observed gravity values.
• PL0314
• PL0314 North East
  Units Scale Factor Converg.
• PL0314SPC MI C - 149,194.606
  5,888,865.237 MT 0.99992569 -0 59 23.3
• PL0314SPC MI C - 489,483.62 19,320,424.01
  iFT 0.99992569 -0 59 23.3
• PL0314UTM 16 - 4,944,883.803
  597,700.224 MT 0.99971738 0 51 57.6
• PL0314
• PL0314! - Elev Factor x Scale
  Factor Combined Factor
• PL0314!SPC MI C - 0.99996501 x
  0.99992569 0.99989070
• PL0314!UTM 16 - 0.99996501 x
  0.99971738 0.99968240
• PL0314
• PL0314 SUPERSEDED
  SURVEY CONTROL
• PL0314
• PL0314 ELLIP H (02/03/97) 223.19 (m)
  GP( ) 4 1
• PL0314 NAD 83(1986)- 44 39 02.41257(N) 085
  46 04.28315(W) AD( ) 1
• PL0314 NAD 83(1986)- 44 39 02.38347(N) 085
  46 04.27988(W) AD( ) 3
• PL0314 NAVD 88 (09/30/91) 257.84 (m)
  845.9 (f) LEVELING 3
• PL0314 NGVD 29 (??/??/92) 257.915 (m)
  846.18 (f) ADJ UNCH 1 2

29
Sample Datasheet

• PL0314_U.S. NATIONAL GRID SPATIAL ADDRESS
  16TEQ9770044884(NAD 83)
• PL0314_MARKER DB BENCH MARK DISK
• PL0314_SETTING 7 SET IN TOP OF CONCRETE
  MONUMENT
• PL0314_SP_SET CONCRETE POST
• PL0314_STAMPING V 27 1930 846.176
• PL0314_MARK LOGO CGS
• PL0314_MAGNETIC N NO MAGNETIC MATERIAL
• PL0314_STABILITY B PROBABLY HOLD
  POSITION/ELEVATION WELL
• PL0314_SATELLITE THE SITE LOCATION WAS REPORTED
  AS SUITABLE FOR
• PL0314SATELLITE SATELLITE OBSERVATIONS -
  October 24, 1992
• PL0314
• PL0314 HISTORY - Date Condition
  Report By
• PL0314 HISTORY - 1930 MONUMENTED
  CGS
• PL0314 HISTORY - 1951 GOOD
  NGS
• PL0314 HISTORY - 1984 GOOD
  NGS
• PL0314 HISTORY - 19890428 GOOD
  NGS
• PL0314 HISTORY - 1990 GOOD
  USPSQD
• PL0314 HISTORY - 19910701 GOOD
  NGS
• PL0314 HISTORY - 19920824 GOOD
  MIDT

30
Sample Datasheet

• National Geodetic Survey, Retrieval
  Date DECEMBER 28, 2005
• PL0314
  
• PL0314 DESIGNATION - V 27
• PL0314 PID - PL0314
• PL0314 STATE/COUNTY- MI/GRAND TRAVERSE
• PL0314 USGS QUAD -
• PL0314
• PL0314 CURRENT SURVEY
  CONTROL
• PL0314 _________________________________________
  __________________________
• PL0314 NAD 83(1994)- 44 39 02.41202(N) 085
  46 04.27942(W) ADJUSTED
• PL0314 NAVD 88 - 257.838 (meters)
  845.92 (feet) ADJUSTED
• PL0314 _________________________________________
  __________________________
• PL0314 X - 335,419.145 (meters)
  COMP
• PL0314 Y - -4,532,722.532 (meters)
  COMP
• PL0314 Z - 4,459,971.520 (meters)
  COMP
• PL0314 LAPLACE CORR- 5.18 (seconds)
  DEFLEC99
• PL0314 ELLIP HEIGHT- 223.17 (meters)
  (07/17/02) GPS OBS
• PL0314 GEOID HEIGHT- -34.68 (meters)
  GEOID03

NAVD88 Ellip Ht Geoid Ht 257.838 223.17
34.953 -0.285 USGG2003 257.838 223.17
34.68 -0.012 GEOID03
31
Whats Left?

• Leveling-Derived Orthometric Heights
• Modeled Geoid Heights
• GPS-Derived Ellipsoid Heights

32
Guidelines
Available On-Line at the NGS Web
Site www.ngs.noaa.gov
33
GPS Error Sources

• Orbit and clock error
• Broadcast v.s. Predicted Precise v.s.
  Post-processed
• Clock error corrections
• Atmospheric Effects
• Ionosphere, Troposphere
• Multipath
• Height of phase center above mark

34
Atmosphere-based Ionospheric Delay
Ionosphere
gt 10 km
lt 10 km
35
Multipath
h
ø
ø
Figure 1 Multipath Description
August 1987 -Ionospheric refraction and Multipath
Effects in GPS Carrier Phase Observations Yola
Georgiadou and Alfred Kleusberg
IUGG XIX General
Assembly Meeting, Vancouver, Canada
36
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37
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38
Components of NGS-58

• Equipment requirements
• Field Procedures/Data Collection Parameters
• Basic Control Requirements
• Processing/Analysis Procedures

39
Equipment Requirements

• Dual-frequency, full-wavelength GPS receiver
• Required - observations gt 10 km
• Preferred - ALL observations regardless of length
• Geodetic quality antennas with ground planes
• Choke ring antennas highly recommended
• Successfully modeled L1/L2 offsets and phase
  patterns
• Use identical antenna types if possible
• Corrections must be utilized by processing
  software when mixing antenna types

40
Equipment Requirements
Fixed Height Tripod
Fixed-height tripods required for 2 cm
standard Fixed-height poles preferred for 5 cm
standard
41
Data Collection Parameters

• VDOP lt 6 for 90 or longer of 30 minute session
• Shorter session lengths stay lt 6 always
• Schedule travel during periods of higher VDOP
• Session lengths gt 30 minutes collect 15 second
  data
• Session lengths lt 30 minutes collect 5 second
  data
• Track satellites down to 10 elevation angle
• Repeat Baselines
• Different days
• Different times of day
• Detect, remove, reduce effects due to multipath
  and having almost the same satellite geometry

42
Gg Gg gg
Station pairs with large residuals, i.e., greater
than 2.5 cm, also have large repeat base
line differences. NGS guidelines for estimating
GPS-derived ellipsoid heights require user to
re-observe these base lines. Following NGS
guidelines provides enough redundancy for
adjustment process to detect outliers and apply
residual on appropriate observation, i.e., the
bad vector.
43
After performing minimum constraint adjustment,
plot ellipsoid height residuals (or dU
residuals) and investigate all residuals greater
than 2 cm.
44
Two Days/Same Time
-10.254 -10.251
gt -10.253
Difference 0.3 cm
Truth -10.276
Difference 2.3 cm
Two Days/ Different Times
-10.254
gt -10.275
-10.295
Difference 4.1 cm
Truth -10.276
Difference 0.1 cm
45
Four Basic Control Requirements

• Occupy stations with known NAVD 88 orthometric
  heights
• Stations should be evenly distributed throughout
  project
• Project areas lt 20 km on a side, surround project
  with NAVD 88 bench marks
• i.e., minimum number of stations is four one in
  each corner of project
• Project areas gt 20 km on a side, keep distances
  between GPS-occupied NAVD 88 bench marks to less
  than 20 km
• Projects located in mountainous regions, occupy
  bench marks at base and summit of mountains, even
  if distance is less than 20 km

46
Sample Project

• Area East San Francisco Bay Project
• Latitude 37 50 N to 38 10 N
• Longitude 121 45 W to 122 25 W
• Receivers Available 5
• Standards 2 cm GPS-Derived Heights

47
Primary Base Stations
3820N
CORS HARN NAVD88 BM New Station
D191
10CC
19.0km
Primary Base Station
28.7km
25.7km
LATITUDE
38.3km
31.6km
38.7km
25.8km
LAKE
MART
29.6km
MOLA
3750N
12235W
12140W
LONGITUDE
48
GPS-Usable Stations
Spacing Station
Primary Base Station
49
Observation Sessions
50
Independent Base Lines
51
Processing Five Basic Procedures

• Perform 3-D minimally constrained (free)
  adjustment
• Analyze adjustment results
• Compute differences between GPS-derived
  orthometric heights from free adjustment and
  published NAVD88 BMs
• Evaluate differences to determine which BMs have
  valid NAVD88 height values
• Perform constrained adjustment with results from
  previous step

52
Appendix B GPS Ellipsoid Height Hierarchy
53
Start with CORS
Harbor Beach
Mt. Pleasant
Bayer at Saginaw
54
Next Level - Michigan HARN
55
Have good NAVD88 Control
L26235, phases 1 2, courtesy of students at
Ferris State University
56
Height Modernization Project
HARN - Average 50km, max 75km
Secondary - Average 12-15km, max 15km
Local Average 6-8 km, max 10km
Primary 20-25km, max 40km
57
Basic Concept of Guidelines

• Stations in local 3-dimensional network connected
  to NSRS to at least 5 cm uncertainty
• Stations within a local 3-dimensional network
  connected to each other to at least 2 cm
  uncertainty
• Stations established following guidelines are
  published to centimeters by NGS

58
Network / Local Accuracy
59
Sample Datasheet Leveling

• 1 National Geodetic Survey, Retrieval
  Date NOVEMBER 25, 2003
• AI6151
  
• AI6151 DESIGNATION - 2K76
• AI6151 PID - AI6151
• AI6151 STATE/COUNTY- WI/WASHINGTON
• AI6151 USGS QUAD - ALLENTON (1971)
• AI6151
• AI6151 CURRENT SURVEY
  CONTROL
• AI6151 _________________________________________
  __________________________
• AI6151 NAD 83(1997)- 43 25 39.39446(N) 088
  18 24.15369(W) ADJUSTED
• AI6151 NAVD 88 - 343.002 (meters)
  1125.33 (feet) ADJUSTED
• AI6151 _________________________________________
  __________________________
• AI6151 X - 137,097.884 (meters)
  COMP
• AI6151 Y - -4,637,622.691 (meters)
  COMP
• AI6151 Z - 4,362,336.158 (meters)
  COMP
• AI6151

AI6151 . . . AI6151 The orthometric height was
determined by differential leveling AI6151 and
adjusted by the National Geodetic Survey in
October 2000. AI6151
60
Sample Datasheet - GPS

• 1 National Geodetic Survey, Retrieval
  Date JUNE 7, 2004
• HL0673
  
• HL0673 DESIGNATION - FAA 5CO0 B
• HL0673 PID - HL0673
• HL0673 STATE/COUNTY- CO/LA PLATA
• HL0673 USGS QUAD - LOMA LINDA (1968)
• HL0673
• HL0673 CURRENT SURVEY
  CONTROL
• HL0673 _________________________________________
  __________________________
• HL0673 NAD 83(1992)- 37 12 34.23430(N) 107
  51 59.34354(W) ADJUSTED
• HL0673 NAVD 88 - 2038.7 (meters)
  6689. (feet) GPS OBS
• HL0673 _________________________________________
  __________________________
• HL0673 X - -1,560,867.458 (meters)
  COMP
• HL0673 Y - -4,842,221.299 (meters)
  COMP
• HL0673 Z - 3,837,158.007 (meters)
  COMP

HL0673. . . HL0673 The orthometric height was
determined by GPS observations and a HL0673
high-resolution geoid model. HL0673
61
Sample Datasheet GPS Using NGS58

• OM1256 CBN - This is a Cooperative
  Base Network Control Station.
• OM1256 DESIGNATION - CAMBRIA GPS
• OM1256 PID - OM1256
• OM1256 STATE/COUNTY- WI/COLUMBIA
• OM1256 USGS QUAD - RANDOLPH (1980)
• OM1256
• OM1256 CURRENT SURVEY
  CONTROL
• OM1256 _________________________________________
  __________________________
• OM1256 NAD 83(1997)- 43 34 10.47581(N) 089
  06 09.35995(W) ADJUSTED
• OM1256 NAVD 88 - 303.84 (meters)
  996.8 (feet) GPS OBS
• OM1256 _________________________________________
  __________________________
• OM1256 X - 72,495.418 (meters)
  COMP
• OM1256 Y - -4,628,194.515 (meters)
  COMP
• OM1256 Z - 4,373,750.772 (meters)
  COMP

OM1256 . . . OM1256.The orthometric height was
determined by GPS observations and a
OM1256.high-resolution geoid model using precise
GPS observation and OM1256.processing techniques.
62
Goal Achieved?

• With the means to get more accurate ellipsoid
  heights, we can now use these ellipsoid heights
  on benchmarks to further improve the geoid model.
• With the improved geoid model we can use GPS to
  compute accurate orthometric heights.

63
Questions?
http//www.ngs.noaa.gov/heightmod/MichiganMarquett
eAgenda.pdf
http//www.ngs.noaa.gov/heightmod/MichiganFlintAge
nda.pdf

• Renee Shields
• Grants Manager
• N/NGS1, SSMC3
• 1315 East-West Highway
• Silver Spring, MD 20910
• 301-713-3231, x116
• www.ngs.noaa.gov
• Renee.Shields_at_noaa.gov