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NOAA Technical Memorandum NOS NGS-58
GUIDELINES FOR ESTABLISHING GPS-DERIVED ELLIPSOID HEIGHTS (STANDARDS: 2 CM AND 5 CM) VERSION 4.3 David B. Zilkoski Joseph D. D'Onofrio Stephen J. Frakes Silver Spring, MD November 1997
U.S. DEPARTMENT OF National Oceanic and National Ocean National Geodetic COMMERCE Atmospheric Administration Service Survey
LINK TO SLIDES & OTHER INFORMATION:
ftp://ftp.ngs.noaa.gov/dist/whenning/GLRHM2010/
WORKSHOP PLAN
HEIGHTS/DATUMS/GRAVITY
GEOID + ELLIPSOID vs LEVELING
NGS 58
NGS 59
GNSS DERIVED HEIGHTS Summary of expected orthometric
precisions/accuraciesREMEMBER REDUNDANCY AND A CHECK ON KNOWN POINTS
CORS = 0.05 m
OPUS-S = 0.05 m
OPUS-RS = 0.05 m
NGS 58/59 = 0.02 m local, 0.05 m to NSRS
SINGLE BASE REAL TIME = 0.03 m ≤ 10 Km, remember GIGO
RTN = 0.03 m - 0.06 m,
NGS DATASHEET ELEMENTS
6
Vertical Datums
and the Geoid
7
NAVD 88 minus
LMSL (1960-1978)(units = cm)
8
9
10
CLASSICAL LEVELING
“GEODETIC” LEVELING CORRECTIONS
• Rod Scale (Invar strip)
• Temperature (expansion/contraction)
• Collimation (use balanced turns)
• Refraction (effect on different rod height readings)
• Astronomic (Sun/Moon effects on earth tides)
• Orthometric (NGVD 29 = normal gravity-height, NAVD 88 = Geopotentials, latitude)
GEODETIC LEVELING ACCURACY STANDARDS
CLASSIFICATION MAXIMUM ELEV. DIFFERENCE ACCURACY
FIRST - CLASS I 0.5 mm √Km
FIRST - CLASS II 0.7 mm √Km
SECOND – CLASS I 1.0 mm √Km
SECOND – CLASS II 1.3 mm √Km
THIRD 2.0 mm √Km
(NOTE: REMEMBER THAT THERE ARE PROCEDURES AND EQUIPMENT SPECIFICATIONS TO FOLLOW FOR THESE CLASSES AS WELL)
13
HCHA
HAC hAB + hBC
Observed difference in orthometric
height, H, depends on the leveling route.
AC
B Topography
hAB
h = local leveled differences
= hBC
H = relative orthometric heights
Leveled Height vs. Orthometric Height
14
Leveling Routes Give Different Results
GRAVITY FOR ORTHOMETRIC HEIGHTS (“ELEVATIONS”)
NO GRAVITY = NO HEIGHTSKNOW GRAVITY = KNOW HEIGHTS
http://www.ngs.noaa.gov/GRAV-D/pubs/GRAV-D_v2007_12_19.pdf
GRAV-D PROGRAMNEW VERTICAL DATUM AROUND 2018
16
GRAVITY AND HEIGHTSH = C / G
OR C = H . G
Geopotential numbers “C” are taken as relativequantities of gravity potential (measured in
“gals”. 1 GALILEO = 1 CM/SEC2
ACCELERATION). “C” is usually given in geopotential units –
“gpu”1 gpu = 1 k gal m (a non-geometrical value)
17
18
N 45
19
NGS data sheet- N 45
21
• For Helmert orthometric heights, G is approximated from a measured surface gravity value at the point and evaluated at the midpoint of the plumb line using the formula:
HHE = C / (G surface + 0.0424 H)where C is an estimated geopotential number in gpu, G is the
modeled gravity at the point in gals, and H is the orthometric heightin Km.This is an iterative process
ORTHOMETRIC HEIGHTS
22
Heights Based on Geopotential Number(C): C = G × H or H = C/ G
• NORMAL HEIGHT (NGVD 29) H* = C /
= AVERAGE NORMAL GRAVITY ALONG PLUMB LINE
• DYNAMIC HEIGHT ( NEAR IGLD 55, 85) HDYN
= C / 45
45 = NORMAL GRAVITY AT 45° LATITUDE
• “TRUE” ORTHOMETRIC HEIGHT H = C / G
G = AVERAGE GRAVITY ALONG THE PLUMB LINE
• HELMERT HEIGHT (NAVD 88) H0 = C / (G + 0.0424 H0)
G = NAVD 88 SURFACE GRAVITY MEASUREMENT (MGAL)
Ortho = 501 mDynam = 498 m
Ortho = 503 mDynam = 498 m
Ortho = 502 mDynam = 498 m
The Geoid(W = constant = W0)
Some Equipotential Surface
(W = constant = W1)
Plumb Lines
Orthometric versus Dynamic Heights
Equipotential : Having constant gravity potential energy (W)
[Not the same as “constant gravity (g)”]
45 = A constant arbitrary gravity value
• At the Geoid: Ortho. = Dynamic = 0• As ortho Height increases, so does the potential discrepancy betweenorthometric and dynamic height
Dynamic Heights are directly related to water levels!!
Ortho = 500 mDynam = 498 m
Orthometric Height = Physical Length along Plumb Line from Geoid to SurfaceDynamic Height = (W0-W1) / 45 : Has no geometrical meaning
Points with the same dynamic heights (or geopotential numbers) are “level”. Water
will not flow between them (same hydraulic head, SAME EQUIPOTENTIAL)
24
GPS - Derived Ellipsoid Heights
Z Axis
X Axis
Y Axis
(X,Y,Z) = P (,,h)
h
Earth’s
Surface
Zero
Meridian
Mean Equatorial Plane
Reference Ellipsoid
P
H88 = h83 – N03
GEOID HEIGHTS (SEPARATIONS)
29
CONVERSION SURFACE:GEOCENTERED GEOID TO HYBRID GEOID
• EGM08 + NGSDEM99 +KMS98 (Andersen and Knudsen 1998) offshore Free-air gravity anomaly (FAGA) field with the GSFC00.1 model (Wang 2001)
• ITRF00/NAD83 TRANSFORMATION
• NAVD 88 BIAS (-57 CM geoid09)
• TILT (0.15 PPM, 327 AZIMUTH)LOCAL GPS/LEVELING/GEOID MISFIT
• THEREFORE:
USGG2009 - CONVERSION SURFACE = GEOID09
30
GEOID SEPARATIONS – BA. CO., MD
GEOID COMPARISONS-VARIOUS BENCHMARKS-
BALTIMORE COUNTY AREA
WEST TO EAST
-32.1
36
-32.2
62
-32.0
75
-32.1
84
-32.0
96
-32.1
79
-32.2
23
-32.2
21
-32.2
30
-32.3
01
-32.3
33
-32.3
62
-32.3
65
-32.3
61
-32.3
58
-32.3
89
-32.5
47
-32.4
97
-32.4
23
-32.5
00
-32.5
86
-32.4
94
-32.6
29 -3
2.4
78
-32.5
36
-32.7
66
-32.7
63
-32.7
02
-32.0
86
-32.2
11
-32.0
29
-32.1
29
-32.0
5
-32.1
23
-32.1
69
-32.1
75
-32.1
76
-32.2
46
-32.2
75
-32.3
23
-32.3
23
-32.3
15
-32.3
11
-32.3
36
-32.5
1
-32.4
42
-32.3
76
-32.4
46
-32.5
51
-32.4
44
-32.5
97
-32.4
35
-32.5
01
-32.7
4
-32.7
39
-32.6
78
-33.000
-32.800
-32.600
-32.400
-32.200
-32.000
-31.800
283 5
283 7 5
3
283 9
283 1
3
283 1
5 4
2
283 1
5 4
8
283 1
6 8
283 1
9 3
3
283 1
9 4
5
283 2
0 6
283 2
0 2
6
283 2
1 8
283 2
2 3
4
283 2
3 4
2
283 2
5 3
283 2
5 4
4
283 2
6 5
283 2
6 4
1
283 2
7 3
8
283 2
8 2
283 2
8 3
7
283 2
8 5
0
283 3
0 5
283 3
3 3
1
283 3
4 7
283 3
5 8
EAST LONGITUDE
GE
OID
SE
PA
RA
TIO
N (
ME
TE
RS
)
GEOID96 GEOID99 GEOID03
31
GEOID COMPARISONS-REMOVING LOCAL BIAS
MINIMALLY CONSTRAINED ADJUSTMENT- PUBLISHED LESS
GPS DERIVED ORTHOS RELATIVE TO GPS LR28
0.00
7
0.00
50.
0060.
008
0.00
10.
003
-0.0
06-0
.004
0.00
6
-0.0
26
-0.0
15
-0.0
25
-0.0
26
-0.0
02
-0.0
20
-0.0
02
-0.0
08
-0.0
13
-0.0
22
-0.0
05
-0.0
12
-0.0
18
-0.0
40
-0.0
02
-0.0
11
-0.0
26-0
.016
0.00
0
-0.060
-0.050
-0.040
-0.030
-0.020
-0.010
0.000
0.010
0.020
0.030
0.040
ME
TE
RS
GEOID96 GEOID99 GEOID03
32
Expected Height Accuracies
• GPS-Derived Ellipsoid Heights
2 centimeters (following NOS NGS-58 Guidelines)
• Geoid Heights (GEOID09)
– Relative differences typically less than 1 cm in 10 km
2.x (?) cm RMS about the mean nationally
0.5 cm error in 10 Km
• Leveling-Derived Heights
– Less than 1 cm in 10 km for third-order leveling
NOAA Technical Memorandum NOS NGS-58
GUIDELINES FOR ESTABLISHING GPS-DERIVED ELLIPSOID HEIGHTS (STANDARDS: 2 CM AND 5 CM) VERSION 4.3 David B. Zilkoski Joseph D. D'Onofrio Stephen J. Frakes Silver Spring, MD November 1997
U.S. DEPARTMENT OF National Oceanic and National Ocean National Geodetic COMMERCE Atmospheric Administration Service Survey
This means we could expect 0.12’ orthometric accuracy from the CORS
NGS Data Sheet - GEOID03
Published NAVD88 to GPS Derived
HT2268 DESIGNATION - S 1320
HT2268 PID - HT2268
HT2268 STATE/COUNTY- CA/SAN FRANCISCO
HT2268 USGS QUAD - SAN FRANCISCO NORTH (1975)
HT2268
HT2268 *CURRENT SURVEY CONTROL
HT2268 ___________________________________________________________________
HT2268* NAD 83(1992)- 37 45 25.30727(N) 122 28 36.34687(W) ADJUSTED
HT2268* NAVD 88 - 102.431 (meters) 336.06 (feet) ADJUSTED
HT2268 ___________________________________________________________________
HT2268 EPOCH DATE - 1997.30
HT2268 X - -2,711,121.437 (meters) COMP
HT2268 Y - -4,259,419.310 (meters) COMP
HT2268 Z - 3,884,200.262 (meters) COMP
HT2268 LAPLACE CORR- 5.53 (seconds) DEFLEC03
HT2268 ELLIP HEIGHT- 69.78 (meters) GPS OBS
HT2268 GEOID HEIGHT- -32.60 (meters) GEOID03
HT2268 DYNAMIC HT - 102.363 (meters) 335.84 (feet) COMP
HT2268 MODELED GRAV- 979,964.0 (mgal) NAVD 88
HT2268
HT2268 HORZ ORDER - FIRST
HT2268 VERT ORDER - FIRST CLASS I
HT2268 ELLP ORDER - FOURTH CLASS I
HT2268
H =
102.431 =
102.431 102.38
102.429! GEOID 09
69.78 - (-32.60)
- Nh
GEOID96 = 0.17 m
GEOID99 = 0.11 m
GEOID03 = 0.05 m
GEOID 09 = 0.002 m
NOAA Technical Memorandum NOS NGS-58
GUIDELINES FOR ESTABLISHING GPS-DERIVED ELLIPSOID HEIGHTS(STANDARDS: 2 CM AND 5 CM)VERSION 4.3
David B. ZilkoskiJoseph D. D'OnofrioStephen J. Frakes
Silver Spring, MD
November 1997
U.S. DEPARTMENT OF National Oceanic and National Ocean National GeodeticCOMMERCE Atmospheric Administration Service Survey
Available “On-Line” at
the NGS Web Site:
www.ngs.noaa.gov
SEARCH: “NGS 58”
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
• Quality is shown by: REPEATABILITY, RMS, & LOOP CLOSURES
Network / Local Accuracy
NSRS
EQUIPMENT REQUIREMENTS
• DUAL-FREQUENCY, FULL-WAVELENGTH GPS RECEIVERS
– Required for all observations greater than 10 km
– Preferred type for 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
Antenna
Type A
Antenna
Type B
Different
Phase Patterns
Note that SV elevation and varying phase
patterns affect signal interpretation
differently
RELATIVE VS. ABSOLUTE PHASE CENTER MODELS
GNSS Absolute Antenna Calibration-
This will make a difference for very long baselines (1000 Km)
NGS Antenna Calibration facility in Corbin, VA, is available for private
sector & government use
DATA COLLECTION PARAMETERS
• VDOP < 6 for 90% or longer of 30 minute session
– Shorter session lengths stay < 6 always
– Schedule travel during periods of higher VDOP
• Session lengths for baselines ≤ 10 KM = 30 minutes & collect at 5 second data interval
• Session lengths for baselines 10 – 15 KM = 1 hour & collect at 15 second data interval
• Track satellites down to 10° elevation angle
REDUNDANCY
If extra measurements are included then a least squares adjustment will provide a check on the accuracy of control
point coordinates and can also be used to identify bad observations.
More measurements should be included than the minimum - needed to determine the origin and possibly the orientation and scale of the survey
Redundant measurements taken with different satellites and satellite geometry provide a mitigation for multipath
effects.
Each local station must have at least two acceptable baselines to its closest neighbor
Comparison of 30 Minute Solutions - Precise Orbit; Hopfield (0); IONOFREE
(30 Minute solutions computed on the hour and the half hour)
S132 to L132 7.9 Km
Day 264dh
(m)
Hours
Diff.Day 265
dh
(m)
Day 264
minus
Day 265
(cm)
*
diff
>2
cm
Mean dh
(m)
Mean dh
minus
"Truth"
(cm)
*
diff
>2
cm
14:00-14:30 20.599 27hrs 17:00-17:30 20.624 -2.5 * 20.612 -0.3
14:30-15:00 20.610 27hrs 17:30-18:00 20.613 -0.3 20.612 -0.3
15:00-15:30 20.613 27hrs 18:00-18:30 20.620 -0.7 20.617 0.2
15:30-16:00 20.607 27hrs 18:30-19:00 20.611 -0.4 20.609 -0.5
16:00-16:30 20.594 27hrs 19:00-19:30 20.615 -2.1 * 20.605 -1.0
16:30-17:00 20.612 27hrs 19:30-20:00 20.619 -0.7 20.616 0.1
17:00-17:30 20.610 27hrs 20:00-20:30 20.662 -5.2 * 20.636 2.1 *
17:30-18:00 20.615 27hrs 20:30-21:00 20.621 -0.6 20.618 0.3
18:00-18:30 20.614 21hrs 15:00-15:30
18:30-19:00 20.608 21hrs 15:30-16:00 20.625 -1.7 20.617 0.2
19:00-19:30 20.609 21hrs 16:00-16:30 20.601 0.8 20.605 -0.9
19:30-20:00 20.620 21hrs 16:30-17:00 20.628 -0.8 20.624 1.0
20:00-20:30 20.660 18hrs 14:00-14:30 20.614 4.6 * 20.637 2.3 *
20:30-21:00 20.618 18hrs 14:30-15:00 20.630 -1.2 20.624 0.9
"Truth"
14:00-21:00 20.609 14:00-21:00 20.620 -1.1 20.615
Two Days/Same Time
20.66020.662
> 20.661
Difference = -0.2 cm
“Truth” = 20.615
Difference = 4.6 cm
Two Days/Different Times
20.66020.614
> 20.637
Difference = 4.6 cm
“Truth” = 20.615
Difference = 2.3 cm
PLANNING FOR THE FIELD OBSERVATIONS
HARN/Control Stations(75 km)
Primary Base(40 km)
Secondary Base(15 km)
Local Network Stations(7 to 10 km)
GPS ELLIPSOID HEIGHT HIERARCHY
Sample Project Showing Connections
CS1
PB2
SB2
LN4LN3
LN2
LN5
LN1
SB1
SB3
SB5SB4
PB4
PB1
PB3
CS2
CS4CS3
STATION SELECTION AND RECONNAISSANCE
• ASSURE ACCURATE CONNECTIONS TO CONTROL STATIONS
– NGS approved CORS
– TCORS (temporary or project CORS)
– HARN
• Federal Base Network (FBN)
• Cooperative Base Network (CBN)
• User Densified Network (UDN)
– NAVD 88 Bench Marks
• NGS DATABASE AND DATA SHEETS
• IDENTIFY GPS-USABLE STATIONS
PRIMARY OR SECONDARYSTATION SELECTION CRITERIA
1. HARN either FBN or CBN
– Level ties to A or B stability bench marks during this project
2. Bench marks of A or B stability quality
– Or HARN previously tied to A or B stability BMs
3. UDN stations
– Level ties to A or B stability bench marks during this project
4. Bench marks of C stability quality
• Special guidelines for areas of subsidence or uplift
Poured in place
concrete post
Physically Monumented
Points= “PASSIVE
MONUMENTATION”
Stainless steel rod driven to
refusal
Disk in outcrop
B Stability
C StabilityA Stability
Obstruction Visibility
Diagram
A StabilityFirst Order Class II
NAVD88 Bench MarkIt’s Gotta be Good!
Bench MarkG 506
ESTABLISH A STABLE ECCENTRIC POINT AND
TRANSFER THE ORTHOMETRIC HEIGHT
USING PROPER LEVELING TECHNIQUES
FAIRFAX COUNTY, VA HTMOD PROJECT
450 SQ. MILES
4-6 RECEIVERS
131 stations
462 baselines
PRIMARY BASE STATIONS
• Basic Requirements:
– 5 Hour Sessions / 3 Days
– Spacing between PBS cannot exceed 40 km
– Each PBS must be connected to at least its nearest PBS neighbor and nearest control station
– PBS must be traceable back to 2 control stations along independent paths
SECONDARY BASE STATIONS
• Basic Requirements:
– 30 Minute Sessions / 2 Days /Different times of day
– Spacing between SBS (or between primary and SBS) cannot exceed 15 km
– All base stations (primary and secondary) must be connected to at least its 2 nearest primary or secondary base station neighbors
– SBS must be traceable back to 2 PBS along independent paths; i.e., base lines
– SBS need not be established in surveys of small area extent
LOCAL NETWORK STATIONS
• Basic Requirements:
– 30 Minute Sessions / 2 Days / Different times of the day
– Spacing between LNS (or between base stations and local network stations) cannot exceed 10 km
– All LNS must be connected to at least its two nearest neighbors
– LNS must be traceable back to 2 primary base stations along independent paths
OBSERVATION PLANNING
FIELD OBSERVATIONS
• Observation logs
– Record complete receiver/antenna manufacturer, model part number, and serial numbers
– Record meteorological data and unusual conditions
– Record station and observer information
– Record height of antenna and measurement computations
• Obtain a clear station rubbing
– Rubbing for each occupation of station
– Make complete plan sketch of mark when rubbing not feasible
– OR – Take digital snapshots (time & date stamp is good)
METEOROLOGICAL DATA
• Weather data must be collected at control, primary, and secondary base stations at height of antenna PC
– Wet and dry temperatures, atmospheric pressure
• Sessions > 2 hrs; record beginning, midpoint, ending
• Sessions < 2 hrs > 30 min; record beginning and ending
• Sessions < 30 min; record at midpoint
• Note on obs log where recorded and unusual conditions
• Stabilize equipment to ambient conditions
• Check equipment prior to observations
Sample
Observation Log
http://www.ngs.noaa.gov/PROJECTS/FBN/
http://www.ngs.noaa.gov/PROJECTS/FBN/
Sample
Station Rubbing
OR SEARCH:“FBN SURVEYS”
BASELINE PROCESSING
BASELINE PROCESSING
• “MULTI-STATION” PROCESSING MODE
• DOUBLE DIFFERENCING (ELIMINATES SAT/RECEIVER CLOCK, HARDWARE BIASES, REDUCES NOISE PARAMETERS)
• PRECISE EPHEMERIS
• 15° CUT OFF
• FIX ALL INTEGERS FOR BASELINES LESS THAN 40 KM
• USE A TROPO MODEL RATHER THAN FIELD MET DATA UNLESS PROVEN
BETTER
• USE RELATIVE TROPO SCALE PARAMETER FOR STATIONS OVER 15 KM
AND FOR LARGE INTERSTATION RELIEF
• BASELINE RMS ≤ 1.5 CM
• REDUNDANT BASELINES DIFFER BY ≤ 2.0 CM
Independent Baselines in GPS
# of Baselines =
N(N-1)
2
# of Independent
Baselines =(N-1)
N = Number of receivers observing simultaneously
Precise (Final)•14 days latency•1 cm accuracy•updated weekly
Rapid•1 day latency•2 cm accuracy•updated daily
UltraRapid•24 hrs observed / 24 hrs predicted•5 cm / 10 cm accuracy•updated 4 times/day
NGS/IGS PRECISE ORBITS
BASELINE PROCESSINGREDUNDANCY NEEDED: ≤ 1.5 CM, ≤ 2.0
DIFFERENCE IN “h”
ELLIPSOID ADJUSTMENT
FAIRFAX COUNTY, VA HTMOD PROJECT
450 SQ. MILES
4-6 RECEIVERS
124 stations
439 baselines
Summary-Vector Processing Accomplished
• Elevation Mask - 15 degrees
• Ephemeris - Precise (typ. 14 days latency)
• Tropospheric Correction Model
• Iono Corrections - All baselines longer than 5 km.
• Fix Integers
Baselines less than 5 km: L1 fixed solution
Baselines greater than 5 km: Iono free (L3) solution
• Baselines must have RMS values ≤ 1.5 cm
• Baselines must have difference in “up” ellipsoid height ≤ 2.0 cm
Table 1. -- Summary of Guidelines
Table 1. -- Summary of Guidelines
(continued)
Guidelines for Establishing
GPS-Derived Orthometric
Heights
(Standards: 2 cm and 5 cm)
http://www.ngs.noaa.gov/
SEARCH: “NGS 59”
• Three Basic Rules
• Four Basic Control Requirements
• Five Basic Procedures
3-4-5 System
A Guide for Establishing GPS-Derived Orthometric Heights
(Standards: 2 cm and 5 cm)
(Assumes we have completed NGS 58 – ellipsoid heights and met criteria:-all local monuments ≤ 10 km, avg ≤7 km-Ellipsoid heights from processing compare ≤ 2.0 cm-- baselines RMS ≤ 1.5 cm)
3 BASIC RULES:
A Guide for Establishing GPS-Derived Orthometric Heights
(Standards: 2 cm and 5 cm)
• USE NOS-NGS 58 – GPS DERIVED ELLIPSOID HEIGHTS
• USE PUBLISHED NAVD 88 CONTROL
•USE CURRENT HYBRID GEOID MODEL
78
Estimating GPS-Derived Orthometric Heights
Four Basic Control Requirements-Occupy stations with known NAVD 88 orthometric heights
(Stations should be evenly distributed throughout project)
-Project areas less than 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 greater than 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
FAIRFAX COUNTY VERTICALS USED
40 KM
80
Procedure 1: Perform a 3-D minimum-constraint least
squares adjustment of the GPS survey project, i.e.,
constrain one latitude, one longitude, and one orthometric
height value.
Estimating GPS-Derived Orthometric Heights
Five Basic Adjustment Procedures
Procedure 2: Using the results from the adjustment in
procedure 1 above, detect and remove all data outliers. The
user should repeat procedures 1 and 2 until all data outliers
are removed.
81
Procedure 3: Compute differences between the set of
GPS-derived orthometric heights from the minimum
constraint adjustment from procedure 2 above and
published NAVD 88 bench marks.
Procedure 4: Using the results from procedure 3 above,
determine which bench marks have valid NAVD 88 height
values. All differences between valid bench marks need to
agree within 2 cm for 2-cm surveys and 5 cm for 5-cm
surveys.
Estimating GPS-Derived Orthometric Heights
Five Basic Adjustment Procedures
82
Procedure 5: Using the results from procedure 4
above, perform a constrained adjustment fixing one
latitude and one longitude value and all valid NAVD
88 height values.
Estimating GPS-Derived Orthometric Heights
Five Basic Adjustment Procedures
Topography
AB
C
D
E
F
GPS-Derived Heights from GEOID03 Separation
= Published NAVD88 Orthometric Height = New Control
Ellipsoid
hh
h
h
h
h
GEOID09
N N
N NN
N
Hh-N
Hh-N
Hh-N
Hh-N
Hh-N
Hh-N
Constrained Vertical Adjustment
Topography
AB
C
D
E
F
hadj
hadjhadj
hadj
ha
dj
hadj
AdjustedEllipsoid
Ellipsoid Height Adjusted to Fit Constrained Orthometric Heights
GPS-Derived Orthometric Heights
= Published NAVD88 Orthometric Height= New Control
H
HH
H
Geoid based on Ortho Heights
GEOID09
Ellipsoid
hh
h
h
h
hHGPS
HGPS
N N
N NN
N
GEOID09
Summary
• Mistakes and systematic errors must be removed before the adjustment
• A least squares adjustment handles random errors and provides a single solution
• The Minimally Constrained adjustment checks the internal consistency of the network
• The Constrained adjustment checks the existing control and references the network to the datum
• The vertical adjustment estimates GPS-derived Orthometric heights
CONTROL COMPARISON
OUTLIERS?
PASSIVE CONTROL QUALITY
(OVER TIME)
GEOID MODEL QUALITY
Elevation published
to centimeters
Orthometric height
determined by GPS
Identified as
Height Mod
survey station
ADJUSTMENT TO PASSIVE CONTROL
SUMMARY• Mistakes (blunders) and systematic errors must be
removed before the adjustment
• A least squares adjustment handles random errors and provides a single solution (Try to eliminate all systematic errors)
• The Minimally Constrained adjustment checks the internal consistency of the network
• The Constrained adjustment checks the existing control and references the network to the datum
• The vertical adjustment estimates GPS-derived Orthometric heights- Approaching 3rd order leveling accuracies
• OPUS with redundant observations can produce 5 cm orthometric heights in areas of high accuracy hybrid geoid coverage