Transcript GPS-Derived Orthometric Heights

Class 27: 28 April 2008 Planning and Analysis of a
Height Modernization Survey using TM 58/59
GISC3325
28 April 2007
GPS-Derived Heights
Part II
Planning and Evaluating a
GPS Vertical Survey
NOAA, NOS, National Geodetic Survey
Topics To Be Discussed
Review of heights and accuracies
A Guide for Establishing GPS-derived Orthometric Heights
Sample project following NGS’ guidelines
Discussion on base line processing and analysis of repeat base
line results
Discussion of adjustment procedures and analysis of results
Height Modernization Initiative
NGS web site and services
Ellipsoid, Geoid, and Orthometric Heights
“h = H + N”
P
Plumb Line
Ellipsoid
h
Q
Mean
Sea
Level
N
“Geoid”
PO
Ocean
h (Ellipsoid Height) = Distance along ellipsoid normal (Q to P)
N (Geoid Height) = Distance along ellipsoid normal (Q to PO)
H (Orthometric Height) = Distance along plumb line (PO to P)
GPS - Derived Ellipsoid Heights
Z Axis
P
(X,Y,Z) = P (,,h)
h
Earth’s
Surface
Zero
Meridian
Reference Ellipsoid
Y Axis


X Axis
Mean Equatorial Plane
Simplified Concept of ITRF 00 vs. NAD 83
h83
h00
Earth’s
Surface
ITRF 00
Origin
NAD 83
Origin
Identically shaped ellipsoids (GRS-80)
a = 6,378,137.000 meters (semi-major axis)
1/f = 298.25722210088 (flattening)
Expected Accuracies
NOAA Technical Memorandum NOS NGS-58
GUIDELINES FOR ESTABLISHING GPS-DERIVED ELLIPSOID HEIGHTS
(STANDARDS: 2 CM AND 5 CM)
VERSION 4.3
• GPS-Derived Ellipsoid Heights
David B. Zilkoski
Joseph D. D'Onofrio
Stephen J. Frakes
Silver Spring, MD
November 1997

2 centimeters (following NOS NGS-58 Guidelines)
U.S. DEPARTMENT OF
COMMERCE
• Geoid Heights (GEOID03)


Relative differences typically less than 1 cm in 10 km
2.4 cm RMS about the mean nationally
• Leveling-Derived Heights

Less than 1 cm in 10 km for third-order leveling
National Oceanic and
Atmospheric Administration
National Ocean
Service
National Geodetic
Survey
Recommendations to Guidelines
Based on Tests and Sample Projects
• Must repeat base lines
Different days
 Different times of day
» Detect, remove, reduce effects due to multipath and
having almost the same satellite geometry

• Must FIX integers
• Base lines must have low RMS values, i.e., < 1.5 cm
NOAA Technical Memorandum NOS NGS-58
GUIDELINES FOR ESTABLISHING GPS-DERIVED ELLIPSOID HEIGHTS
(STANDARDS: 2 CM AND 5 CM)
VERSION 4.3
Available “On-Line” at
the NGS Web Site:
www.ngs.noaa.gov
David B. Zilkoski
Joseph D. D'Onofrio
Stephen J. Frakes
Silver Spring, MD
November 1997
U.S. DEPARTMENT OF
COMMERCE
National Oceanic and
Atmospheric Administration
National Ocean
Service
National Geodetic
Survey
Table 1. -- Summary of Guidelines
Table 1. -- Summary of Guidelines.
Control
2 and 5 cm
Dual Frequency
Required
Primary Base
2 cm
Primary Base
5 cm
Secondary Base
2 cm
Secondary Base
5 cm
Local Network
2 cm
Local Network
5 cm
Yes, if base line is Yes, if base line is Yes, if base line is Yes, if base line is Yes, if base line is Yes, if base line is Yes, if base line is
greater than 10 km
greater than 10 km
greater than 10 km
greater than 10 km
greater than 10 km
greater than 10 km
greater than 10 km
Geodetic Quality
Antenna with Ground
Plane
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Min. Number of
Stations
3
3
3
No
Minimum
No
Minimum
No
Minimum
No
Minimum
Occupation Time
5 Hours
5 Hours
5 Hours
30 Minutes1
30 Minutes1
30 Minutes1
No Minimum1
Number of Days Station
Is Occupied
3
3
3
22
22
22
22
Max. Distance Between
Same or Higher-Order
Stations
75 km
40 km
50 km
20 km
10 km
20 km
Average Distance
Between Stations
No Maximum
No Maximum
No Maximum
No Maximum
7 km
10 km
15 km
No Maximum
Repeat
"Base Line"
YES3
YES3
YES3
YES3
YES3
YES3
YES3
Collect Met Data
Yes
Yes
Yes
Yes
Yes
No
No
Fixed Height Pole
Yes
Yes
No
Yes
No
Yes
No
Rubbing of Mark
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Precise Ephemerides
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Fix Integers
Yes4
Yes5
Yes5
Yes
Yes
Yes
Yes
Notes for Table of Summary of Guidelines:
1
Analyses have indicated that when following all guidelines in this document, 30 minutes of observations over base lines that are typically less than 10 kilometers will meet the standards.
For base lines greater than 10 km, but less than 15 km, 1 hour sessions should meet the standards. For observing sessions greater than 30 minutes, collect data at 15-second epoch interval.
For sessions less than 30 minutes, collect data at 5-second epoch interval. Track satellites down to at least 10-degree elevation cut-off.
2
Base lines must be reobserved on different days with significantly different satellite geometry.
3
The observing scheme requires that all adjacent stations have base lines observed at least twice on two different days with significantly different geometry.
4
If base line is greater than 40 kilometers, a partially fixed or float solution is permitted.
5
For all station pairs except those involved with control stations (see note 4
Sample Project Showing Connections
CS2
CS1
LN1
LN2
LN4
LN3
PB2
PB1
SB1
LN5
LN6
SB2
LN7
SB3
PB3
CS3
SB4
SB5
PB4
CS4
A Guide for Establishing
GPS-Derived Orthometric
Heights
(Standards: 2 cm and 5 cm)
A Guide for Establishing GPS-Derived
Orthometric Heights
(Standards: 2 cm and 5 cm)
3-4-5 System
• Three Basic Rules
• Four Basic Control Requirements
• Five Basic Procedures
Three Basic Rules
• Rule 1:

Follow NGS’ guidelines for establishing GPS-derived
ellipsoid heights (Standards: 2 cm and 5 cm)
• Rule 2:

Use latest National Geoid Model, i.e., GEOID03
• Rule 3:

Use latest National Vertical Datum, i.e., NAVD 88
Four Basic Control Requirements
• BCR-1: Occupy stations with known NAVD 88 orthometric
heights

Stations should be evenly distributed throughout project
• BCR-2: 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
• BCR-3: Project areas greater than 20 km on a side, keep distances
between GPS-occupied NAVD 88 bench marks to less than 20 km
• BCR-4: Projects located in mountainous regions, occupy bench
marks at base and summit of mountains, even if distance is less
than 20 km
NAVD
NAVD88
88Bench
BenchMarks
MarksOccupied
Occupiedwith
withGPS
GPS
0----------5-----0----------5----Kilometer
Kilomete
BCR Example
Geoid
Geoid99
99
Units
Unitscm
cm
BCR1: Sketch indicates that
the 20 km rule was met.
BCR2: This requirement is not applicable because the project is greater than 20 km on a side.
0----------5----------10---------15---------20
0----------5----------10---------15---------20
BCR3:
Circled bench marks are mandatory. Analysis must indicate bench marks have valid
Kilometers
NAVD 88 heights. Other
BMs can be substituted but user must adhere to 20 km requirement.
Kilometers
BCR4: This requirement is not applicable because project is not in a mountainous region.
Five Basic Procedures
• BP-1: Perform 3-D minimum-constraint least squares
adjustment of GPS survey project

Constrain 1 latitude, 1 longitude, 1 orthometric height
• BP-2: Analyze adjustment results from BP-1

Detect and remove all data outliers
FREE ELLIPSOID HEIGHT RESIDUAL BY BASELINE
LENGTH
455 BASE LINES - 2.6% ABOVE 3 cm
7
6
0092-0039
5.1
0113-H83A
3.1
5
0092-0039
3.8
4
RESIDUAL (CM)
3
6666-6669
-4.9
0114-0913
2.6
1933--0121
3.1
2
1
0
-1
-2
-3
6666-6669
-4.9
1933-0092
-3.1
-4
-5
0038-0913
-3.7
-6
6669-0092
-6.5
0127-6294
--3.5
1933-0092
-6.5
-7
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
BASE LINE LENGTH (KM)
BP2: After performing minimum constraint adjustment, plot ellipsoid height
residuals (or dU residuals) and investigate all residuals greater than 2 cm.
40.0
REPEAT BASELINE DIFFERENCES BY DISTANCE
172 BASELINES - 3% Above 3 cm
REPEAT DIFFERENCES (CM)
6
6669-6666
4.9
5
4
6669-0092
4.7
0113-H83A
3.1
1933-0121
3.1
0092-1933
3.1
3
2
1
0
0
5000
10000
15000
20000
25000
30000
35000
40000
BASELINE LENGTH (M)
BP2: 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.
Five Basic Procedures
(continued)
• BP-3: Compute differences between GPSderived orthometric heights from minimumconstraint adjustment in BP-2 and published
NAVD88 BMs
GPS-Derived
GPS-DerivedOrthometric
OrthometricHeight
Heightminus
minusNAVD
NAVD88
88Height
Heigh
0.8
0.8
3.5
3.5
1.7
1.7
0--0-3.8
3.8
1.9
1.9
3.6
3.6
2.8
2.8
2.4
2.4
0.6
0.6
3.0
3.0
1.9
1.9
3.2
3.2
1.8
1.8
-0.1
-0.1
0.4
0.4
2.2
2.2
0.8
0.8
0.0
0.0
BP3: All height differences are under 5 cm and most are less than 2 cm. Almost all relative
2.0
height differences between adjacent station pairs are less than2.0
2 cm. However, most of the
height differences appear to be positive relative to the southwest corner of the project.
1.2
1.2
Five Basic Procedures
(continued)
• BP-4: Determine which BMs have valid NAVD88
height values from results from BP-3
Differences need to agree 2 cm for 2 cm survey
 Differences need to agree 5 cm for 5 cm survey
 May detect systematic tilt over large areas
» Solve for geoidal slope and scale

• BP-5: Perform constrained adjustment with results
from BP-4
Constrain 1 latitude, 1 longitude, all valid orthometric
height values
 Ensure final heights not distorted in adjustment

GPS-Derived
GPS-DerivedOrthometric
OrthometricHeight
Heightminus
minusNAVD
NAVD88
88He
H
-2.4
-2.4
0.8
0.8
-1.0
-1.0
1.2
1.2
-0.9
-0.9
1.4
1.4
0.5
0.5
G
0.3
0.3
-1.1
-1.1
1.0
1.0
0.5
0.5
0.4
0.4
-0.5
-0.5
-1.4
-1.4
1.6
1.6
0.7
0.7
-1.3
-1.3
-0.4
-0.4
BP4: To detect and remove any systematic trend, a tilted plane is best fit to the height
1.4
1.4
differences (Vincenty 1987, Zilkoski and Hothem 1989). After a trend has been removed, all
the differences are less than +/- 2 cm except for one and almost all relative differences between
adjacent station are less than 2 cm.
-0.6
BP5: After rejecting the largest height difference (-2.4 cm), of all the closely spaced station
pairs only 3 are greater than 2 cm, 1 is greater than 2.5 cm and none are greater than 3 cm.
1
National Geodetic Survey,
Retrieval Date = JANUARY 4, 1999
AW5439
***********************************************************************
AW5439 DESIGNATION - HGCSD 18
AW5439 PID
- AW5439
AW5439 STATE/COUNTY- TX/HARRIS
AW5439 USGS QUAD
- SATSUMA (1982)
AW5439
AW5439
*CURRENT SURVEY CONTROL
AW5439 ___________________________________________________________________
AW5439* NAD 83(1993)- 29 52 45.31262(N)
095 36 41.68709(W)
ADJUSTED
AW5439* NAVD 88
36.28
(meters)
119.0
(feet) GPS OBS
AW5439 ___________________________________________________________________
AW5439 X
-541,229.237 (meters)
COMP
AW5439 Y
- -5,508,419.298 (meters)
COMP
AW5439 Z
3,158,779.472 (meters)
COMP
AW5439 LAPLACE CORR0.34 (seconds)
DEFLEC96
AW5439 ELLIP HEIGHT8.96 (meters)
GPS OBS
AW5439 GEOID HEIGHT-27.43 (meters)
GEOID96
AW5439
AW5439 HORZ ORDER - FIRST
AW5439 ELLP ORDER - THIRD
CLASS I
AW5439
AW5439.The horizontal coordinates were established by GPS observations
AW5439.and adjusted by the National Geodetic Survey in October 1996.
AW5439
AW5439.The orthometric height was determined by GPS observations and a
AW5439.high-resolution geoid model using precise GPS observation and
AW5439.processing techniques.
AW5439
AW5439.The X, Y, and Z were computed from the position and the ellipsoidal ht.
AW5439
AW5439.The Laplace correction was computed from DEFLEC96 derived deflections.
AW5439
AW5439.The ellipsoidal height was determined by GPS observations
AW5439.and is referenced to NAD 83.
AW5439
AW5439.The geoid height was determined by GEOID96.
AW5439
AW5439;
North
East
Units
Scale
Converg.
AW5439;SPC TXSC
- 4,231,486.301
927,255.302
MT 0.99990823 +1 39 36.1
AW5439;UTM 15
- 3,308,270.740
247,770.501
MT 1.00038501 -1 18 06.2
AW5439
AW5439
SUPERSEDED SURVEY CONTROL
AW5439
AW5439 NAD 83(1986)- 29 52 45.32657(N)
095 36 41.66906(W) AD(
) 1
AW5439 NAD 83(1993)- 29 52 45.31197(N)
095 36 41.68755(W) AD(
) 1
AW5439 ELLIP HT
9.33 (m)
GP(
) 5
AW5439 NGVD 29
36.86
(m)
120.9
(f) LEVELING
3
AW5439
AW5439.Superseded values are not recommended for survey control.
Elevation published
to centimeters.
Orthometric height
determined by GPS.
GPS-Derived
Orthometric Heights
Project
PA
MD
CARROLL
COUNTY


HARFORD
COUNTY
Baltimore County Maryland,
NAVD88
GPS-Derived Orthometric
Height Project


BALTIMORE
CITY
70
HOWARD
COUNTY


ANNE ARUNDEL
COUNTY
0
0
2
4 6
2.5
8 10 12 14 km
5.0
7.5
10.0mi


KEY
= HARN STATION
= NEW MONUMENT
= GPS LEVELING MONUMENT
TABLE 1
Baltimore County, Maryland,
NAVD88
PROJECT
GPS-derivedHORIZONTAL
Orthometric
Height Project
and VERTICAL CONTROL
Project Horizontal and Vertical Control
Station Name
GIS 431
GIS 911
GIS 921
GIS 1071
HYDE2
LINE3
MELSAGE2,3
Vertical Control
NAVD88 Height
(meters)
84.777
167.910
187.751
145.228
130.143
161.989
Horizontal Control
NAD83 (1991)
Latitude
39-28-53.41339N
39-25-35.54491N
1
New bench mark leveled to in project.
2
HARN station
3
Existing bench mark
Longitude
76-29-05.76845W
76-46-03.21432W
TABLE 2
OCCUPATION SCHEDULE
SESSION
DATE
STARTING
TIME
SESSION
DURATION CODE
SEPT 19
(DOY 263)
08:00am
5 HRS
1A
GIS 43
MELSAGE
HYDE
GIS 92
SEPT 20
(DOY 264)
08:00am
5 HRS
2A
GIS 43
MELSAGE
HYDE
GIS 92
SEPT 24
(DOY 268)
08:00am
5 HRS
3A
GIS 43
MELSAGE
HYDE
GIS 92
SEPT 25
(DOY 269)
08:00am
09:30am
11:00am
01:00pm
02:30pm
45
45
45
45
45
4A
4B
4C
4D
4E
GIS 91
GIS 91
GIS 97
GIS 97
LINE
GIS 84
SAUTER RESET
SAUTER RESET
GIS 82
GIS 82
GIS 94
GIS 90
MELSAGE
MELSAGE
MELSAGE
GIS
GIS
GIS
GIS
GIS
SEPT 26
(DOY 270)
--------SEPT 26
(DOY 270)
09:00am
10:30am
-------12:00am
01:30pm
03:00pm
45 mins
45 mins
------45 mins
45 mins
45 mins
LINE
GIS 79
-----------GIS 91
GIS 91
GIS 97
GIS 98
GIS 107
-----------GIS 84
SAUTER RESET
SAUTER RESET
GIS 78
HYDE
----------GIS 94
GIS 90
MELSAGE
GIS 80
GIS 80
--------GIS 92
GIS 43
GIS 92
SEPT 27
(DOY 271)
09:00am
10:30am
12:00am
01:30am
45
45
45
45
GIS 97
LINE
LINE
GIS 79
GIS
GIS
GIS
GIS
MELSAGE
MELSAGE
GIS 78
HYDE
GIS
GIS
GIS
GIS
mins
mins
mins
mins
mins
mins
mins
mins
mins
5A
5B
----5C
5D
5E
6A
6B
6C
6D
OCCUPIED
STATIONS
82
82
98
107
92
43
92
92
81
92
81
80
80
Observation Sessions; Primary Control
Day 263 = Project Day 1
Day 264 = Project Day 2
Day 268 = Project Day 3
Session A for all days; 5 hour observations
92
HYDES
HARN
1A, 2A, 3A
MELSAGE
HARN
KEY
Existing HARN
New Primary Control
43
Baltimore
City
Observation Sessions; Local Control
Day 269 = Project Day 4
Day 270 = Project Day 5
Day 271 = Project Day 6
Session =A, B, C, D, E; 45 minute observations
92 4C
4D
5E 6A
4A
5C
84
82
97
4E 6B
4D 6A
4C
94
4A
4A
5C
5C
5C
4A
4D
4D
5E
6A
6A
91
4B
4E
6B
6C, 5A
5A
LINE
6C
78
6C
5A
6D
5B
6D
5A
6C
79
5B
6D
5B
6D
5B
HYDES
HARN
107
98
5E
KEY
4C
4B
5E
5D
5D 4B
43
80
MELSAGE
HARN
4C
5D
4E
6B
6B
4E
4B 5D
90
81
SAUTER
RESET
Baltimore
City
Repeat Baseline Differences
Repeat Baseline Differences
(Baselines less than 10 KM)
Height Differences (du) 5 Hour Sessions
FROM
STATION
MELSAGE
MELSAGE
MELSAGE
GIS 92
GIS 43
GIS 92
TO
STATION
(Distance,
meters)
GIS 92
9,692
SESSION
NUMBER
OBSERVED
MET DATA
x1
x2
DIFF
cm
(x1
-
x2)
STANDARD
MET DATA
y1
y2
DIFF
cm
(y1-y2)
DIFF
cm
(x1-y1),
(x2-y2)
1A
2A
8.769
8.703
6.6
8.664
8.668
-0.4
10.5
3.5
1A
3A
8.769
8.644
12.5
8.664
8.669
-0.5
10.5
-0.5
2A
3A
8.703
8.644
5.9
8.668
8.669
-0.1
3.5
-0.5
GIS 43
13,576
1A
2A
- 94.766
- 94.724
-4.2
- 94.725
- 94.740
1.5
-4.1
1.6
HYDE
25,079
1A
2A
- 89.525
- 89.457
-6.8
- 89.498
- 89.483
-1.5
-2.7
2.6
1A
3A
- 89.525
- 89.473
-5.2
- 89.498
- 89.492
-0.6
-2.7
1.9
2A
3A
- 89.457
- 89.473
1.6
- 89.483
- 89.492
0.9
2.6
1.9
GIS 43
15,768
1A
2A
-103.533
-103.423
-11.0
-103.389
-103.406
1.7
-14.4
-1.7
HYDE
36,954
1A
2A
5.249
5.256
-0.7
5.230
5.248
1.8
1.9
0.8
HYDE
32,400
1A
2A
- 98.297
- 98.167
-13.0
- 98.164
- 98.148
-1.6
-13.3
-1.9
1A
3A
- 98.297
- 98.117
-18.0
- 98.164
- 98.166
-0.2
-13.3
4.9
2A
3A
- 98.167
- 98.117
-5.0
- 98.148
- 98.166
-1.8
-1.9
4.9
Height Differences (du) 45 Minute Sessions
FROM
STATION
SAUTER RESET
GIS 43
GIS 90
GIS 91
GIS 84
GIS 94
GIS 92
GIS 91
SAUTER RESET
SAUTER RESET
1
2
TO
STATION
(Distance, meters)
SESSION
NUMBER
OBSERVED
MET DATA
x1 (m)
x2
DIFF
(cm)
(x1-x2)
STANDARD
MET DATA
y1 (m)
y2
DIFF
cm
(y1-y2)
DIFF
cm
(x1-y1),
(x2-y2)
GIS 43
7,882
4B
5D
- 68.058
- 68.076
1.8
- 68.101
- 68.109
- 0.8
4.3
3.3
GIS 90
6,242
4B
5D
63.809
63.879
7.0
63.897
63.908
- 1.1
- 8.8
- 2.9
GIS 91
4,062
4B
5D
24.404
24.392
1.2
24.421
24.407
1.4
- 1.7
- 1.5
GIS 84
2,088
4A
5C
- 42.298
- 42.286
- 1.2
- 42.331
- 42.325
- 0.6
3.3
3.9
GIS 94
3,483
4A
5C
39.767
39.741
2.6
39.801
39.781
2.0
- 3.4
- 4.0
GIS 92
3,288
4A
5C
17.595
17.574
2.1
17.614
17.591
2.3
- 1.9
- 1.7
GIS 91
5,703
4A
5C
- 15.079
- 15.067
- 1.2
- 15.094
- 15.076
1.8
1.5
0.9
4B
1
5D
- 20.205
- 20.167
- 3.8
- 20.217
- 20.191
- 2.6
1.2
2.4
GIS 92
18,029
4C
5E
35.296
35.252
4.4
35.308
35.298
1.0
- 1.2
- 4.6
MELSAGE
11,120
4C
5E
26.646
26.605
4.1
26.655
26.618
3.7
- 0.9
- 1.3
SAUTER RESET
13,036
2
SAUTER RESET are outside allowable tolerance for base line misclosures and will be reobserved at later date.
Large residuals in adjustment, 2.1 cm, and base line lengths are greater than 10 km.
Height Differences (du) 45 Minute Sessions (continued)
FROM
STATION
GIS 92
GIS 92
MELSAGE
MELSAGE
GIS 97
GIS 82
GIS 81
3
4
TO
STATION
(Distance, meters)
GIS 97
2,831
MELSAGE
9,692
SESSION
NUMBER
4
4C
4
5E
4D
6A
17.867
17.840
17.869
17.844
5E
6A
17.840
17.844
4
4D
4
6A
4C
5E
GIS 97
7,821
4C
5E
GIS 82
6,722
4D
6A
4E
6B
3
GIS 82
7,958
4D
6A
3
GIS 81
6,186
LINE
2,462
Rejected in adjustment
Another set of base lines meet allowable misclosure
OBSERVED
MET DATA
x1
x2
-
8.687
8.657
8.651
8.649
26.518
26.489
DIFF
(cm)
(x1-x2)
STANDARD
MET DATA
y1
y2
DIFF
cm
(y1-y2)
DIFF
cm
(x1-y1),
(x2-y2)
2.5
17.878
17.849
17.824
17.843
- 1.9
- 1.1
- 0.9
4.5
0.1
- 0.4
17.849
17.843
0.6
- 0.9
0.1
2.7
3.0
0.2
2.9
-
8.704
8.664
8.660
8.671
26.529
26.524
33.542
33.351
33.343
33.403
- 6.0
33.361
33.369
33.389
7.048
6.855
19.3
7.017
6.855
4E
6B
-101.434
-101.513
7.9
-101.529
-101.533
4E
6B
34.841
34.822
1.9
34.846
34.822
19.1
2.9
1.1
1.7
0.7
0.9
2.2
0.5
- 1.1
- 3.5
- 2.0
- 1.0
- 2.6
1.4
16.2
3.1
0.0
- 4.0
0.4
2.4
9.5
2.0
- 0.5
0.0
Height Differences (du) 45 Minute Sessions (continued)
FROM
STATION
MELSAGE
LINE
LINE
GIS 98
GIS 78
GIS 80
GIS 79
GIS 107
GIS 80
5
6
TO
STATION
(Distance, meters)
SESSION
NUMBER
LINE
10,497
4E
6B
GIS 78
6,068
5
OBSERVED
MET DATA
x1
x2
DIFF
(cm)
(x1-x2)
STANDARD
MET DATA
y1
y2
DIFF
cm
(y1-y2)
DIFF
cm
(x1-y1),
(x2-y2)
- 33.261
- 33.286
2.5
- 33.271
- 33.313
4.2
1.0
2.7
5A
6C
- 56.742
- 56.733
- 0.9
- 56.771
- 56.782
1.1
2.9
4.9
GIS 98
6,135
5A
6C
- 55.900
- 55.886
- 1.4
- 55.924
- 55.937
1.3
2.4
5.1
GIS 78
2,375
5A
6C
- 0.847
- 0.842
- 0.5
- 0.845
- 0.842
- 0.3
- 0.2
0.0
GIS 80
366
5A
6C
- 0.310
- 0.312
0.2
- 0.310
- 0.312
0.2
0.0
0.0
GIS 79
1,839
5B
6
6D
341
- 6.530
- 6.545
1.5
- 6.536
- 6.545
- 6.547
0.9
1.1
GIS 107
2,532
5B
6
6D
341
62.854
62.842
1.2
62.894
62.842
62.903
5.2
- 0.9
HYDE
4,674
5B
6
6D
341
- 55.423
- 55.401
2.2
- 55.439
- 55.400
- 55.449
- 3.9
1.0
HYDE
8,294
5B
6
6D
341
0.909
0.907
0.2
0.924
0.907
0.914
1.7
1.0
Large residual, -4.0 cm, in adjustment and base line length greater than 10 km.
Session reobserved on December 6, 1996 (DOY 341).
0.6
0.0
- 4.0
0.0
1.6
0.1
- 1.5
0.0
Vertical Free Adjustment Results
GEOID96
Station
Name
Ellipsoid
Height
meters
(h)
Geoid
Height
meters
(GEOID96)
NAVD88
Orthometric
Height
meters
(H88)
84.777
HGPS96 - H88
(cm)
-32.085
GPS-derived
Orthometric
Height
meters
(HGPS96)
84.749
- 2.8
HGPS -H88
differences
relative to
MELSAGE
(cm)
-1.5
GIS 43
52.664
GIS 91
135.831
-32.062
167.893
167.910
- 1.7
-0.4
GIS 92
155.658
-32.074
187.732
187.751
- 1.9
-0.6
GIS 107
112.555
-32.651
145.206
145.228
- 2.2
-0.9
LINE
97.736
-32.399
130.135
130.143
- 0.8
0.5
MELSAGE
129.785
-32.191
161.976
161.989
- 1.3
0.0
Vertical Free Adjustment Results
G96SSS
Station
Name
Ellipsoid
Height
meters
(h)
Geoid
Height
meters
(GEOID96)
NAVD88
Orthometric
Height
meters
(H88)
84.777
HGPS96 - H88
(cm)
-32.961
GPS-derived
Orthometric
Height
meters
(HGPS96)
85.625
84.8
HGPS -H88
differences
relative to
MELSAGE
(cm)
-1.0
GIS 43
52.664
GIS 91
135.831
-32.934
168.765
167.910
85.5
-0.3
GIS 92
155.658
-32.944
188.602
187.751
85.1
-0.7
GIS 107
112.555
-33.519
146.074
145.228
84.6
-1.2
LINE
97.736
-33.268
131.004
130.143
86.1
0.3
MELSAGE
129.785
-33.062
162.847
161.989
85.8
0.0
Vertical Free Adjustment Results
GEOID93
Station
Name
Ellipsoid
Height
meters
(h)
Geoid
Height
meters
(GEOID93)
NAVD88
Orthometric
Height
meters
(H88)
84.777
HGPS93 - H88
(cm)
-32.421
GPS-derived
Orthometric
Height
meters
(HGPS93)
85.085
30.8
HGPS -H88
differences
relative to
MELSAGE
(cm)
-0.2
GIS 43
52.664
GIS 91
135.831
-32.390
168.221
167.910
31.1
0.0
GIS 92
155.658
-32.398
188.056
187.751
30.5
-0.5
GIS 107
112.555
-32.962
145.517
145.228
28.9
-2.1
LINE
97.736
-32.716
130.452
130.143
30.9
-0.1
MELSAGE
129.785
-32.514
162.299
161.989
31.0
0.0
Baltimore County GPS-Derived
Orthometric Height Project
H GPS - H Leveling(88)
(Units = cm)
-0.5
-0.6
-0.7
92
82
97
81
78
79
94
91
84
0.0
-0.4
-0.3
90
-0.2
-1.5
LINE
-0.1
MELSAGE
HARN
0.0
0.0
0.5
98
107
-2.1
-0.9
-1.2
0.3
KEY
0.0
GEOID93
GEOID96
-1.0
43
HYDES
HARN
80
SAUTER
RESET
Baltimore
City
G96SSS
Final Set of GPS-Derived Orthometric Heights
GPS-derived Orthometric
height relative to
MELSAGE from
minimally constrained
adjustment
(m)
GPS-derived Orthometric
height from final
constrained adjustment
(m)
C=Constrained
Minimally
constrained minus
final constrained
adjustment (cm)
GIS 43
84.762
84.777C
-1.5
GIS 78
80.697
80.694
0.3
GIS 79
77.587
77.589
-0.2
GIS 80
81.094
81.094
0.0
GIS 81
97.356
97.357
-0.1
GIS 82
199.366
199.372
-0.6
GIS 84
129.844
129.851
-0.7
GIS 90
146.039
146.046
-0.7
GIS 91
167.906
167.910C
-0.4
Station Name
Final Set of GPS-Derived Orthometric Heights (cont.)
GPS-derived Orthometric
height relative to
MELSAGE from
minimally constrained
adjustment
(m)
GPS-derived Orthometric
height from final
constrained adjustment
(m)
C=Constrained
Minimally
constrained minus
final constrained
adjustment (cm)
GIS 92
187.745
187.751C
-0.6
GIS 94
168.846
168.851
-0.5
GIS 97
200.692
200.703
-1.1
GIS 98
79.076
79.076
0.0
GIS 107
145.219
145.228C
-0.9
HYDE
102.932
102.935
-0.3
LINE
130.148
130.143C
0.5
MELSAGE
161.989
161.989C
0.0
SAUTER RESET
140.895
140.918
-2.3
Station Name
Data Processing and
Analysis
of Repeat Base Line
Results
Vector Processing Controls
• Elevation Mask - 15 degrees
• Ephemeris - Precise
• 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
• Looking for RMS - Less than 1.5 cm
Washington Monument
Survey
1934
1999
L1, Float Solution, Predicted Weather
From
To
Session
DX (m)
DY (m)
DZ (m)
Vector
1st - Next
1st - Next
1st - Next
Length (m)
000A
WASH
231B
230B
229B
229A
231A
23.3958
-0.2463
-0.1140
0.1718
0.1387
-101.5071
-0.2060
0.1148
-0.2620
-0.2439
142.1077
-0.0313
-0.0838
0.2073
0.2101
176.198
0.060
-0.149
0.341
0.328
868H
WASH
229A
230B
229B
231A
230A
231B
194.0185
-0.0135
-0.1019
-0.0053
-0.0354
-0.0983
-335.8332
0.2206
0.1925
0.0117
0.0883
0.1579
-176.4013
-0.2093
-0.1924
-0.0331
-0.1207
-0.1745
426.080
-0.093
-0.119
0.002
-0.036
-0.097
JEFF
WASH
231B
231A
230A
229B
230B
146.1021
0.1341
-0.0595
-0.1014
0.0961
-129.6425
-0.2111
-0.0776
0.1360
0.0648
80.2985
0.1901
0.0688
-0.1639
-0.0276
211.189
0.295
0.033
-0.216
0.016
L1, Partial Fixed Solution, Predicted Weather
From
To
Session
DX (m)
DY (m)
DZ (m)
Vector
1st - Next
1st - Next
1st - Next
Length (m)
000A
WASH
229A
231A
230B
229B
231B
23.2992
0.0054
-0.0435
-0.0236
-0.1005
-101.3609
-0.0414
0.1553
0.0825
0.1497
141.9511
0.0020
-0.1650
-0.0953
-0.1596
175.974
0.026
-0.228
-0.128
-0.228
868H
WASH
229A
229B
230B
231B
231A
230A
194.0163
-0.0323
-0.0366
-0.1028
-0.0302
-0.0070
-335.8572
0.1054
0.1522
0.1360
0.0540
0.0198
-176.3620
-0.0964
-0.1457
-0.1370
-0.0590
-0.0440
426.082
-0.058
-0.076
-0.097
-0.032
-0.001
JEFF
WASH
230A
230B
229B
231B
231A
146.1764
0.1508
-0.0509
0.0809
0.1914
-129.6260
0.0315
0.1939
0.0107
-0.1280
80.2979
-0.0017
-0.2241
0.0039
0.1387
211.230
0.084
-0.239
0.051
0.264
L1, Float Solution, Recorded Weather
From
To
Session
DX (m)
DY (m)
DZ (m)
Vector
1st - Next
1st - Next
1st - Next
Length (m)
000A
WASH
229B
231B
231A
229A
230B
23.4735
0.0349
0.1006
0.1578
0.1569
-101.5769
-0.0099
-0.0148
-0.0754
-0.0359
142.1521
-0.0105
0.0467
0.0643
0.0296
176.284
0.002
0.060
0.116
0.065
868H
WASH
229A
229B
230A
231B
230B
231A
194.1045
-0.0472
0.0599
-0.0604
0.0733
0.0061
-336.0715
-0.0049
-0.0952
-0.0141
-0.0290
-0.0184
-176.2377
-0.0677
0.0204
-0.0716
-0.0379
-0.0120
426.240
0.010
0.094
0.013
0.072
0.022
JEFF
WASH
230A
230B
231B
229B
231A
146.1589
0.1522
0.0187
0.0319
0.1027
-129.5715
0.1006
0.1229
0.0955
0.1151
80.2348
-0.0685
-0.1099
-0.1089
-0.0498
211.161
0.018
-0.104
-0.078
-0.019
Analysis of the Data Processing
• Fixed solutions / low RMS
• Repeatability of measurements
• Analysis of loop misclosures
• Be aware that repeatability and loop
misclosures do not disclose all problems
Repeat Vector Analysis
From
To
Station Station
BR13
BR13
BR14
BR19
BR20
BR20
BR14
Session
0780-0780
0770-0770
0761-0762
K251
0780-0780
0770-0770
0762-0761
GR15
0780-0780
0770-0770
0762-0765
CL20
0781-0781
0771-0771
0762-0763
BR30
0782-0782
0772-0772
0760-0763
VINT HILL 0782-0782
0772-0772
0760-0763
dh
Meters
Diff
cm
45.974*
46.004
-3.0
46.009
-3.5
-12.397
-12.400
0.3
-12.408
1.1
43.680
43.654*
2.6
43.607*
7.3
54.703*
55.031 -32.8
55.007* -30.4
28.939
28.947
-0.8
28.940
-0.1
33.045
33.051
-0.6
33.063
-1.8
Dist
Meters
RMS
1628
0.016
0.017
0.015
0.006
0.006
0.006
0.022
0.024
0.020
0.047
0.022
0.019
0.014
0.014
0.020
0.011
0.009
0.013
673
1133
365
9850
11967
Solution
Type
L1 float double
L1 fixed double
L1 fixed double
L1 fixed double
L1 fixed double
L1 fixed double
L1 fixed double
L1 fixed double
L1 fixed double
L1 fixed double
L1 fixed double
L1 fixed double
Iono free fixed
Iono free fixed
Iono free fixed
Iono free fixed
Iono free fixed
Iono free fixed
*NOTE - Reprocess all vectors which have difference greater than 2 cm.
Repeat Vector Analysis After Re-Processing
From
To
Station Station
BR13
BR13
BR14
BR19
BR20
BR20
BR14
Session
0761-0762
0770-0770
0780-0780
K251
0770-0770
0780-0780
0762-0761
GR15
0780-0780
0765-0762
0770-0770
CL20
0771-0771
0781-0781
0762-0763
BR30
0782-0782
0772-0772
0760-0763
VINT HILL 0782-0782
0760-0763
0772-0772
dh
Meters
46.009
46.004
46.007
-12.400
-12.397
-12.408
43.680
43.658
43.654
55.031
55.027
55.019
28.939
28.947
28.940
33.045
33.063
33.051
Diff
cm
Dist
Meters
1628
0.5
0.2
673
-0.3
0.8
1133
2.2
2.6
365
0.4
1.2
9850
-0.8
-0.1
11967
-1.8
-0.6
RMS
0.015
0.017
0.015
0.006
0.006
0.006
0.022
0.020
0.024
0.022
0.023
0.018
0.014
0.014
0.020
0.011
0.013
0.009
Solution
Type
L1 fixed double
L1 fixed double
L1 fixed double
L1 fixed double
L1 fixed double
L1 fixed double
L1 fixed double
L1 fixed double
L1 fixed double
L1 fixed double
L1 fixed double
L1 fixed double
Iono free fixed
Iono free fixed
Iono free fixed
Iono free fixed
Iono free fixed
Iono free fixed
Adjustment Procedures to Obtain
GPS-Derived NAVD’88
Orthometric Heights
Least Squares Adjustments
• The adjustment minimizes the effects of
random errors
• A least squares adjustment computes a single
network solution, even with redundant vectors
• Least squares will highlight blunders and large
errors
• It will provide estimates on the precision of the
coordinates for the stations
Errors
• All real observations contain errors
v  lˆ  l
where lˆ is the true parameterwhich is consistantwith themodel
l is thereal observation
v is theresidual
Random error

Two types of errors
» Random errors which mean to zero
» Systematic errors which do not
• Least squares will only give improved
results if your errors are predominantly
random
Systematic error
Least Squares
• Least squares is a mathematical procedure that takes a series of
survey measurements
 which must contain some extra or redundant measurements
• and calculates a single set of coordinates for the stations that will
satisfy all of the measurements while minimizing the sum of the
squares of the misfit (or residuals)
Critical value
Critical value
Least Squares Condition



v 2  minimum
v are the residuals
4 3 2 1
Outliers
v
1 2 3 4
Outliers
Standard Error of Unit Weight
SEUW =
S (residuals)2
S (estimated errors)2
• If the residuals from a least squares adjustment are equal to the
errors expected for the order of survey we have performed
 The standard error of unit weight will have a value of unity
• If the residuals are lower than we would expect given our initial
estimates of the errors
 SEUW will be less than 1
• If they are too high
 SEUW will be greater than 1
• Often used as a rough indication of whether a survey meets
specifications
Minimally Constrained Adjustment
• Hold the minimum number of
control points fixed to allow the
least squares process to work
 One fixed point for GPS
 2 for triangulation survey
without distance measurements
• The purpose of this adjustment is to
 Check the internal consistency of
the network
 Detect blunders or ill-fitting
observations
How big do you make the bolt holes?
 Obtain accurate error estimates
Constrained Adjustment
• Hold all control points in the network fixed
at values from the NGS database
 Minimum of 2 for GPS surveys
 3 for triangulation survey without
distance measurements
• The purpose of this adjustment is to
 Reference the network to existing
control and develop final coordinates
for the new control points that are
being established
 Verify existing control. If any control
points are wrong the standard error of
unit weight and the residuals will
increase compared to the minimally
constrained adjustment
Adjustment of Primary Network Stations
Horizontal Adjustment
(Latitude, Longitude, Ellipsoid Heights)
• Minimum Constrained



Fix latitude, longitude and ellipsoid height at one station
Resolve all blunders and large residuals
Determine which Control and known Primary Base Station
coordinates should be fixed
• Constrained


[One fixed station]
[All suitable stations fixed]
Fix latitude, longitude, and ellipsoid heights at Control and
known Primary Base Stations
Make sure the constraints did not distort the project
NOTE - Geoid model NOT applied at this time
Adjustment of Primary Base Stations
38°20’N
CORS
HARN
NAVD’88 BM
New Station
Primary Base Station
D191
10CC
MART
LAKE
MOLA
122°35’W
LONGITUDE
•CORS, Control Points (known Primary Control) horizontal
•latitude, longitude, and ellipsoid heights
•No NAVD88 orthometric heights constrained at this time
121°40’W
Adjustment of Local Network Stations
Horizontal Adjustment
(Latitude, Longitude, Ellipsoid Heights)
• Minimum Constrained



Fix latitude, longitude and ellipsoid height at one station
Resolve all blunders and large residuals
Evaluate coordinates at Control and Primary Base Station
» should not be greatly affected by Local Station baselines
• Constrained


[One fixed station]
[All suitable stations fixed]
Fix latitude, longitude, and ellipsoid heights at Control and
Primary Base Stations
Make sure the constraints did not distort the project
NOTE - Geoid model NOT applied at this time
Adjustment of Local Network Stations
38°16’N
CORS
HARN
NAVD’88 BM
New Station
Spacing Station
Primary Base Station
122°20’W
LONGITUDE
•Existing and newly derived Primary Control horizontal
• latitude, longitude, and ellipsoid heights
•No NAVD88 orthometric heights constrained at this time
121°40’W
Combined Network Horizontal Adjustment
• Perform combined adjustment

Control and Primary Base network along with local
network

Latitude, longitude, and ellipsoid height
• Use GEOID model to obtain geoid heights
• Make sure combined adjustment did not
distort the project
Combined Horizontal Adjustment
38°20’N
CORS
HARN
NAVD’88 BM
New Station
Spacing Station
Primary Base Station
122°35’W
LONGITUDE
•CORS, Control Points and existing and new Primary Control horizontal
• latitude, longitude, and ellipsoid heights
•No NAVD88 orthometric heights constrained at this time
121°40’W
Combined Network Vertical Adjustment
3-D Vertical Adjustment
(Orthometric Heights)
•
Minimum Constrained [One fixed station]




Fix latitude, longitude, and orthometric height at one station
Resolve all blunders and large residuals
Compare orthometric heights from adjustment with published NAVD 88
Determine which NAVD 88 bench marks should be fixed
• Constrained



[All suitable orthometric heights fixed]
Fix latitude, longitude at one station
Fix orthometric heights at all suitable stations
Make sure the constraints did not distort the project
Constrained Vertical Adjustment
38°20’N
CORS
HARN
NAVD’88 BM
New Station
Spacing Station
Primary Base Station
122°35’W
LONGITUDE
•1 horizontal latitude and longitude
•All valid NAVD88 orthometric heights
121°40’W
GPS-Derived Heights from GEOID03 Separation
D
E
C
Topography
B
F
A
Hh-N
h
Hh-N h
h
h
Hh-N
Hh-N
h
Hh-N
Hh-N
h
Ellipsoid
N
N
N
N
N
GEOID03
= Published NAVD88 Orthometric Height
= New Control
N
Constrained Vertical Adjustment
Ellipsoid Height Adjusted to Fit Constrained Orthometric Heights
GPS-Derived Orthometric Heights
D
E
C
Topography
B
F
A
h
H
h
hadj
H
HGPS
H
h H
GPS
hadj
h
H
hadj
N
N
h
hadj
N
N
Ellipsoid
hadj
N
Adjusted
Ellipsoid
GEOID03
Geoid
= Published NAVD88 Orthometric Height
= New Control
h
hadj
N
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
Analysis of a
Height Project
This project plan is for measuring the vertical
clearance for the Cooper River Bridges, known
as the Grace Memorial Bridge and Silias
Pearman Bridge.
The project consists of 3 different parts as follows:
1. Determine ellipsoid height of the two bridges using three different GPS receivers
on the two bridges, one receiver at the pilot house, and a CORS site.
2. Determine the difference between Geoid96 with NAVD 88 by observing a minimum
of four NAVD 88 bench marks including one primary bench mark at the tidal station.
3. Determine the height from the bottom of the bridges to each of the antenna mounts
on the bridges using classical and trig leveling.
Implementation of real-time, using GPS, sensors that will determine the maximum
height of a vessel at the lowest point of a bridge.
This project plan is for measuring the vertical clearance for the Cooper River Bridges.
Vertical clearance is critical for ensuring safe navigation for the Port of Charleston,
South Carolina.
MOUNTING THE ANTENNAS
1. Determine ellipsoid height of the two
bridges using three different GPS
receivers on the two bridges, one receiver
at the pilot house, and a CORS site.
GPS OCCUPATION
CLASSICAL LEVELING
2. Determine the difference between Geoid96 with NAVD 88 by observing a
minimum of four NAVD 88 bench marks including one primary bench mark at
the tidal station.
TRIG-LEVELING
3. Determine the height from the bottom of
the bridges to each of the antenna mounts on
the bridges using classical and trig leveling.
Height Project
TBM SILE
ARP
C 69
HOLLINS
10 012
TIDAL 13
(Connection to water surface)
NAVD88 Bench Mark
Temporary (Project) CORS
(Mounted to each end of bridge)
CHA1
CORS
CBPA
Repeat Vector Analysis
From
To
Session Length
(Hrs)
1001 TIDE 036A
034B
DX (m)
1st - Next
DY (m)
1st - Next
DZ (m)
1st - Next
Vector
Length (m)
ppm
2
2
-611.0438
-0.0001
-1427.9448
0.0092
-2098.1300
-0.0018
2610.469
-0.004
1.36
CBPA CHA1 040A 24
037A 24
036A 24
7737.4970
-0.0029
-0.0043
311.1515
0.0051
0.0088
-1656.7241
-0.0020
-0.0042
7918.990
-0.002
-0.003
0.28
0.38
CHA1 SILE 034A 24 -7178.4232
039A 24
0.0007
035A 24
-0.0006
1466.8512
0.0018
0.0030
4311.2394
-0.0094
-0.0076
8501.070
-0.005
-0.003
0.59
0.33
CPBA TIDE 036A
034B
2
2
-54.7070
-0.0001
365.4396
-0.0016
546.3072
-0.0011
659.538
-0.002
2.71
HOLL SILE 034B
036C
2
2
2418.6237
0.0028
255.6238
-0.0270
-149.0401
0.0257
2436.657
-0.002
0.67
Free Adjustment Horizontal Positions
Compared to Published NAD83 Positions
STATION NAME
10 012
CHARLESTON 1 CORS ARP
866 5530 TIDAL 13
* No Published Ellipsoid Height
LAT / LON
SHIFT (cm)
32.8
0.0
0.8
ELLIPSOID
SHIFT (cm)
*
0.0
1.8
Free Adjustment minus NAD83 Published
TBM SILE
ARP
C 69
HOLLINS
10 012
Residuals plotted to help
determine inconsistencies
32.8cm Horiz
TIDAL 13
0.8cm Horiz
1.8cm Ellip. Ht.
CHA1
CORS
FIXED
CBPA
NAVD88 Bench Mark
Temporary (Project) CORS
Sample Data Sheets
CJ0085
CJ0085
CJ0085*
CJ0085*
CJ0085
CJ0085
CJ0085
CJ0085
CJ0085
DESIGNATION - 866 5530 TIDAL 13
______________________________________________________________
NAD 83(1992)- 32 46 5233453(N)
079 55 28.70969(W)
ADJUSTED
NAVD 88
2.219 (meters)
7.28
(feet) ADJUSTED
______________________________________________________________
ELLIP HEIGHT-30.96 (meters)
GPS OBS
HORZ ORDER
VERT ORDER
-
FIRST
FIRST
CLASS I
******************************************************************************
CJ0578 DESIGNATION - 10 012
CJ0578
CJ0578 ______________________________________________________________
CJ0578* NAD 83(1986)- 32 47 31.79561(N)
079 54 20.99377(W)
ADJUSTED
CJ0578* NAVD 88
5.336 (meters)
17.51
(feet) ADJUSTED
CJ0578 ______________________________________________________________
CJ0578
CJ0578 HORZ ORDER - FIRST
CJ0578 VERT ORDER - FIRST
CLASS II
NOTE - Different adjustments for the positions
Adjusted Constrained Horizontal
Compared to Free Horizontal Positions
[Station 10 012 Not Fixed]
STATION NAME
C 69
HOLLINGS
866 5530 TIDAL 13
10 012
TBM SILE ARP
CHARLESTON POLIT HOUSE ARP
TBM SILW ARP
TBM GRAC ARP
CHARLESTON 1 CORS ARP
TBM SALAIS BOTTOM OF BRIDGE
LAT / LON
SHIFT (cm)
0.4
0.4
0.8
0.4
0.3
0.3
0.3
0.3
0.2
0.5
•Minimum shifts between free and constrained adjustments
•Constraints did not adversely affect adjustment
ELLIPSOID
SHIFT (cm)
-1.4
-1.3
-1.8
-1.3
-0.8
-0.9
-0.6
-0.7
-0.1
-1.7
Adjusted Constrained Horizontal
Compared to Free Horizontal Positions
[Station 10 012 Fixed]
STATION NAME
C 69
HOLLINGS
866 5530 TIDAL 13
10 012
TBM SILE ARP
CHARLESTON POLIT HOUSE ARP
TBM SILW ARP
TBM GRAC ARP
CHARLESTON 1 CORS ARP
TBM SALAIS BOTTOM OF BRIDGE
LAT / LON
ELLIPSOID
SHIFT (cm)
SHIFT (cm)
5.8
6.0
5.3
32.8
6.3
5.2
5.9
5.9
0.0
5.2
•A bad constraint in position also affects the ellipsoid heights
-2.3
-2.9
-1.8
-9.0
-2.9
-1.6
-2.0
-2.1
-0.0
-1.7
Free Vertical Adjustment Compared
to Published NAVD88 Elevations
STATION NAME
C 69
HOLLINGS
866 5530 TIDAL 13
10 012
TBM SILE ARP
TBM SILW ARP
LAT / LON
SHIFT (cm)
ORTHOMETRIC
SHIFT (cm)
0.1
0.2
0.0
0.8
0.3
0.3
0.6
0.1
0.0
-8.2
0.9
0.8
•GPS-derived orthometric height does not agree with published orthometric height
Free Vertical Adjustment minus NAVD88
Published
C 69
TBM SILE
0.9cm
ARP
0.6cm
HOLLINS
0.1cm
10 012
Residuals plotted to help
determine trends or
inconsistencies
-8.2cm
TIDAL 13
FIXED
CHA1
CORS
CBPA
NAVD88 Bench Mark
Temporary (Project) CORS
Adjusted Constrained Vertical
Compared to Free Vertical Elevations
[Station 10 012 Not Fixed]
STATION NAME
C 69
HOLLINGS
866 5530 TIDAL 13
10 012
TBM SILE ARP
CHARLESTON POLIT HOUSE ARP
TBM SILW ARP
TBM GRAC ARP
CHARLESTON 1 CORS ARP
TBM SALAIS BOTTOM OF BRIDGE
LAT / LON
SHIFT (cm)
0.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
•Minimum shifts between free and constrained adjustments
•Constraints did not adversely affect adjustment
ORTHOMETRIC
SHIFT (cm)
-0.6
-0.1
0.0
-0.4
-0.7
-0.4
-0.8
-0.6
-0.6
-0.0
Adjusted Constrained Vertical
Compared to Free Vertical Elevations
[Station 10 012 Fixed]
STATION NAME
C 69
HOLLINGS
866 5530 TIDAL 13
10 012
TBM SILE ARP
CHARLESTON POLIT HOUSE ARP
TBM SILW ARP
TBM GRAC ARP
CHARLESTON 1 CORS ARP
TBM SALAIS BOTTOM OF BRIDGE
LAT / LON
SHIFT (cm)
ORTHOMETRIC
SHIFT (cm)
0.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
•A bad constraint in orthometric height affects all orthometric heights
-0.6
-0.1
0.0
-8.2
-0.7
-2.4
-0.8
-0.6
-4.2
-1.2
NGS Data Sheet GEOID03
HT2268
HT2268
HT2268
HT2268
HT2268
HT2268
HT2268
HT2268*
HT2268*
HT2268
HT2268
HT2268
HT2268
HT2268
HT2268
HT2268
HT2268
HT2268
HT2268
HT2268
HT2268
HT2268
HT2268
HT2268
DESIGNATION PID
STATE/COUNTYUSGS QUAD
-
H= h -N
102.431 = 69.78 - (-32.60)
102.431  102.38
S 1320
HT2268
CA/SAN FRANCISCO
SAN FRANCISCO NORTH (1975)
*CURRENT SURVEY CONTROL
___________________________________________________________________
NAD 83(1992)- 37 45 25.30727(N)
122 28 36.34687(W)
ADJUSTED
NAVD 88
102.431 (meters)
336.06
(feet) ADJUSTED
___________________________________________________________________
EPOCH DATE 1997.30
X
- -2,711,121.437 (meters)
COMP
Y
- -4,259,419.310 (meters)
COMP
Z
3,884,200.262 (meters)
COMP
LAPLACE CORR5.53 (seconds)
DEFLEC03
ELLIP HEIGHT69.78 (meters)
GPS OBS
GEOID HEIGHT-32.60 (meters)
GEOID03
DYNAMIC HT 102.363 (meters)
335.84 (feet) COMP
MODELED GRAV979,964.0
(mgal)
NAVD 88
HORZ ORDER
VERT ORDER
ELLP ORDER
-
FIRST
FIRST
FOURTH
CLASS I
CLASS I
GEOID96 = 0.17 m
GEOID99 = 0.11 m
GEOID03 = 0.05 m
NAVD ‘88 Relative to (h - N) GEOID03
San Francisco Bay Demonstration Project
Station
NAVD ’88
–(h - N) cm
Ellipsoid
Vertical
Orthometric
Order/Class Order/Class Height (m)
L 1241
+3.6
Fourth / I
First / I
123.180
U 1320
+3.5
Fourth / I
First / I
83.942
S 1320
+4.5
Fourth / I
First / I
102.431
941 4819 TIDAL 32
+0.4
Fourth / I
First / II
3.569
RV 223
+0.4
Fourth / I
First / II
2.335
R 1393
-1.3
Fourth / I
First / II
3.198
941 4750 TIDAL 7
-2.4
Fourth / I
First / II
2.783
M 554
-0.6
Fourth / I
First / I
4.329
M 148
+1.1
Fourth / I
First / II
12.335
N 1197
+2.9
Fourth / I
First / II
22.731
San Francisco Bay Demonstration Project
H=h-N
R 1393 (-1.3)
Comparisons with Published
Station Heights (Centimeters)
GPS Site
RV 223 (+0.4)
0
5
10
KM
941 4819 TIDAL 32 (+0.4)
941 4750 TIDAL 7 (-2.4)
S 1320 (+4.5)
U 1320 (+3.5)
M 554 (-0.6)
M 148 (+1.1)
L 1241 (+3.6)
N 1197 (+2.9)
H = Orthometric Height
h = Ellipsoid Height
N = Geoid Height
GEOID03
“Real
World”
“Mapping
World”
8002
8002
8002
8002
8002
8002
8002
8002
8002
8002
The Opus solution for your submitted RINEX file appears to be
quite close to an NGS published control point. This suggests that
you may have set your GPS receiver up over an NGS control point.
Furthermore, our files indicate that this control point has not
been recovered in the last five years.
If you did indeed recover an NGS control point, we would
appreciate receiving this information through our web based
Mark Recovery Form at
http://www.ngs.noaa.gov/products_services.shtml#MarkRecoveryForm.
First station : SURVEYOR 290
Second station : SURVEYOR 284
Delta height =
-.0220
Ellipsoidal distance =
.0070
Mark to mark distance =
.0231
DX =
.0122
DN =
DY =
.0163
DE =
DZ =
-.0109
DU =
OPUS Processing
Comparisons
.0068
.0015
-.0220
Day 277
Day 278
Day 284
Day 290
First station : SURVEYOR 290
Second station : SURVEYOR 278
Delta height =
-.0150
Ellipsoidal distance =
.0089
Mark to mark distance =
.0174
DX =
.0114
DN =
DY =
.0122
DE =
DZ =
-.0048
DU =
.0083
.0030
-.0150
First station : SURVEYOR 290
Second station : SURVEYOR 277
Delta height =
-.0080
Ellipsoidal distance =
.0083
Mark to mark distance =
.0115
DX =
.0079
DN =
DY =
.0084
DE =
DZ =
-.0001
DU =
.0080
.0022
-.0080
2 hr 7 min
9 hr 23 min
7 hr 14 min
2 hr 7 min
OPUS - Multiple CORS Providing
Position to Base Receiver
= CORS
= Base Receiver
= Rover Receiver
P
+P
2 P
P
CORS 1
Two 2+ Hour Sessions
Two Receivers
N
+N
2 N
N

P Published Position
- P OPUS Mean Position
How well OPUS fits Published

How well
OPUS 1
OPUS 1 fits
OPUS 2
OPUS 2
O 1+2
OPUS Mean Position
P-N
+ P-N
2 P-N
P-N
How well
OPUS 1
OPUS 1 fits OPUS 2
OPUS 2
O 1+2
OPUS Mean Position
P

N
P = Published Point
N = New Point
How well
Process 1
Process 1 fits
Process 2
Process 2
Process 1+2
Process Mean Position

P-N Process Mean Position
- N OPUS Mean Position
How well Process fits OPUS

CORS 3
CORS 2
FINAL POSITION
N Process Mean Position
+ N OPUS Mean Position
2 N Process+OPUS Position
N Final Position