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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/

ftp://ftp.ngs.noaa.gov/dist/whenning/mss2008/

ftp://ftp.ngs.noaa.gov/dist/whenning/mss2008/

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)

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)

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



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!!


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)

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

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


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


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


– 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


– 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


(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


• 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.


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.



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.



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

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