GNSS DERIVED HEIGHTS- PART 2NOS/NGS - 59

Bill Henning

Senior Geodesist, PLS.

301-713-3196 x 111, william.henning@noaa.gov

NGS WEBINAR – OCTOBER 7, 2009

GNSS DERIVED HEIGHTS

DAY 1

• HT MOD• GNSS HT

METHODS• NOS/NGS-58

DAY 2• NOS/NGS-59-

Baltimore County and Fairfax County

• REAL TIME HT ISSUES

http://www.ngs.noaa.gov/

“NGS 59”

“NGS 58”

“Geoid”

PO

P

H (Orthometric Height) = Distance along plumb line (PO to P)

Earth’s

Surface

Ocean

Ellipsoid

“h = H + N”

N

h

Q

N (Geoid Height) = Distance along ellipsoid normal (Q to PO)

h (Ellipsoid Height) = Distance along ellipsoid normal (Q to P)

Plumb Line

Mean SeaLevel

H88 = h83 – N09

ELLIPSOID, GEOID & ORTHO HEIGHTS

Expected Height Accuracies• GPS-Derived Ellipsoid Heights

4 2 centimeters (following NOS NGS-58 Guidelines)

• Geoid Heights (GEOID03)4 Relative differences typically less than 1 cm in

10 km4 2.4 cm RMS about the mean nationally

4 0.5 cm error in 10 Km

• Leveling-Derived Heights4 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

N O A A T e c h n ic a l M e m o r a n d u m N O S N G S - 5 8

G U ID E L IN E S F O R E S T A B L IS H IN G G P S - D E R IV E D E L L IP S O ID H E IG H T S( S T A N D A R D S : 2 C M A N D 5 C M )V E R S IO N 4 .3

D a v id B . Z i lk o s k iJ o s e p h D . D 'O n o f r ioS t e p h e n J . F r a k e s

S i lv e r S p r in g , M D

N o v e m b e r 1 9 9 7

U .S . D E P A R T M E N T O F N a t io n a l O c e a n ic a n d N a t io n a l O c e a n N a t io n a l G e o d e t icC O M M E R C E A t m o s p h e r ic A d m in is t r a t io n S e r v ic e S u r v e y

Available “On-Line” at

the NGS Web Site:

www.ngs.noaa.gov

SEARCH: “NGS 58”

What has been accomplished using NGS 58?

• Control recovery, campaign planning/logistics• Obs schedulules, equipment checks• Observations: Repeat base lines

Different days

Different times of day (“15 hours, 27 hours”)

(Detect, remove, reduce effects due to multipath and using the same satellite geometry)

FAIRFAX COUNTY HEIGHT MODERNIZATION PROJECT 2004-2006

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

From To Session dh Diff Dist RMS Solution Station Station Meters cm Meters Type

BM20 04KU 076G 46.009 3628 0.015 L1 fixed double 077G 46.004 0.5 0.017 L1 fixed double 078R* 46.007 0.2 0.015 L1 fixed double ZINC PT14 078A 15.397 3173 0.006 L1 fixed double 077A 15.400 0.3 0.006 L1 fixed double 076A 15.408 1.1 0.006 L1 fixed double TIDE 04KU 078G 43.680 3133 0.022 L1 fixed double 077R* 43.654 2.6 0.024 L1 fixed double 076R* 43.658 2.2 0.020 L1 fixed double PT14 TIDE 077A -55.031 3765 0.022 L1 fixed double 078R* -55.027 0.4 0.023 L1 fixed double 076R* -55.019 1.2 0.018 L1 fixed double 04KU 5144 078G 28.939 7250 0.014 Iono free fixed 077G 28.947 -0.8 0.014 Iono free fixed 076G 28.940 -0.1 0.020 Iono free fixed 5144 ZINC 078A -33.045 6167 0.011 Iono free fixed 077A -33.051 -0.6 0.009 Iono free fixed 076A -33.063 -1.8 0.013 Iono free fixed

*NOTE - Reprocessed vectors which had differences greater than 2 cm.

Repeat Vector Analysis After Re-Processing

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

• HARN/Control Stations• (75 km)

• Primary Base• (40 km)

• Secondary Base• (15 km)

• Local Network Stations• (7 to 10 km)

• GPS ELLIPSOID HEIGHT HIERARCHY

Project Adjustment Following Guidelines

CORSHARNNAVD’88 BMNew Station

121°40’W122°35’W

37°50’N

38°20’N

LA

TIT

UD

E

LONGITUDE

Spacing StationPrimary Base Station

8.2km

Adjustment of Primary Network Stations From Control

Horizontal Adjustment(Latitude, Longitude, Ellipsoid Heights)

• Minimum Constrained [One fixed station]4 Fix latitude, longitude and ellipsoid height at one station4 Resolve all blunders and large residuals4 Determine which Control and known Primary Base

Station coordinates should be fixed

• Constrained [All suitable stations fixed]4 Fix latitude, longitude, and ellipsoid heights at Control

and known Primary Base Stations4 Make sure the constraints did not distort the project

NOTE - Geoid model NOT applied at this time

FAIRFAX COUNTY

CONTROL & PRIMARY STATIONS

CORSHARNNAVD’88 BMNew Station

121°40’W122°35’W37°50’N

38°20’N

LA

TIT

UD

E

LONGITUDE

Primary Base Station

Adjustment of Primary Base Stations

MOLAMART

LAKE

10CCD191

29.6km25.8km

38.7

km

19.0km

28.7km

25.7km 38.3km

31.6

km• CORS, Control Points (known Primary Control) horizontal

• latitude, longitude, and ellipsoid heights• No NAVD88 orthometric heights constrained at this time

Constrained Horizontally

Adjustment of Local Network Stations

Horizontal Adjustment(Latitude, Longitude, Ellipsoid Heights)

• Minimum Constrained [One fixed station]4 Fix latitude, longitude and ellipsoid height at one station4 Resolve all blunders and large residuals4 Evaluate coordinates at Control and Primary Base

Station» should not be greatly affected by Local Station

baselines

• Constrained [All suitable stations fixed]4 Fix latitude, longitude, and ellipsoid heights at Control

and Primary Base Stations4 Make sure the constraints did not distort the project

NOTE - Geoid model NOT applied at this time

CORSHARNNAVD’88 BMNew StationSpacing Station

121°40’W122°20’W37°55’N

38°16’N

LA

TIT

UD

E

LONGITUDE

Primary Base Station

8.2km

Adjustment of Local Network Stations

• Existing and newly derived Primary Control horizontal• latitude, longitude, and ellipsoid heights

• No NAVD88 orthometric heights constrained at this time

Constrained Horizontally

Combined Network Horizontal Adjustment

• Perform combined adjustment

4 Control and Primary Base network along with local network

4 Latitude, longitude, and ellipsoid height

• Use GEOID model to obtain geoid heights

• Make sure combined adjustment did not distort the project

Combined Horizontal AdjustmentCORSHARNNAVD’88 BMNew Station

121°40’W122°35’W

37°50’N

38°20’N

LA

TIT

UD

E

LONGITUDE

Spacing StationPrimary Base Station

8.2km

• CORS, Control Points and existing and new Primary Control horizontal• latitude, longitude, and ellipsoid heights

• No NAVD88 orthometric heights constrained at this time

Constrained Horizontally

FAIRFAX HORIZONTAL

BASELINE ADJUSTMENT SUMMARY

From To Session dh Diff Dist RMS Solution Station Station Meters cm Meters Type

BM20 04KU 078G 45.974* 3628 0.016 L1 float double 077G 46.004 -3.0 0.017 L1 fixed double 076G 46.009 -3.5 0.015 L1 fixed double ZINC PT14 078A 15.397 3173 0.006 L1 fixed double 077A 15.400 0.3 0.006 L1 fixed double 076A 15.408 1.1 0.006 L1 fixed double TIDE 04KU 078G 43.680 3133 0.022 L1 fixed double 077G 43.654* 2.6 0.024 L1 fixed double 076G 43.607* 7.3 0.020 L1 fixed double PT14 TIDE 078A -54.703* 3765 0.047 L1 fixed double 077A -55.031 -32.8 0.022 L1 fixed double 076A -55.007* -30.4 0.019 L1 fixed double 04KU 5144 078G 28.939 7250 0.014 Iono free fixed 077G 28.947 -0.8 0.014 Iono free fixed 076G 28.940 -0.1 0.020 Iono free fixed 5144 ZINC 078A -33.045 6167 0.011 Iono free fixed 077A -33.051 -0.6 0.009 Iono free fixed 076A -33.063 -1.8 0.013 Iono free fixed

Repeat Vector Analysis

*NOTE - Reprocess all vectors which have difference greater than 2 cm.

Guidelines for Establishing

GPS-Derived OrthometricHeights

(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)

Three Basic Rules

• Rule 1:4 Follow NGS’ guidelines for establishing GPS-derived

ellipsoid heights (NGS 58:Standards: 2 cm and 5 cm)

• Rule 2:4 Use latest National Geoid Model, i.e., GEOID09

• Rule 3:4 Use latest National Vertical Datum, i.e., NAVD 88

FOUR BASIC CONTROL REQUIREMENTS

• BCR-1: Occupy stations with known NAVD 88 orthometric heights4 Stations should be evenly distributed throughout project

• BCR-2: Project areas less than 20 km on a side, surround project with NAVD 88 bench marks4 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

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.

BCR4: This requirement is not applicable because project is not in a mountainous region.

BCR Example

BCR3: Circled bench marks are mandatory. Analysis must indicate bench marks have valid

NAVD 88 heights. Other BMs can be substituted but user must adhere to 20 km requirement.

FAIRFAX COUNTY VERTICALS USED

40 KM

Five Basic Procedures

• BP-1: Perform 3-D minimum-constraint least squares adjustment of GPS survey project4 Constrain 1 latitude, 1 longitude, 1 orthometric height

(Recall that ellipsoid heights have already been analyzed and adjusted)

• BP-2: Analyze adjustment results from BP-14 Detect and remove all data outliers

After performing minimum constraint adjustment, plot ellipsoid height residuals (or dU residuals) and investigate all residuals greater than 2 cm.

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.

• BP-3: Compute differences between GPS-derived orthometric heights from minimum-constraint adjustment in BP-2 and published NAVD88 orthometric heights for all known bench marks

Five Basic Procedures(continued)

CONTROL COMPARISON

OUTLIERS?

• PASSIVE CONTROL QUALITY (OVER TIME)

• GEOID MODEL QUALITY

GPS-Derived Orthometric Heights Minus NAVD88 Heights

All height differences are under 5 cm and most are less than 2 cm. Almost all relative height differences between adjacent station pairs are less than 2 cm. However, most of the height differences appear to be positive relative to the southwest corner of the project.

Geoid99Units = Centimeters

Five Basic Procedures(continued)

• BP-4: Determine which BMs have valid NAVD88 height values from results from BP-34 Differences need to agree 2 cm for 2 cm survey4 Differences need to agree 5 cm for 5 cm survey4 May detect systematic tilt over large areas

» Solve for geoidal slope and scale

• BP-5: Perform constrained adjustment with results from BP-44 Constrain 1 latitude, 1 longitude, all valid orthometric

height values4 Ensure final heights not distorted in adjustment

To detect and remove any systematic trend, a tilted plane is best fit to the height 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 stations are less than 2 cm.

GPS-Derived Orthometric Heights Minus NAVD88 Heights

Geoid99Units = Centimeters

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.

GPS-Derived Orthometric Heights Minus NAVD88 Heights

Geoid99Units = Centimeters

The stations in blue designated as "Height Mod" in the NGS Integrated Database

The red stars are the CORS used in the "Height Mod" projects.

Elevation published

to centimeters

Orthometric height

determined by GPS

Identified as Height Mod

survey station

Topography

AB

C

D

E

F

GPS-Derived Heights from GEOID03 Separation

= Published NAVD88 Orthometric Height = New Control

Ellipsoid

hh

hh

hh

GEOID03

N NN N

NN

Hh-N

Hh-NHh-N

Hh-N

Hh-N

Hh-N

Constrained Vertical Adjustment

Topography

AB

C

D

E

F

hadj

hadjhadj

hadj

hadj

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

GEOID03

Ellipsoid

hh

hh

hhHGPS

HGPS

N NN N

NN

GEOID03

ADJUSTMENT TO PASSIVE CONTROL

3-D Vertical Adjustment(Orthometric Heights)

• Minimum Constrained [One fixed station]4 Fix latitude, longitude, and orthometric height at one station4 Resolve all blunders and large residuals4 Compare orthometric heights from adjustment with published

NAVD 884 Determine which NAVD 88 bench marks should be fixed

• Constrained [All suitable orthometric heights fixed]4 Fix latitude, longitude at one station4 Fix orthometric heights at all suitable stations4 Make sure the constraints did not distort the project

Combined Network Vertical Adjustment

Minimally Constrained Vertical Adjustment

• 1 horizontal latitude and longitude• 1 NAVD88 orthometric heights

CORSHARNNAVD’88 BMNew Station

121°40’W122°35’W

37°50’N

38°20’N

LA

TIT

UD

E

LONGITUDE

Spacing StationPrimary Base Station

8.2km

Constrained Vertically

Constrained Vertical Adjustment

• 1 horizontal latitude and longitude• All valid NAVD88 orthometric heights

CORSHARNNAVD’88 BMNew Station

121°40’W122°35’W

37°50’N

38°20’N

LA

TIT

UD

E

LONGITUDE

Spacing StationPrimary Base Station

8.2km

Constrained Vertically

NGS Data Sheet - GEOID03Published 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

SUMMARY• Mistakes 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

ORTHOMETRIC HEIGHTS FROM REAL TIME GNSS POSITIONING

• NAD 83 ELLIPSOID + NGS HYBRID GEOID MODELOR

• LOCK TO PASSIVE MONUMENTATION (INCLINED PLANE + NGS HYBRID GEOID MODEL)OR

• DIFFERENCE IN ELLIPSOID HEIGHTS FOR ≤ 10 Km

REAL TIME GNSS POSITIONING USERS GUIDELINES

>200 RTN WORLD WIDE

>80 RTN IN USA

35+ STATE DOT

MANY COOP EFFORTS

SUMMARY TABLE FROM THE SINGLE-BASE GUIDELINES

BEST METHODS FROM THE GUIDELINES:THE 7 “C’S” of NOAA’s NGS

• CHECK EQUIPMENT• COMMUNICATION• CONDITIONS• CALIBRATION (OR NOT)• COORDINATES• COLLECTION• CONFIDENCE

• THE CONTROL IS AT THE POLE

http://www.ngs.noaa.gov/PUBS_LIB/NGSRealTimeUserGuidelines.v2.0.4.pdf

http://www.ngs.noaa.gov/SEARCH: “CLASSICAL REAL TIME”

METADATA• BESIDES ATTRIBUTE FIELDS, THE RT PRACTICIONER

MUST KEEP RECORDS OF ITEMS NOT RECORDED IN THE FIELD,FOR INSTANCE:

WHAT IS THE SOURCE OF THE DATA? WHAT IS THE DATUM/ADJUSTMENT/EPOCH? WHAT ARE THE FIELD CONDITIONS? WHAT EQUIPMENT WAS USED, ESPECIALLY- WHAT

ANTENNA? WHAT FIRMWARE WAS IN THE RECEIVER &

COLLECTOR? WHAT REDUNDANCY, IF ANY, WAS USED?

QUICK FIELD SUMMARY:

• Set the base at a wide open site• Set rover elevation mask between 12° & 15°• The more satellites the better• The lower the PDOP the better• The more redundancy the better• Beware multipath• Beware long initialization times• Beware antenna height blunders• Survey with “fixed” solutions only• Always check known points before, during and after new location sessions• Keep equipment adjusted for highest accuracy• Communication should be continuous while locating a point• Precision displayed in the data collector can be at the 68 percent confidence level,

which is only about half the error spread to get 95 percent confidence• Have back up batteries & cables• RT doesn’t like tree canopy or tall buildings

• Set the base at a wide open site• Set rover elevation mask between 12° & 15°• The more satellites the better• The lower the PDOP the better• The more redundancy the better• Beware multipath• Beware long initialization times• Beware antenna height blunders• Survey with “fixed” solutions only• Always check known points before, during and after new location sessions• Keep equipment adjusted for highest accuracy• Communication should be continuous while locating a point• Precision displayed in the data collector can be at the 68 percent confidence level,

which is only about half the error spread to get 95 percent confidence• Have back up batteries & cables• RT doesn’t like tree canopy or tall buildings

THE QUICK SUMMARY BOILED DOWN:• COMMUNICATIONS: THE KEY TO SUCCESS

• CHECK SHOT: FIRST BEFORE NEW WORK

• REDUNDANCY: FOR CONFIDENCE

CONSTRAINING PASSIVE MARKS

CALIBRATIONS/VERTICAL LOCALIZATIONS

USING OPUS-S OR OPUS –RS WITH REAL TIME POSITIONING FOR

SMALL PROJECTS

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 = 0.02 m ≤ 10 Km, remember GIGO

• RTN = 0.03- 0.05 m,