GNSS DERIVED HEIGHTS- PART 2 - PowerPoint Presentation

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GNSS DERIVED HEIGHTS- PART 2NOS/NGS - 59

Bill HenningSenior Geodesist, PLS.301-713-3196 x 111, william.henning@noaa.gov

NGS WEBINAR – OCTOBER 7, 2009

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GNSS DERIVED HEIGHTSDAY 1HT MODGNSS HT METHODSNOS/NGS-58DAY 2NOS/NGS-59- Baltimore County and Fairfax County

REAL TIME HT ISSUES

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http://www.ngs.noaa.gov/“NGS 59”

“NGS 58”

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“Geoid”

P

O

P

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

O

to P)

Earth’s

Surface

Ocean

Ellipsoid

“

h

= H +

N

”

N

h

Q

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

O

)

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

Plumb Line

Mean

Sea

Level

H

88

=

h

83

–

N

09

ELLIPSOID, GEOID & ORTHO HEIGHTS

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Expected Height AccuraciesGPS-Derived Ellipsoid Heights2 centimeters (following NOS NGS-58 Guidelines) Geoid Heights (GEOID03)Relative differences typically less than 1 cm in 10 km2.4 cm RMS about the mean nationally0.5 cm error in 10 KmLeveling-Derived HeightsLess than 1 cm in 10 km for third-order leveling

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Available “On-Line” at

the NGS Web Site:www.ngs.noaa.govSEARCH: “NGS 58”

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What has been accomplished using NGS 58?Control recovery, campaign planning/logisticsObs schedulules, equipment checksObservations: Repeat base linesDifferent daysDifferent times of day (“15 hours, 27 hours”)(Detect, remove, reduce effects due to multipath and using the same satellite geometry)

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FAIRFAX COUNTY HEIGHT MODERNIZATION PROJECT 2004-2006

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Vector Processing AccomplishedElevation Mask - 15 degreesEphemeris - Precise (typ. 14 days latency)Tropospheric Correction ModelIono Corrections - All baselines longer than 5 km.Fix Integers

Baselines less than 5 km: L1 fixed solutionBaselines greater than 5 km: Iono free (L3) solutionBaselines must have RMS values ≤ 1.5 cmBaselines must have difference in “up” ellipsoid height ≤ 2.0 cm

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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

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Adjustment Procedures to ObtainGPS-Derived NAVD’88 Orthometric Heights

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Least Squares AdjustmentsThe adjustment minimizes the effects of random errorsA least squares adjustment computes a single network solution, even with redundant vectorsLeast squares will highlight blunders and large errorsIt will provide estimates on the precision of the coordinates for the stations

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HARN/Control Stations(75 km)

Primary Base(40 km)Secondary Base(15 km)

Local Network Stations(7 to 10 km)

GPS ELLIPSOID HEIGHT HIERARCHY

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Project Adjustment Following Guidelines

CORS

HARN

NAVD’88 BM

New Station

121°40’W

122°35’W

37°50’N

38°20’N

LATITUDE

LONGITUDE

Spacing Station

Primary Base Station

8.2km

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Adjustment of Primary Network Stations From ControlHorizontal Adjustment(Latitude, Longitude, Ellipsoid Heights)Minimum Constrained [One fixed station]

Fix latitude, longitude and ellipsoid height at one stationResolve all blunders and large residualsDetermine which Control and known Primary Base Station coordinates should be fixed Constrained [All suitable stations fixed]Fix latitude, longitude, and ellipsoid heights at Control and known Primary Base StationsMake sure the constraints did not distort the projectNOTE - Geoid model NOT applied at this time

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FAIRFAX COUNTYCONTROL & PRIMARY STATIONS

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CORS

HARN

NAVD’88 BM

New Station

121°40’W

122°35’W

37°50’N

38°20’N

LATITUDE

LONGITUDE

Primary Base Station

Adjustment of Primary Base Stations

MOLA

MART

LAKE

10CC

D191

29.6km

25.8km

38.7km

19.0km

28.7km

25.7km

38.3km

31.6km

CORS, Control Points (known Primary Control) horizontal

latitude, longitude, and ellipsoid heights

No NAVD88 orthometric heights constrained at this time

Constrained Horizontally

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Adjustment of Local Network StationsHorizontal Adjustment(Latitude, Longitude, Ellipsoid Heights)Minimum Constrained [One fixed station]Fix latitude, longitude and ellipsoid height at one stationResolve all blunders and large residuals

Evaluate coordinates at Control and Primary Base Stationshould not be greatly affected by Local Station baselines Constrained [All suitable stations fixed]Fix latitude, longitude, and ellipsoid heights at Control and Primary Base StationsMake sure the constraints did not distort the projectNOTE - Geoid model NOT applied at this time

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CORS

HARN

NAVD’88 BM

New Station

Spacing Station

121°40’W

122°20’W

37°55’N

38°16’N

LATITUDE

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

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Combined Network Horizontal AdjustmentPerform combined adjustmentControl and Primary Base network along with local networkLatitude, longitude, and ellipsoid heightUse GEOID model to obtain geoid heightsMake sure combined adjustment did not distort the project

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Combined Horizontal Adjustment

CORS

HARN

NAVD’88 BM

New Station

121°40’W

122°35’W

37°50’N

38°20’N

LATITUDE

LONGITUDE

Spacing Station

Primary 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

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FAIRFAX HORIZONTAL

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BASELINE ADJUSTMENT SUMMARY

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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.

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Guidelines for EstablishingGPS-Derived OrthometricHeights(Standards: 2 cm and 5 cm)

http://www.ngs.noaa.gov/ SEARCH: “NGS 59”

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Three Basic RulesFour Basic Control RequirementsFive Basic Procedures3-4-5 SystemA Guide for Establishing GPS-Derived Orthometric Heights(Standards: 2 cm and 5 cm)

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Three Basic RulesRule 1:Follow NGS’ guidelines for establishing GPS-derived ellipsoid heights (NGS 58:Standards: 2 cm and 5 cm)Rule 2:Use latest National Geoid Model, i.e., GEOID09Rule 3:Use latest National Vertical Datum, i.e., NAVD 88

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FOUR BASIC CONTROL REQUIREMENTSBCR-1: Occupy stations with known NAVD 88 orthometric heightsStations should be evenly distributed throughout projectBCR-2: Project areas less than 20 km on a side, surround project with NAVD 88 bench marksi.e., minimum number of stations is four; one in each corner of projectBCR-3: Project areas greater than 20 km on a side, keep distances between GPS-occupied NAVD 88 bench marks to less than 20 kmBCR-4: Projects located in mountainous regions, occupy bench marks at base and summit of mountains, even if distance is less than 20 km

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BCR1: Sketch indicates thatthe 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 ExampleBCR3: Circled bench marks are mandatory. Analysis must indicate bench marks have validNAVD 88 heights. Other BMs can be substituted but user must adhere to 20 km requirement.

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FAIRFAX COUNTY VERTICALS USED40 KM

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Five Basic ProceduresBP-1: Perform 3-D minimum-constraint least squares adjustment of GPS survey projectConstrain 1 latitude, 1 longitude, 1 orthometric height(Recall that ellipsoid heights have already been analyzed and adjusted)BP-2: Analyze adjustment results from BP-1Detect and remove all data outliers

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

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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.

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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)

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CONTROL COMPARISONOUTLIERS?PASSIVE CONTROL QUALITY (OVER TIME)GEOID MODEL QUALITY

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GPS-Derived Orthometric Heights Minus NAVD88 HeightsAll 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

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Five Basic Procedures(continued)BP-4: Determine which BMs have valid NAVD88 height values from results from BP-3Differences need to agree 2 cm for 2 cm surveyDifferences need to agree 5 cm for 5 cm surveyMay detect systematic tilt over large areasSolve for geoidal slope and scaleBP-5: Perform constrained adjustment with results from BP-4Constrain 1 latitude, 1 longitude, all valid orthometric height valuesEnsure final heights not distorted in adjustment

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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 HeightsGeoid99Units = Centimeters

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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

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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.

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Elevation publishedto centimeters

Orthometric heightdetermined by GPSIdentified as Height Mod survey station

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Topography

A

B

C

D

E

F

GPS-Derived Heights from GEOID03 Separation

= Published NAVD88 Orthometric Height

= New Control

Ellipsoid

h

h

h

h

h

h

GEOID03

N

N

N

N

N

N

H

h

-

N

H

h

-

N

H

h

-

N

H

h

-

N

H

h

-

N

H

h

-

N

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Constrained Vertical AdjustmentTopography

A

B

C

D

E

F

h

adj

h

adj

h

adj

h

adj

h

adj

h

adj

Adjusted

Ellipsoid

Ellipsoid Height

Adjusted

to Fit Constrained Orthometric Heights

GPS-Derived Orthometric Heights

= Published NAVD88 Orthometric Height

= New Control

H

H

H

H

Geoid based on Ortho Heights

GEOID03

Ellipsoid

h

h

h

h

h

h

H

GPS

H

GPS

N

N

N

N

N

N

GEOID03

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ADJUSTMENT TO PASSIVE CONTROL

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3-D Vertical Adjustment (Orthometric Heights) Minimum Constrained [One fixed station]Fix latitude, longitude, and orthometric height at one stationResolve all blunders and large residuals

Compare orthometric heights from adjustment with published NAVD 88Determine which NAVD 88 bench marks should be fixedConstrained [All suitable orthometric heights fixed]Fix latitude, longitude at one stationFix orthometric heights at all suitable stationsMake sure the constraints did not distort the projectCombined Network Vertical Adjustment

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Minimally Constrained Vertical Adjustment1 horizontal latitude and longitude1 NAVD88 orthometric heights

CORS

HARN

NAVD’88 BM

New Station

121°40’W

122°35’W

37°50’N

38°20’N

LATITUDE

LONGITUDE

Spacing Station

Primary Base Station

8.2km

Constrained Vertically

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Constrained Vertical Adjustment1 horizontal latitude and longitudeAll valid NAVD88 orthometric heights

CORS

HARN

NAVD’88 BM

New Station

121°40’W

122°35’W

37°50’N

38°20’N

LATITUDE

LONGITUDE

Spacing Station

Primary Base Station

8.2km

Constrained Vertically

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NGS Data Sheet - GEOID03Published NAVD88 to GPS DerivedH =

102.431 =102.431  102.38 102.429! GEOID 09

69.78

-

(-32.60)

-

N

h

GEOID96 = 0.17 m

GEOID99 = 0.11 m

GEOID03 = 0.05

m

GEOID 09 = 0.002 m

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SUMMARYMistakes and systematic errors must be removed before the adjustmentA 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 networkThe Constrained adjustment checks the existing control and references the network to the datumThe vertical adjustment estimates GPS-derived Orthometric heights- Approaching 3rd order leveling accuracies

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ORTHOMETRIC HEIGHTS FROM REAL TIME GNSS POSITIONING NAD 83 ELLIPSOID + NGS HYBRID GEOID MODELORLOCK TO PASSIVE MONUMENTATION (INCLINED PLANE + NGS HYBRID GEOID MODEL)

ORDIFFERENCE IN ELLIPSOID HEIGHTS FOR ≤ 10 Km

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REAL TIME GNSS POSITIONING USERS GUIDELINES

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>200 RTN WORLD WIDE>80 RTN IN USA35+ STATE DOTMANY COOP EFFORTS

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SUMMARY TABLE FROM THE SINGLE-BASE GUIDELINES

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BEST METHODS FROM THE GUIDELINES:THE 7 “C’S” of NOAA’s NGSCHECK EQUIPMENTCOMMUNICATIONCONDITIONSCALIBRATION (OR NOT)

COORDINATESCOLLECTIONCONFIDENCETHE CONTROL IS AT THE POLEhttp://www.ngs.noaa.gov/PUBS_LIB/NGSRealTimeUserGuidelines.v2.0.4.pdfhttp://www.ngs.noaa.gov/

SEARCH: “

CLASSICAL REAL TIME”

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METADATABESIDES 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?

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QUICK FIELD SUMMARY:Set the base at a wide open site

Set rover elevation mask between 12° & 15°The more satellites the betterThe lower the PDOP the betterThe more redundancy the betterBeware multipathBeware long initialization timesBeware antenna height blundersSurvey with “fixed” solutions onlyAlways check known points before, during and after new location sessions

Keep equipment adjusted for highest accuracy

Communication should be continuous while locating a pointPrecision 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 confidenceHave back up batteries & cablesRT doesn’t like tree canopy or tall buildings

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

CHECK SHOT: FIRST BEFORE NEW WORK

REDUNDANCY:

FOR CONFIDENCE

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CONSTRAINING PASSIVE MARKS

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CALIBRATIONS/VERTICAL LOCALIZATIONS

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

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GNSS DERIVED HEIGHTS Summary of expected orthometric precisions/accuraciesREMEMBER REDUNDANCY AND A CHECK ON KNOWN POINTS CORS = 0.05 mOPUS-S = 0.05 m

OPUS-RS = 0.05 mNGS 58/59 = 0.02 m local, 0.05 m to NSRSSINGLE BASE REAL TIME = 0.02 m ≤ 10 Km, remember GIGORTN = 0.03- 0.05 m,