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Agenda What is a site calibration? Calibration – how it works! Control requirements Interpreting results Calibration scenarios The agenda for this class is as follows: An overview of the GPS site calibration. An explanation of the parameters computed in the site calibration An explanation of the control point requirements for a site calibration. A discussion on interpreting the results of the site calibration A guide to the project settings for the site calibration. For example, which settings to use for different calibration scenarios.
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ST236Site Calibrations
with Trimble GNSS
Peter MestemakerTrimble Navigation
Westminster, Colorado
Agenda
• What is a site calibration?• Calibration – how it works!• Control requirements• Interpreting results• Calibration scenarios
Section 1 – General Overview
• Site calibration–Why do we need it?–What does it do?– How is it done?– How is it used?
Site Calibration – Why we need it
• Why use a calibration?– GPS with grid
coordinates
GPS Coordinates (WGS84)
• WGS84– Latitude (φ)– Longitude (λ)– Height (h)
• Cartesian– (X,Y, Z)
Green
wich M
eridi
an
h
Z
X
Y
P
Equator
Surveyors want grid
• (X) Easting
• (Y) Northing
• (Z) Elevation– vertical datum
ZY
X
WGS84
Grid
Site Calibration – What it does
• Compute transformation parameters–WGS84– grid
Site Calibration – How it’s done
• Control (Grid)
• Measure (GPS)
• Match point pairs
• Calibrate!
Site Calibration – How it’s used
• Computes grid–WGS84 measured
• Computes WGS84– Stakeout from grid
Section 2 – How it works!
• Coordinate systems
• Elements of the calibration
• Calibration parameters
Coordinate System
• Transform WGS84 to grid
• Requires:– Datum transformation
– Map projection
Datum Transformation
• WGS84 to local ellipsoid
• Not required if:– Local ellipsoid = WGS-84– Arbitrary local grid
• Known parameters?– Use them!
WGS84
LocalEllipsoid
Map Projection
• Projection to local grid(φ, λ) (N, E)
• Always required
• Not specified?– default TM at project
location
Calibration Elements
• Horizontal adjustment
• Vertical adjustment– Geoid model
• Adjustment parameters
Horizontal Adjustment
• 2 coordinates per control–Measured (projected)– Control grid
= GPS observation= Control Point
• Least squares adjustment– Rotation– Translations– scale
Horizontal Rotation
• Rotation about project centroid
• 2 control points – no redundancy
Horizontal Translations
• Points shifted (X,Y)– same amount– same direction
• 1 control point – no redundancy
Horizontal Scale Factor
• Ratio– GPS to grid
distance
• 2 control points – no redundancy
Horizontal Residuals
• Redundancy = residuals
Residual• Residual– GPS vs. control
coordinate
• 3 control points–minimum
• Least squares best fit– WGS84 heights– Elevations
• Parameters– Vertical shift– Vertical tilts (N & E)
• Geoid model (optional)
Vertical Adjustment
Geoid Model (Optional)
WGS84 Ellipsoid
Earth’s Surface
Geoid
N
• Geoid separation (N)
• 3 control points – minimum
Adjustment – No Geoid Model
Earth’s Surface
Inclined Plane
WGS-84 Ellipsoid
Geoid
NNP
• Best fit inclined plane– approximates local Geoid
Residuals – No Geoid Model
• Residuals at all vertical control
Earth’s Surface
H HH H H
eh
h hh
NNNNN
Inclined Plane
Ellipsoid
Geoid
N
Geoid
Inclined Plane Residual
NP
• 4 benchmarks minimum
Inclined Plane – Geoid Model
NNNNN
Geoid Model
Ellipsoid
GeoidNmNm
NmNm Nm
Inclined PlaneN
+
- Residual
• Corrections to Geoid model
• Inclined plane through ΔN
Geoid Model - Benefits
• Improved modeling results when working with a larger calibrated site that incorporates a high degree of geoid undulation– Performing a site calibration along the front range
of Colorado
Calibration Results - Applied
• Computed using control points
• Applied to all points
Section 3 – Control Requirements
• Horizontal control requirements
• Vertical control requirements
• Recommendations
Control Requirements
• Minimum redundancy– 3 Horizontal– 4 Vertical
• Trimble recommends– 5 Horizontal– 5 Vertical
• More is better!
Project Area
Control Placement
• Critical to success
• Cover entire project
Control Placement
• Stay inside control– especially vertical
• Vertical tilts • magnified outside
control
No Survey HereVertical tilts magnified
Limits of control
Horizontal and Vertical Control
• H & V–may be
different
• You decide:– H– V– 3D
Horizontal and Vertical Control
• Mix and match– as required
▲= Horizontal ■ = Vertical
Site Recommendations
10 km
• Limit calibration size–minimize scale
distortion
• Practical limitation– 10 km x 10 km
Site Recommendations
• Multiple zones– long linear projects
• Overlap– common control
Calibration 2
Calibration 1
Overlap area
Site Recommendations
• Large ΔH– scale errors
• Split into zones
• Minimize ΔHCalibration 2
Calibration 1
ΔH
Section 4 – Interpreting Results
• Residuals
• Horizontal adjustment parameters
• Vertical adjustment parameters
Interpreting Results - Residuals
• Residuals– H and V
• Large residuals– Control or
measurement error
Horizontal Adjustment Parameters
• Scale factor – close to 1
• Rotation–match local
orientation
• Max. H. Residual
Vertical Adjustment Parameters
• Slope N & E– vertical tilts
• Constant Adjustment– vertical shift– all points
• Max. V Residual
Section 5 – Calibration Scenarios
• Defined coordinate system– (US state plane zone)
• Arbitrary grid system– (local ground coordinates)
• 1 point calibration– (scenarios for H & V adjustment)
Calibrating to Pre-defined Grid
• Select from library
• “GRID” coordinates
• Project height– ellipsoid
Calibrating to Pre-defined Grid
Position at ground surface
Mapping Plane at Ellipsoid
A B
TO CENTER
OF ELLIPSO
ID
SF ≈ 1.0000WGS-84
Coordinate
Projected Grid Coordinate
• Projected to mapping plane
• Horizontal adjustment– scale ~ 1– small rotation
Calibrating to Assumed Grid
• “no projection / no datum”
• “Ground” coordinates
• Project height
• Geoid model– if available
Calibrating to Assumed Grid
Project height
Scaled to project height A B
TO CENTER
OF ELLIPSO
ID
SF ≈ 1.0000WGS84
Projected to grid
SF > 1.0000
• Projected to map grid
• Grid scaled to ground
Control at ground
• Horizontal adjustment– scale ~ 1– rotation – any value
• depends on local orientation
1 Point Calibration to Ground
• “no projection / no datum”
• “Ground” coordinates
• Project height
• Geoid model– if available
1 Point Calibration to Ground
Scaled to Project Height
Project HeightA B
TO CENTER
OF ELLIPSO
ID
SF = 1.0000WGS84
Projected to Grid
SF > 1.0000• Projected to map grid
• Grid scaled to ground
• Horizontal adjustment– scale = 1– no rotation
• geodetic North
Earth’s Surface
WGS-84 Ellipsoid
Geoid
• With geoid model– maintains shape of
Geoid
– vertical shift
– no vertical tilts
1 Point Vertical Calibration
Geoid Model
h
N
H
Summary
• GPS site calibration– Computes transformation parameters• WGS84 to grid• Grid to WGS84
Summary
• Calibration requires a coordinate system• Datum transformation– WGS84 to local ellipsoid
• Map projection– Ellipsoid to map grid
• Use published – if available
Summary
• Elements of the calibration
– Horizontal adjustment• Rotation, translations (2), scale
– Vertical adjustment• Vertical shift, tilts (2)
• Geoid model - optional
• Control requirements:
• For redundancy (residuals)– 3 Horizontal– 4 Vertical
• Trimble recommends:– 5 Horizontal and Vertical
Summary
• Site recommendations– Stay inside control– Limit calibration size–Multiple calibrations for:• Long linear projects• Large elevation range
Summary
• Interpreting calibration results– Pay attention to residuals
– Horizontal• Scale and rotation
– Vertical• Tilts and vertical shift
Summary
• Calibration scenarios– Defined grid• Use the projection and parameters
– Arbitrary grid • No projection / no datum
– 1 point calibration• Horizontal • Vertical
Summary
Questions?