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?