ST 236 Site Calibrations with Trimble GNSS Peter

ST 236 Site Calibrations with Trimble GNSS Peter Mestemaker Trimble 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 (WGS 84) Z • WGS 84 – Latitude (φ) – Longitude (λ) – Height (h) P h • Cartesian Y j – (X, Y, Z) G re e M h nw ic X er id ia n l ator Equ

Surveyors want grid • (X) Easting Z Y • (Y) Northing • (Z) Elevation – vertical datum X

Site Calibration – What it does • Compute transformation parameters WGS 84 – grid Grid

Site Calibration – How it’s done • Control (Grid) • Measure (GPS) • Match point pairs • Calibrate!

Site Calibration – How it’s used • Computes grid – WGS 84 measured • Computes WGS 84 – Stakeout from grid

Section 2 – How it works! • Coordinate systems • Elements of the calibration • Calibration parameters

Coordinate System • Transform WGS 84 to grid • Requires: – Datum transformation – Map projection

Datum Transformation • WGS 84 to local ellipsoid WGS 84 • Not required if: – Local ellipsoid = WGS-84 – Arbitrary local grid • Known parameters? – Use them! Local Ellipsoid

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 • Least squares adjustment – Rotation – Translations – scale = GPS observation = Control Point

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 – GPS vs. control coordinate • 3 control points – minimum Re l a u sid

Vertical Adjustment • Least squares best fit – WGS 84 heights – Elevations • Parameters – Vertical shift – Vertical tilts (N & E) • Geoid model (optional)

Geoid Model (Optional) Earth’s Surface Geoid N WGS 84 Ellipsoid • Geoid separation (N)

Adjustment – No Geoid Model Earth’s Surface • 3 control points – minimum WGS-84 Ellipsoid NP N e Inclined Plan • Best fit inclined plane – approximates local Geoid

Residuals – No Geoid Model • Residuals at all vertical control Earth’s Surface H H NP h h. Ellipsoid e N h N N H h N Plane N d e n i l c Geoid In Inclined Plane Geoid • 4 benchmarks minimum l Residua

Inclined Plane – Geoid Model Ellipsoid • Inclined plane through ΔN N Nm Geoid N N Nm Nm N Nm Geoid Model Inclined Plane DN + - • Corrections to Geoid model Residual

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!

Control Placement • Critical to success Project Area • Cover entire project

Control Placement • Stay inside control – especially vertical • Vertical tilts No Survey magnified Here • magnified outside control Limits of control

Horizontal and Vertical Control • H&V – may be different • You decide: –H –V – 3 D

Horizontal and Vertical Control • Mix and match – as required ▲= Horizontal ■ = Vertical

Site Recommendations • Limit calibration size • Practical limitation – 10 km x 10 km 10 k m – minimize scale distortion

Site Recommendations • Multiple zones – long linear projects • Overlap Calibration 1 Overlap area – common control Calibration 2

Site Recommendations • Large ΔH – scale errors • Split into zones ion t a r 2 ΔH lib a C • Minimize ΔH li Ca on i t bra 1

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 • Projected to mapping plane Position at ground surface A B Mapping Plane at Ellipsoid Projected Grid Coordinate – scale ~ 1 – small rotation WGS-84 Coordinate SF ≈ 1. 0000 ER ENT ID TO C LLIPSO OF E • Horizontal adjustment

Calibrating to Assumed Grid • “no projection / no datum” • “Ground” coordinates • Project height • Geoid model – if available

Calibrating to Assumed Grid • Projected to map grid • Grid scaled to ground Project height Scaled to project height Control at ground SF > 1. 0000 A B Projected to grid SF ≈ 1. 0000 WGS 84 – scale ~ 1 – rotation – any value • depends on local orientation ER ENT ID TO C LLIPSO OF E • Horizontal adjustment

1 Point Calibration to Ground • “no projection / no datum” • “Ground” coordinates • Project height • Geoid model – if available

1 Point Calibration to Ground • Projected to map grid • Grid scaled to ground Project Height A SF = 1. 0000 WGS 84 ER ENT ID TO C LLIPSO OF E • geodetic North B Projected to Grid • Horizontal adjustment – scale = 1 – no rotation SF > 1. 0000 Scaled to Project Height

1 Point Vertical Calibration • With geoid model – maintains shape of Geoid Earth’s Surface WGS-84 Ellipsoid – vertical shift h – no vertical tilts N H Geoid Model

Summary • GPS site calibration – Computes transformation parameters • WGS 84 to grid • Grid to WGS 84

Summary • Calibration requires a coordinate system • Datum transformation – WGS 84 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

Summary • 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

Questions?