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ST236 Site Calibrations with Trimble GNSS

ST236 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

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ST236 Site Calibrations with Trimble GNSS

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  1. ST236Site Calibrations with Trimble GNSS Peter Mestemaker Trimble Navigation Westminster, Colorado

  2. Agenda • What is a site calibration? • Calibration – how it works! • Control requirements • Interpreting results • Calibration scenarios

  3. Section 1 – General Overview • Site calibration • Why do we need it? • What does it do? • How is it done? • How is it used?

  4. Site Calibration – Why we need it • Why use a calibration? • GPS with grid coordinates

  5. Z P h Y j l Equator X Greenwich Meridian GPS Coordinates (WGS84) • WGS84 • Latitude (φ) • Longitude (λ) • Height (h) • Cartesian • (X,Y, Z)

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

  7. Site Calibration – What it does • Compute transformation parameters • WGS84 • grid WGS84 Grid

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

  9. Site Calibration – How it’s used • Computes grid • WGS84 measured • Computes WGS84 • Stakeout from grid

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

  11. Coordinate System • Transform WGS84 to grid • Requires: • Datum transformation • Map projection

  12. WGS84 Local Ellipsoid Datum Transformation • WGS84 to local ellipsoid • Not required if: • Local ellipsoid = WGS-84 • Arbitrary local grid • Known parameters? • Use them!

  13. Map Projection • Projection to local grid (φ, λ) (N, E) • Always required • Not specified? • default TM at project location

  14. Calibration Elements • Horizontal adjustment • Vertical adjustment • Geoid model • Adjustment parameters

  15. = GPS observation = Control Point Horizontal Adjustment • 2 coordinates per control • Measured (projected) • Control grid • Least squares adjustment • Rotation • Translations • scale

  16. Horizontal Rotation • Rotation about project centroid • 2 control points • no redundancy

  17. Horizontal Translations • Points shifted (X,Y) • same amount • same direction • 1 control point • no redundancy

  18. Horizontal Scale Factor • Ratio • GPS to grid distance • 2 control points • no redundancy

  19. Horizontal Residuals • Redundancy = residuals Residual • Residual • GPS vs. control coordinate • 3 control points • minimum

  20. Vertical Adjustment • Least squares best fit • WGS84 heights • Elevations • Parameters • Vertical shift • Vertical tilts (N & E) • Geoid model (optional)

  21. Geoid Model (Optional) • Geoid separation (N) Earth’sSurface Geoid N WGS84Ellipsoid

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

  23. Earth’s Surface H H H H N h H NP h h Ellipsoid h N N N N e Residual Inclined Plane N Geoid Inclined Plane Geoid Residuals – No Geoid Model • Residuals at all vertical control • 4 benchmarks minimum

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

  25. 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

  26. Calibration Results - Applied • Computed using control points • Applied to all points

  27. Section 3 – Control Requirements • Horizontal control requirements • Vertical control requirements • Recommendations

  28. Control Requirements • Minimum redundancy • 3 Horizontal • 4 Vertical • Trimble recommends • 5 Horizontal • 5 Vertical • More is better!

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

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

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

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

  33. Site Recommendations • Limit calibration size • minimize scale distortion • Practical limitation • 10 km x 10 km 10 km

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

  35. ΔH Calibration 2 Calibration 1 Site Recommendations • Large ΔH • scale errors • Split into zones • Minimize ΔH

  36. Section 4 – Interpreting Results • Residuals • Horizontal adjustment parameters • Vertical adjustment parameters

  37. Interpreting Results - Residuals • Residuals • H and V • Large residuals • Control or measurement error

  38. Horizontal Adjustment Parameters • Scale factor • close to 1 • Rotation • match local orientation • Max. H. Residual

  39. Vertical Adjustment Parameters • Slope N & E • vertical tilts • Constant Adjustment • vertical shift • all points • Max. V Residual

  40. 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)

  41. Calibrating to Pre-defined Grid • Select from library • “GRID”coordinates • Project height • ellipsoid

  42. Calibrating to Pre-defined Grid • Projected to mapping plane Position at ground surface Mapping Plane at Ellipsoid A B Projected Grid Coordinate • Horizontal adjustment • scale ~ 1 • small rotation WGS-84 Coordinate SF ≈ 1.0000 TO CENTER OF ELLIPSOID

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

  44. Calibrating to Assumed Grid • Projected to map grid • Grid scaled to ground Control at ground Project height Scaled to project height SF > 1.0000 A B Projected to grid SF ≈ 1.0000 WGS84 • Horizontal adjustment • scale ~ 1 • rotation – any value • depends on local orientation TO CENTER OF ELLIPSOID

  45. 1 Point Calibration to Ground • “no projection / no datum” • “Ground” coordinates • Project height • Geoid model • if available

  46. 1 Point Calibration to Ground • Projected to map grid • Grid scaled to ground SF > 1.0000 Scaled to Project Height Project Height A B Projected to Grid SF = 1.0000 WGS84 • Horizontal adjustment • scale = 1 • no rotation • geodetic North TO CENTER OF ELLIPSOID

  47. 1 Point Vertical Calibration • With geoid model • maintains shape of Geoid • vertical shift • no vertical tilts Earth’s Surface WGS-84 Ellipsoid H h N Geoid Geoid Model

  48. Summary • GPS site calibration • Computes transformation parameters • WGS84 to grid • Grid to WGS84

  49. Summary • Calibration requires a coordinate system • Datum transformation • WGS84 to local ellipsoid • Map projection • Ellipsoid to map grid • Use published – if available

  50. Summary • Elements of the calibration • Horizontal adjustment • Rotation, translations (2), scale • Vertical adjustment • Vertical shift, tilts (2) • Geoid model - optional

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