GPS Calibration: Mastering Co-ordinate Systems for Surveying Success

1. GPS Site Calibration

2. Objectives After this session, you should be able to: • Explain the Co-ordinate systems used in GPS Surveying. • Explain what a calibration is. • Explain the 5 main process steps of a calibration • Recall the software where a calibration can be performed • List the recommended procedures when performing a Calibration. • Correctly site ideal calibration control based on different survey site situations • Explain the required relationship between GPS Base Stations and calibrations • Recall the common base co-ordinate system of a site calibration

3. First of all what can you remember about the GPS Co-ordinate System?

4. +Z Z Y X -Y +X ECEF Coordinate System ECEF X = -2691542.5437 m Y = -4301026.4260 m Z = 3851926.3688 m

5. b b a a Reference Ellipsoid a = semi-major axis b = semi-minor axis H f WGS-84 Ellipsoid a = 6378137.000000 m b = 6356752.314245 m 1/f = 298.2572235630 l

6. +Z H b Z f Y X l a -Y +X ECEF and WGS-84 ECEF X = -2691542.5437 m Y = -4301026.4260 m Z = 3851926.3688 m WGS-84 f = 37o 23’ 26.38035” N l = 122o 02’ 16.62574” W H = -5.4083 m

7. What co-ordinate system would you prefer to work in?

8. What can you remember about the heights you get from GPS and the heights you need to know?

9. GPS Heights vs. Elevations Earth’s Surface H H e e H e N Ellipsoid N N Geoid e = Orthometric Height H = Ellipsoid Height N = Geoid Height e = H - N

10. What do you think a calibration is?

11. A Calibration • Word refers to several related items in RTK surveying: • File -- the file used on RTK rovers to transform from WGS84 (L,L,H) to local (flat plane, E,N,E) coordinates • RTK field survey -- the survey conducted in the field to determine the mathematical relationship between WGS84 and site (flat plane) coordinate system • What it is literally: the mathematical relationship between WGS84 and site (flat plane) coordinate system

12. WGS84 NEE Coordinate System This is the GPS calibration! • Converts coordinates from GPS system to our local site (flat plane) coordinate system • Includes datum transformation, map projection, horizontal & vertical adjustment • REQUIRED to work in local (flat plane) coordinates Must Have!!

13. How do you get from WGS84 ECEF to Easting, Northing and Elevation ?

14. First Things First • To relate one co-ordinate system to another you need a set of points on the ground that have co-ordinates in both systems. • Therefore you need a set of WGS84 co-ordinates and a set of local Northing, Easting and Elevation co-ordinates. WGS84 Local Site Co-ordinates

15. Calibration Process • Datum Transformation • Define Projection • Horizontal Adjustment • Vertical Adjustment • Geoid Model (optional)

16. WGS84 Local Datum Transformation • Usually published parameters • Two basic types: • 3 Parameter • 7 Parameter

17. 3 vs. 7 Parameter 3 Parameter 7 Parameter

18. Calibration Process • Datum Transformation • Define Projection

19. Plane Coordinate Systems

20. Apex of Cone Axis of Cone & Ellipsoid Line of intersection Ellipsoid Intersecting Cone 2 Parallel Lambert Types of Projections Point of Origin Plane Ellipsoid Axis of Ellipsoid Tangent Plane Local Plane Axis of Cylinder Ellipsoid Intersecting Cylinder Transverse Mercator

21. Calibration Process • Datum Transformation • Define Projection • Horizontal Adjustment (on projected plane surface) • Rotation • Translation • Scale

22. = GPS observation = Control Point Horizontal Adjustment • At least 3 horizontal control points are required • 5 points are recommended

23. Rotation

24. Translation

25. Scale

26. Residual Calibration Results • After the calibration you will obtain a set of calibration results, which consist of residuals. These need to be understood so you know how good the calibration is. • Residuals: The difference between the grid co-ordinate and the GPS co-ordinate after the calibration has been applied.

27. Residual Calibration Results • Therefore the smaller the residualthe more accurate the calibration parameters are and the better the relationship between the GPS (WGS84 co-ordinates) and the Local Site Easting and Northing co-ordinates.

28. Residual Calibration Results • You should be looking for residuals ideally less than 20mm, but 30mm may be acceptable. • When you are looking at final co-ordinates your minimum accuracy is: Standard RTK GPS receiver error plus your largest calibration residuals • Your residuals should be spread evenly between the calibration points.

29. Quick Calibration Summary • Start with Latitude & Longitude, in WGS84, as measured with GPS. • Perform Datum Transformation to obtain Latitude & Longitude in local datum. • Today this is often a system very similar to WGS84, such as ETRS89. • Project local Latitude & Longitude onto a flat predefined plane using a projection. • On the projection perform a Horizontal Adjustment to fit the GPS measured points as close as possible to the Local control points in N,E • Obtain residuals. • Difference between GPS derived N,E and Local Control N,E

30. What can you remember?

31. Calibration Process • Datum Transformation • Define Projection • Horizontal Adjustment • Vertical Adjustment

32. Vertical Adjustment • At least 4 vertical control points are required • 5 points are recommended Earth’s Surface H H h h H h N Ellipsoid N N Geoid

33. H H H H H h H h h hE h N N N h N N Inclined Plane Vertical Adjustment (No Geoid Model) Earth’s Surface hE = H - NE Ellipsoid NE Geoid NE= estimated geoid height

34. Earth’s Surface N H H H H h H Ellipsoid h h Residual Inclined Plane h N N N h N Geoid N Geoid Inclined Plane Vertical Residuals

35. Calibration Process • Datum Transformation • Define Projection • Horizontal Adjustment • Vertical Adjustment • Geoid Model (optional)

36. Geoid The Geoid Model • A gridded surface that approximates the geoid • Model of the height difference between the geoid and a specified ellipsoid (normally WGS84) • Some popular global geoid models: Geoid 96 (USA) EGM96 (Global)

37. H H H H h H h h Nm Nm Nm N N h N Nm Nm N h N Vert. Adj. (w/ Geoid Model) Earth’s Surface Ellipsoid Geoid Geoid Model Nm = modeled geoid height

38. Earth’s Surface N Nm H H H H Ellipsoid h H h h Geoid Nm N Nm N h N Geoid Nm DN N Nm Nm N h Geoid Model Geoid Model Modeling Errors

39. N N N Nm Nm Nm N Nm N Nm Residual + DN - Inclined Plane Ellipsoid Geoid Geoid Model Inclined Plane

40. H H H H H h H h h Nm Nm Nm N N h N Nm Nm Nm N h N DN Vertical Adjustment (with Geoid Model) Earth’s Surface hE = H - Nm - NC Ellipsoid hE Geoid Geoid Model Inclined Plane NC = Geoid Model Correction

41. What can you remember?

42. Recommended Procedures • Observe GPS calibration points for at least: • 3 minutes if RTK • 8 minutes if Static / Fast Static (depends on baseline length and no. of SV’s) • Use a stable setup (e.g. bipod or Tripod) • Use ground plane to minimize multipath (if possible) • Enclose the project area with control • Use only reliable ENE positions • Use good network geometry • Note: If you have more than 1 base station on a large project you may need more than 1 calibration. Use your residuals to determine this

43. Let’s expand on the placement of control, project area and network geometry

44. Ideal Situations? • If you have the survey area below. Where ideally will your control be situated? • See the following slides 20km 10km

45. Ideal Situations? • 5 Horizontal and Vertical control points in a straight line down the center of the area? 20km 10km

46. Ideal Situations? • 5 Horizontal and Vertical control points in the center of the area? 20km 10km

47. Ideal Situations? • 5 Horizontal and Vertical control points surrounding the outside of the area? 20km 10km

48. Hz.& V. Control Hz. Control V. Control Making the best of a Situation? • A customer presents you with the following calibration and complains that their elevations are not correct, in the circular area by up to 10cm. What would you advise them? • See the following slides 30km 15km

49. Hz.& V. Control Hz. Control V. Control Making the best of a Situation? • The height from GPS is not as accurate as the horizontal, therefore these differences are acceptable. 30km 15km

50. Hz.& V. Control Hz. Control V. Control Making the best of a Situation? • You have no residuals, therefore you have no idea how good your vertical calibration is. Due to the location of existing points you need to add in at least 3 other vertical control points. As specified below (red squares). 30km 15km