Note that you don't have to work on redoubt today!
We know that GPS coordinates are given in Earth-centered-Earth-fixed (ECEF) reference frame / coordinate system. However, those Cartesian coordinates are very hard to interpret and we need to be able to convert these back into ellipsoidal coordinates (and vice-versa). Today you'll be implementing 2 functions (in your favorite programming language) that do exactly this. You will need these in the following labs for your conversions.
For this exercise use the WGS84 ellipsoid definition:
semi-major a = 6378137.0 m
flattening f = 1/298.257223563
semi-minor b = -f*a+a
The handout from Hoffmann-Wellenhof, 2nd Ed., that I distributed as handout and PDF via canvas lays out the formulas. What you need to do is write some code that takes in arguments, applies the formulas, returns the results.
In your preferred language, write a function that takes WGS84 latitude, longitude, and height (above the ellipsoid!) and returns cartesian X,Y,Z coordinates. The formulas given in the handout are fairly straight forward. Note that you need to convert degrees to radians, though!
In your preferred language, write a function that takes ECEF cartesian coordinates X,Y,Z and returns WGS84 ellipsoid latitude, longitude, and height. I recommend to implement the iterative algorithm from the handouts! Again, note that you'll need to convert radians to degrees.
Your code should convert between these ECEF and WGS84 coordinates for a GPS station in McMurdo, Antarctica station:
| ECEF | WGS84 | ||
| X (m) | -1311703.172 | lat (deg) | -77.8383494704 |
| Y (m) | 310814.982 | lon (deg) | 166.669329308 |
| Z (m) | -6213255.16 | height (m) | 98.0221867058 |
The GPS station is MCMD. I grabbed the approximate XYZ coordinates from a receiver file (rinex) from 2014-12-31. This is by no means its precise position.
rg <at> nmt <dot> edu | Last modified: August 26 2015 20:10.