I am trying to convert an ECEF coordinate to a geodetic coordinate using this procedure, but I don't fully understand the process. It is prefaced by stating the geodetic parameters {a,b,e,e'} are assumed to be known, but does not state what they reference to.
I assume that a and b are the equatorial and polar semi-axes, and that e is just Euler's number. Am I correct in this? And what is e' supposed to be?
You can use this function to perform the conversion of ECEF coordinates to Geodetic coordinates.
The function is implemented in python but can be easily written in java.
Example:
import math
def xyz2llh(x,y,z):
'''
Function to convert xyz ECEF to llh
convert cartesian coordinate into geographic coordinate
ellipsoid definition: WGS84
a= 6,378,137m
f= 1/298.257
Input
x: coordinate X meters
y: coordinate y meters
z: coordinate z meters
Output
lat: latitude rad
lon: longitude rad
h: height meters
'''
# --- WGS84 constants
a = 6378137.0
f = 1.0 / 298.257223563
# --- derived constants
b = a - f*a
e = math.sqrt(math.pow(a,2.0)-math.pow(b,2.0))/a
clambda = math.atan2(y,x)
p = math.sqrt(pow(x,2.0)+pow(y,2))
h_old = 0.0
# first guess with h=0 meters
theta = math.atan2(z,p*(1.0-math.pow(e,2.0)))
cs = math.cos(theta)
sn = math.sin(theta)
N = math.pow(a,2.0)/math.sqrt(math.pow(a*cs,2.0)+math.pow(b*sn,2.0))
h = p/cs - N
while abs(h-h_old) > 1.0e-6:
h_old = h
theta = math.atan2(z,p*(1.0-math.pow(e,2.0)*N/(N+h)))
cs = math.cos(theta)
sn = math.sin(theta)
N = math.pow(a,2.0)/math.sqrt(math.pow(a*cs,2.0)+math.pow(b*sn,2.0))
h = p/cs - N
llh = {'lon':clambda, 'lat':theta, 'height': h}
return llh
After some more research (from here and here), I believe e and e' refer to first and second eccentricity, while a and b do indeed refer to the equatorial and polar semi-axes. Hopefully somebody can confirm this, as I am not 100% certain.
a is one of the defining parameters; and b, e, and e' are some of the derived geometric constants of the WGS84 ellipsoid.
e is the first eccentricity. e' is the second eccentricity.
See page 3-2 and table 3.5 in NGA STND 0036_1 0 0_WGS84.pdf
A better way of doing it can be found at the end of this document: https://hal.archives-ouvertes.fr/hal-01704943v2/document
In this document, it's explained how to do it properly and including a C code so it's easy to copy and paste to see if the solution works.
