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Converting from UTM coords to lat, lon and height uses well established formuae like Redfearn's formula. There are online tools that allow code to be checked against trusted sources. Example code is attached. Just reiterating, the height is assumed to be height above the reference ellipsoid.
E.g. for MWA centre
cent_easting = 467254.490961539 # meters
cent_northing= 7046381.90073077 # meters
cent_alt = 377.8269 # meters
The array centre is: lat -26.70331940, lon 116.67081524 degs.
Converting from lat, lon and height to X,Y,Z
This is analogous to finding the cartesian coords on of a point on a sphere, except it is on the ellipsoid so there are some additional terms. Example python code based on WGS84 ellipsoid:
def Geodetic2XYZ(lat_rad,lon_rad,height_meters):
EARTH_RAD_WGS84 = 6378137.0 # meters in the WGS84 (effectively same as GRS80)
E_SQUARED = 6.69437999014e-3
s_lat = math.sin(lat_rad)
c_lat = math.cos(lat_rad)
s_lon = math.sin(lon_rad)
c_lon = math.cos(lon_rad)
chi = math.sqrt(1.0 - E_SQUARED*s_lat*s_lat)
X = (EARTH_RAD_WGS84/chi + height_meters)*c_lat*c_lon
Y = (EARTH_RAD_WGS84/chi + height_meters)*c_lat*s_lon
Z = (EARTH_RAD_WGS84*(1.0-E_SQUARED)/chi + height_meters)*s_lat
return (X,Y,Z)
This calculation needs to be done for all antennas, and the centre of the array.
E.g. the centre of the MWA in these coords for Array centre: lat -26.70331940, lon 116.67081524 is
X: -2559454.08, Y: 5095372.14, Z: -2849057.18
Converting from X,Y,Z to E,N,U
To do this, we first define the We've defined an array centre. During the early days of MWA, a surveying mark was made on a rock outside the MWA donga, and this point was a well-defined and accurately measured reference point for the surveyors. Since this point is close to the hub of the MWA, it is as good a point as any to define as the centre of the array, so it was.
- Calculate the coords of the antennas in X,Y,Z relative to the array centre's X,Y,Z: this is just a vector difference:
ant_geo_X = ant_X - arr_X
ant_geo_Y = ant_Y - arr_Y
ant_geo_Z = ant_Z - arr_Z