Page Comparison

...

1. Convert the surveyed coords to latitude, longitude and height. This system needs a reference ellipsoid such as the WGS84 system, and the height is assumed to be relative to the reference ellipsoid (it is hard to find definitive information on what the height actually means).
2. Convert the lat, lon and height to the X,Y,Z absolute "Earth centred, Earth fixed" coordinate system where the origin is the centre of the earth. This conversion needs to assume the same ellipsoid as the conversion from UTM coords. The X axis points out of the equator at zero degs longitude, the Z axis points through the north pole along the rotation axis of the earth, and the Y axis completes a right-handed coordinate system. (Y points out of the equator in the Indian ocean at longitude 90 degs.) It is possible to specify the location of the telescope antennas in this X,Y,Z system in many software packages, but the numbers are very large and non-intuitive, so a local coordinate system is often preferred.
3. Convert the X,Y,Z coordinates of the antennas to a local cartesian coordinate system where the origin of the system is the defined centre of the array. The axes of the local system are east (defined at the array centre), north (defined at the array centre) and height or "up". It is also worth noting that some software confusingly defines another "local X,Y,Z" system where the global X,Y,Z system has been rotated around the Z axis such that X points out of the equator at the longitude of the array centre. I'm not sure if there is an official name to this system, and it doesn't help much because the coordinates of the antennas are still large numbers and non-intuitive because the local horizon is angled to all coordinate axes.
   1. To convert to local E,N,U units, a rotation on the sphere is required. Note that rotations on sphere do not commute, and we need to do the longitude rotation before the latitude rotation when going from X,Y,Z to E,N,U. If going from E,N,U to X,Y,Z, then the opposite order would be used.

...

Note that the MWA tile location database seems to actually store E, N and the raw height above the reference ellipsoid (the original survey height value), NOT the height above the tile center (calculated as 'U' above). 

Converting surveyed UTM coordinates to lat/lon

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 attachedbelow. Just reiterating, the height is assumed to be height above the reference ellipsoid.

...

The array centre is: lat -26.70331940, lon 116.67081524 degs.

Here's a function from J-drive in ".../CIRA/Operations/Maps&Locations/MWA/MWA_Ph2_Extended-LB/Long Baselines Coordinate conversions":

def utmToLatLng(zone, easting, northing, northernHemisphere=True):
    if not northernHemisphere:
        northing = 10000000 - northing

    a = 6378137
    e = 0.081819191
    e1sq = 0.006739497
    k0 = 0.9996

    arc = northing / k0
    mu = arc / (a * (1 - math.pow(e, 2) / 4.0 - 3 * math.pow(e, 4) / 64.0 - 5 * math.pow(e, 6) / 256.0))

    ei = (1 - math.pow((1 - e * e), (1 / 2.0))) / (1 + math.pow((1 - e * e), (1 / 2.0)))

    ca = 3 * ei / 2 - 27 * math.pow(ei, 3) / 32.0

    cb = 21 * math.pow(ei, 2) / 16 - 55 * math.pow(ei, 4) / 32
    cc = 151 * math.pow(ei, 3) / 96
    cd = 1097 * math.pow(ei, 4) / 512
    phi1 = mu + ca * math.sin(2 * mu) + cb * math.sin(4 * mu) + cc * math.sin(6 * mu) + cd * math.sin(8 * mu)

    n0 = a / math.pow((1 - math.pow((e * math.sin(phi1)), 2)), (1 / 2.0))

    r0 = a * (1 - e * e) / math.pow((1 - math.pow((e * math.sin(phi1)), 2)), (3 / 2.0))
    fact1 = n0 * math.tan(phi1) / r0

    _a1 = 500000 - easting
    dd0 = _a1 / (n0 * k0)
    fact2 = dd0 * dd0 / 2

    t0 = math.pow(math.tan(phi1), 2)
    Q0 = e1sq * math.pow(math.cos(phi1), 2)
    fact3 = (5 + 3 * t0 + 10 * Q0 - 4 * Q0 * Q0 - 9 * e1sq) * math.pow(dd0, 4) / 24

    fact4 = (61 + 90 * t0 + 298 * Q0 + 45 * t0 * t0 - 252 * e1sq - 3 * Q0 * Q0) * math.pow(dd0, 6) / 720

    lof1 = _a1 / (n0 * k0)
    lof2 = (1 + 2 * t0 + Q0) * math.pow(dd0, 3) / 6.0
    lof3 = (5 - 2 * Q0 + 28 * t0 - 3 * math.pow(Q0, 2) + 8 * e1sq + 24 * math.pow(t0, 2)) * math.pow(dd0, 5) / 120
    _a2 = (lof1 - lof2 + lof3) / math.cos(phi1)
    _a3 = _a2 * 180 / math.pi

    latitude = 180 * (phi1 - fact1 * (fact2 + fact3 + fact4)) / math.pi

    if not northernHemisphere:
        latitude = -latitude

    longitude = ((zone > 0) and (6 * zone - 183.0) or 3.0) - _a3

    return (latitude, longitude)

Converting from lat, lon and height to X,Y,Z

...

1. 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
   
   

2. Rotate the longitude:

   x_local = x_geo*math.cos(lon_rad) + math.sin(lon_rad)*y_geo
   y_local = y_geo*math.cos(lon_rad) - math.sin(lon_rad)*x_geo
   z_local = z_geo

3. Rotate the latitude:

   e_local = y_local
   n_local = z_local*math.cos(lat_rad) - math.sin(lat_rad)*x_local
   u_local = x_local*math.cos(lat_rad) + math.sin(lat_rad)*z_local

Note that the MWA tile location database seems to actually store E, N and the raw height above the reference ellipsoid (the original survey height value), NOT the height above the tile center (calculated as 'u_local' above). 

Some versions of these codes have been put on the J drive under "EECMS/CIRA/Operations/Maps&Locations/MWA", but these are clearly copies of Randall's original code that he had no idea were there, so they should not be considered authoritative. 

...

Dave Emrich notes regarding the original survey data (16 Sep 2022): There is the possibility that one of the tiles on the east side of the “core” was “flipped” after this survey was completed, so that the HTD survey point in this file, actually reflects the SE corner, but that should be easily identified by comparing the E/N values in this spreadsheet with the ‘current’ ones, … an error of 5m true-East should pop out!

Phase II hex tiles

From Dave Emrich:

"So far as I remember the hex tiles only had five coordinates professionally surveyed, a centre, and four cardinals 50m? or so true N,S,E,W from the centre. One of the many spreadsheets should contain the HTD survey information for those ten co-oordinate points (five for each hex). It may also have the flag-pole and other locations in it. (I feel sure we had HTD do more than just the 10 points for the hexes, but I can't remember what). The locations of the individual hex tiles were computed as offsets from those cardinals and set out "manually" by us. Given the entire space was cleared of any vegetation and large rocks, there wasn't any need to move away from the 'desired' locations, so there wasn't a need to survey them after they were placed. (There was some initial mucking around with Hex S1 due to a slight rise in ground level but that was subsequently evened out and the tile set in its proper "desired" location)."

There's one file ("HexesRev4_TST_Output_Edited.txt" in ".../Maps&Locations/MWA/MWA_Ph2_Compact-Hexes/Hex Coordinate conversions/rev4" that has UTM values that match (to within a few cm) the values in the database, after adding 2.5m to E and N values (to convert SE corner to tile centers).

Phase II long baseline tiles

...