Wrong UTM zone settings in GPS receiver

Question

I recently made a survey with an rtk GPS in an area within the UTM zone 32 N. Alas, the instrument was set to work on zone 33 N. When I load the points on a map applying the zone 32 projection (EPSG 32632) they are displayed far more west than they should be. Using the 32 N projection instead (EPSG 32633) puts them way east. The coordinates are in easting and northing format (see first three rows of the dataset here below).

Is there a way of converting the GPS readings "from 33 to 32" UTM zones?

P_Id Easting    Northing    Hellips.Elev
0   503815.028  5069932.565 214.429
1   497760.019  5080841.423 207.929
2   497747.633  5080748.276 205.616

Answer 1

Thanks to all who contributed, in the end, I solved like this:

• From the easting and northing coordinates, create two shapefiles: one with epsg 32632 and the other 32633 (utm zones 32 and 33
  respectively).
• Load the two in qgis (or arcgis) and export the zone 32 (westmost) reprojected in wgs 84 (epsg 4326).
• Make a copy of the westmost one and edit it bringing all the points onto the eastmost one (use snapping for better precision). Now you have a westlayer (wl) and an eastlayer (ey) in the same reference system. Add longitude and latitude fields to the two and compute their values (in qgis $x, $y).
• Use python to iterate through the wl and el, calculate the delta x and delta y of each point and create a new point having: x = wx + (delta_x/2) and y = wy + (delta_y/2).
• Create a shapefile with these points which are now displayed in the correct locations.