I'm having an issue with points shifting their locations when projected differently.
I have several files with undefined coordinate systems (from a Trimble GPS). If I bring these shapefiles into a dataframe that's in WGS84, they appear in what I assume is the correct location based on the aerial. If I then define the coordinate system of the shapefile as WGS84, they continue to appear in the same location. If I then move that shapefile into an MXD with a dataframe that's in state plane, the shapefile projects on-the-fly to the same location. I then export that shapefile with the data frame's coordinate system, the data stays in that location. So far so good.
However--if I define the coordinate system of the shapefile as WGS84, then try to project the file into state plane using the Project tool (no matter which coordinate system the dataframe is in), the points shift by about three feet.
Does anyone know why this is happening? More importantly, which location is in the correct location--the original points or the shifted ones? How do you tell?