I'm working on a project which has been collecting GPS data with ArcPad for three years. The GPS receivers work in D_WGS_1984, however the datum under GPS preferences has been set to D_North_American_1927(the map projection). My understanding is that the GPS preferences datum setting should be set to the GPS receiver datum, and ArcPad re-projects on the fly. Is this correct? And how do I correct the past data? It's a small study area, and doesn't have to be exact. Within a few meters would do.
Yes, you're right. GPS Datum should be set to WGS84 - the only exeption, if you use a GPS receiver with custom/other coordinate system uploaded (very rare case). Anyway, this is a common problem, heaps of customers make the same mistake. ArcPad converts WGS coordinates to your desired system on-the-fly (based on your file's projection) by default.
What you can do to resolve this with your mis-set files (if it's a shapefile): Using Catalog, right click on the file and select Properties. Go to XY Coordinate Sytem tab and press Select button. In Browse... dialog, select Geographic Coordinate Systems/World/WGS 1984.prj than press OK to apply. Your data should be ok now. Before you start to process these data, go to field and check OR compare this corrected file with a reference (basemap or other) to make sure the coordinates are okay.