Ofcourse it 'starts fast' when you leave the receiver fully powered. gpsapp doesn't turn the receiver on or off, so the receiver just keeps tracking the satellites.

Actually, with my particular receiver, once something has been disconnected from the serial port for any length of time, it supposedly turns the receiver off. I think its timeout is 90 seconds. That's what was happening to me, any time the player has been unplugged for a while, it would cold boot again. So it doesn't "just keep tracking the satellites" as long as it has power, it also has to be connected to something. At least that seems to be case in the behavior I've observed. I have no idea how it "knows", but it seems to.

The interesting part is what happens when receiver comes up from nothing. i.e. even the internal battery is drained. Does it remember the coordinates in that case?

Yes, it seems to save the coordinates and spit them back out just fine, even after a complete drain.

However, after the internal battery is drained, it seems to go into the cold boot on the next power application anyway. I am not certain that this is the behavior, but it seems to be the case. I've only tried it once since getting Derrick's patch.

I've got a hunch that my unit's battery may be old and decrepit, as it doesn't seem to hold a charge for long. If I turn off the power feed to the receiver, it still sends data to the player for a little while but it eventually shuts off completely. Or maybe that's the 90-second timeout I'm experiencing, not sure. I'm not completely clear on how this receiver detects that it's "in use" and what its expected behavior is.
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Tony Fabris