GPS logger?

[NavMicroSystems]

Hmmm, where do I start . . .

ok, let's try to start with the NMEA protocol.

I would focus on one single sentence (like GPRMC) and discard all the others.

Right after reception of that sentence I would extract LAT, LON, etc, and discard all unneeded Bytes.

With some smart code you can squeeze TIM, LAT, LON, and ALT into a 12 Byte (or even smaller) Data Packet.
(with full accuracy!)

Now think about your logging interval:
Does it necessarily have to be one log entry per second?
(wouldn't one every 10 (or 30 or . . .) seconds do?)
And do you really have to log data 24hrs a day?
(even if there is no movement?)

with that kind of data compression and a reasonable logging interval you can minimize Storage requirements.

So some EEPROM or FRAM could probably do.

To save even more memory you could check and
cleanup the log regularly (when the system is idle)

Imagine there is an (almost) linear track from A and B at about constant speed between A to B.
So all you really need is the data for A and B, everything in between can be cleared.

Agreed,
this "cleanup" procedure will require some math that is not that easy to implement having only the Integer brain of a PIC.

However,
the active components for the Logger shoudn't be much more than about $25 (dependant on how much Memory you need)

a PIC and some EEPROM or FRAM

I can tell it is possible,
I have built many systems like that.
(NavMicroSystems)