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The speedup you are noticing is probably mostly due to assisted gps, where your phone gets a location using - partial gps information + wifi location + cell tower location all triangulated. Your eg early 2010 car gps unit didn't have any of the addition ways to speed up the location fix

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Downloading the orbital parameters can be done via the internet rather than at the 50 bps that the satellites broadcast them at.

Also the challenge of old receivers was which Doppler shift frequency to listen on depending on if the target satellite is going towards or away. By knowing the rough location (from cell towers, known wifi AP’s etc), they can get an instant lock.

There are three things that lead to fast lock times for cell phones.

* Ephemeris and almanac data updated via the internet so the receiver doesn't have to wait for either and can immediately know what satellites to listen for and acquire.

* Precise clock via NTP so the receiver has a smaller solve space for its internal clock

* AGPS gives a very good position fix to further help with the initial clock and position solving

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