Thanks everybody for this interesting discussion ! Glad I started it with my noob question
As to the GPS solving problems, I just want to mention the Korean Air Lines flight 007, which was shot down by a Soviet fighter jet because it inadvertently flew into the Soviet air space. It's one of the event which led the USA to release the GPS for use in civilian applications, to prevent similar errors in the future.
I now understand that ground speed and absolute altitude is not very relevant to an aircraft. In the case of Aeroperu 603, the lack of another altitude source likely was a cause of the crash (flight crew ignored the GPWS because of too many alarms and because they thought they were high enough). This is why I started this thread.
Thanks guys, it was very interesting. And I'm sure many people who are not aviation specialist will likely find this thread and learn from it as I did.