Any satellite phone I know of has a built-in GPS and can send text messages (not always reliably, especially with Thuraya) containing the GPS position which was current when you first entered the send text message menu (NOT the GPS position which was current when the message was sent).
Not aware of any which can do this automatically every x minutes, and only some satphones can be interrogated for their GPS position, but it is easy enough to program a satphone (using standard Hayes modem commands) to send any text message, from some kind of computer.
It's just not very cheap. Worth doing is flying over a hazardous area, perhaps. In which case one could have an "emergency location transmit" button which just sends the current position.
Satellite phones are much cheaper than most would believe (£300 for a Thuraya 7100, plus USD 160/year for the PAYG scratch card) and are standard equipment on expeditions etc. The main players are Iridium (worldwide coverage and pricey) and Thuraya (basically Europe / Mid East, and much cheaper).