May be the GPS could be another option, but in this case GPS isn't recognised as a official navigation system yet.
It isn't?
How very odd, because...in 1997, I operated Lockheed L1011 aircraft with dual installed Honeywell HT9100 GPS units, that were fully approved for enroute and terminal primary navigation, in Europe, North America, South America, Africa, Asia and oceanic areas including the north Atlantic and north/central Pacific.
This approval has been in force continually, to this very day.
In addition, long before GPS was available, over oceanic areas especially, Doppler navigation was used, combined with astro nav for a positive position fix.
Used this mode of navigation in B707 equipment.