GolfSierra:
"Given the availability of technologies such as GPS, Inertial navigation, radio navigation, radar, AOA sensors - is it possible to build an avionics package which could automatically control (and provide pilots with information to manually control) the flight throughout all phases without requiring a pitot-static system at all?"
Apparently at least one such system exists for the A330. Cited text:
"The BUSS or "Backup Speed Scale"
Air France - Corporate : The BUSS or "Backup Speed Scale"
The "Backup Speed Scale" or BUSS is a tool which pilots use when speed indications cannot be used.
To use the BUSS, the crew must first disconnect the three ADRs (air data reference - anemometric stations). Once these have been disconnected, the crew can no longer use them during the flight.
With the BUSS system, speed is no longer calculated by the Pitot probes, but by the aircraft's incidence probes. The speed indication, which is less precise, is presented in the form of green, ambre and red stripes. In a high turbulence situation at high altitude, the speed indication given is very unstable and difficult to use.
On its A330s and A340s, Air France considered installing the BUSS system offered by Airbus and carried out tests on its flight simulators These tests did not lead Air France to adopt this system.
This is because it has the incovenience of depriving the crew of anemometric data during the flight once the BUSS system is activated, whereas experience has shown that the loss of speed indication is generally for a short time only. Moreover, the system is difficult to use at high altitude.
This has been confirmed by Airbus which recommends in a FOT (Flight Operations Telex) dated 9 September 2009 not to use this system at an altitude higher than 250, i.e. 7,600 metres (25,000 feet)."
Regards