Airbus actually developed a very expensive and heavy laser airspeed measuring system for use on their flight test aircraft. Initial flight testing is a special case in airspeed measurement, as you don't yet know what the errors are in the aircraft's pitot and static pressure systems. The determination of the errors in the pitot and static pressure systems is one of the test phases that must be done early in the flight test program.
The system that Airbus developed is a very large unit mounted next to a cabin window. It shoots three orthogonal laser beams out the cabin window. Some of the laser light bounces off dust particles, and is reflected back to the device. It is able to measure the aircraft velocity on each of the three orthogonal axes, and thus determine the true airspeed, angle of attack and angle of sideslip. They combine the TAS with static pressure from the static ports and outside air temperature and then calculate calibrated airspeed.
I don't know if they are still using this system, but it was used back in the days of the A340 flight testing. It was found to be superior to the usual trailing cone + pitot pressure system in some parts of the flight envelope.
It would theoretically be possible to develop a lighter, smaller version of this system, but it would be fairly expensive.