Is it possible to accurately measure airspeed without pitot tube?
Technically speaking, inertial measurements are not sufficient to derive airspeed. You need pressure measurement (or airspeed measurement, see LIDAR).  Pitot-static probes are the most usual and conventional devices to measure pressure. 

However, several researches have been conducted, to replace pitot-static tubes with different technologies. These technologies are mainly based on measuring surface pressure on a part of the fuselage. Of course the measurements (not a single value but several values from various locations) have to be calibrated via flight tests. 

With the current popularity of machine learning I think the calibration algorithms will not be the main problem.

Some other technology being investigated


there's also ongoing research and trials about using LIDAR to
directly measure airspeed. Which won't need pressure measurement.
ultrasonic devices are also able to measure airspeed directly,
however their real flight usage is unknown (to the author).