How do I measure speed accurately without any turning wheels? Consider a pod (about 50 ft long and 15 square feet wide) that levitates using air pressure that shoots through the bottom and travels through a tube that's at low air pressure (about 100 Pa). It travels using linear induction. If you're wondering, this problems comes from the hyperloop tube specification. The pod will be traveling anywhere from 0 to 800 MPH.
I need to measure the speed of the pod traveling through the tube at every point
Approaches I have considered:


*

*Using an accelerometer and integrating over time

*Using a pitot tube


I've heard that an accelerometer can be bad for measuring velocity because an error bias can propagate. 
I heard that pitot tubes were used for airplanes, but I don't know if they're very accurate or work at the low air pressures I have.
What approach should I use to measure the speed of my pod?
 A: Police use the answer all the time: relativistic Doppler effect with radar or lasers. It's very well understood technologically, theoretically, and practically.
A: As you said, "dead-reckoning" using an accelerometer isn't a good method because errors can easily build up. My feeling is that a pitot tube isn't a good method, either, for a number of reasons. For one, there may be big air pressure variations over vehicle's hull as it moves slightly within its tube, and that may cause chaos with the pitot tube readings. It's not quite like using a pitot tube with an airplane with free airflow all around the aircraft. 
I think that a simple method to implement which would take advantage of the fact that the hyperloop vehicle is within a close-fitting tube would be to but regular markers of some sort on the tube and some sensor in the vehicle so that the vehicle can 'count' the rate at which the markers on the tube are passing it. Some possible markers would be regularly spaced LED lights on the inside of the tube or even painted stripes on the inside of the tube. The vehicle could then determine its speed using a sort of opto-electric sensor system similar in concept to that used in the optical mouse that you are now using at your computer. 
A: Mount an optical or laser  mouse on the pod, 
so that it goes along the tube wall.
The autocorrelator chip in the mouse will do 
the brain work for you. 
