What kind of instruments does a rocket use to track its trajectory and velocity during ascent? Do they use pitot tubes or barometric sensors? What exactly are the instruments used?
First things first: Many launch vehicles initially operate open loop, with guidance and control based solely on time since ignition until main engine cutoff. Precise guidance, navigation, and control becomes much easier when the launch vehicle has left the bulk of the atmosphere behind.
A wide variety of sensors exist for those vehicles that instead use closed loop guidance starting from launch. At a minimum, all modern launch vehicles have inertial measurement units (IMUs) that sense non-gravitational acceleration and sense change in orientation, and GPS receivers (or the equivalent for non-US rockets) that tell the rocket's navigation system where it is. Some rockets have angle of attack sensors, but this is not uniform. Some use pressure sensors so as to address issues related to maximum dynamic pressure, but once again, that is not uniform.
Ground control of the rocket should know the speed. A proven method used since the V-2 of WWII uses the doppler frequency shift of radio signals. A signal with known and very stable constant frequency is send from ground to the rocket. The rocket sends a signal back derived from the received signal, for instance the doubled frequency ( or another constant factor).
The ground control compares the frequencies of the send and received signals to determine the speed of the rocket very precisely. A small change of the ground frequency is compensated by sending the signal in both directions.
If the rocket and ground control both use ultra stable atomic clocks, the rocket may determine its own speed using the frequency difference between the received and the built in clocks.
Rockets were launched decades before GPS, so a method without GPS was needed. When the first GPS satellites were launched, GPS could not be used by those rockets.