This paper presents a novel angular velocity estimation strategy of a Reaction Sphere (RS) for satellite attitude control based on a Linear Parameter-Varying (LPV) Kalman Filter. The reaction sphere is a permanent magnet synchronous spherical actuator whose rotor is magnetically levitated and can be accelerated about any desired axis. The spherical actuator is composed of an 8-pole permanent magnet spherical rotor and of a 20-coil stator. The proposed technique relies on the implementation of a Kalman Filter observer over a LPV state-space model based on the rotor dynamics and the spherical harmonic decomposition of the magnetic flux density generated by the rotor. First, a theoretical development of the aforementioned estimator will be exposed, followed by a description of simulation and experimental set-ups for the tests. Finally, the proposed estimator is compared with the previous method used for angular velocity estimation based on the estimation of the back-EMF voltages induced in the coils, obtaining a significant reduction in amplitude and frequency of oscillations in the angular velocity control loop.