A solution to the problem of global exponential tracking without velocity measurement of mechanical systems with friction and possibly unbounded inertia matrix is given in the paper. The proposed controller is obtained combining a new full--information passivity--based controller with a new immersion and invariance observer. The resulting closed--loop system has, in some suitably defined coordinates, a port--Hamiltonian structure with a desired energy function and a uniformly positive definite damping matrix. In this way, global exponential tracking of position and velocity for all desired reference trajectories is ensured.