This paper focuses on the problem of the initial-pose estimation by means of proprioceptive sensors (self-calibration) of suspended under-actuated Cable-Driven Parallel Robots (CDPRs). For this class of manipulators, the initial-pose estimation cannot be carried out by means of forward kinematics only, but mechanical equilibrium conditions must be considered as well. In addition , forward kinematics solution is based on cable-length measurements, but if the robot is equipped with incremental sensors cables' initial values are unknown. In this paper, the self-calibration problem is formulated as a non-linear least square optimization problem (NLLS), based on the direct geometrico-static problem, where only incremental measurements on cable lengths and on swivel pulley angles are required. In addition, a data acquisition algorithm and an initial value selection procedure for the NLLS are proposed, aiming at automatizing the self-calibration procedure. Simulations and experimental results on a 3-cable 6-degree-of-freedom robot are provided so as to prove the effectiveness of the proposed methodology.