The present study investigates the feasibility, accuracy, and precision of 3-D profile extraction of the human skull bone using a custom-designed ultrasound matrix transducer in Pulse-Echo. Due to the attenuative scattering properties of the skull, the backscattered echoes from the inner surface of the skull are severely degraded, attenuated, and at some points overlapped. Furthermore, the speed of sound (SOS) in the skull varies significantly in different zones and also from case to case; if considered constant, it introduces significant error to the profile measurement. A new method for simultaneous estimation of the skull profiles and the sound speed value is presented. The proposed method is a two-folded procedure: first, the arrival times of the backscattered echoes from the skull bone are estimated using multi-lag phase delay (MLPD) and modified space alternating generalized expectation maximization (SAGE) algorithms. Next, these arrival times are fed into an adaptive sound speed estimation algorithm to compute the optimal SOS value and subsequently, the skull bone thickness. For quantitative evaluation, the estimated bone phantom thicknesses were compared with the mechanical measurements. The accuracies of the bone thickness measurements using MLPD and modified SAGE algorithms combined with the adaptive SOS estimation were 7.93% and 4.21%, respectively. These values were 14.44% and 10.75% for the autocorrelation and cross-correlation methods. Additionally, the Bland-Altman plots showed the modified SAGE outperformed the other methods with -0.35 and 0.44 mm limits of agreement. No systematic error that could be related to the skull bone thickness was observed for this method.