The central aortic blood pressure signal is an important source of information that contains cues about the cardiovascular system condition. Measuring this pulse wave clinically is burdensome as it can be only measured invasively with a catheter. As a result, many mathematical tools have been proposed in the past few decades to reconstruct the aortic pressure signal from the peripheral pressure signals that are usually easier to obtain noninvasively. At the distal level, the blood pressure signal is not directly useful since factors, such as length and stiffness of the arteries, play roles in changing the shape of the pressure signal significantly. In this thesis, multi-channel blind system identification techniques are proposed to estimate the central pressure waveform which vary in their accuracy and complex- ity. First, a simple linear method is applied by approximating the nonlinear arterial system as a linear time-invariant system and applying the cross-relation approach. Next, a more complicated nonlinear Wiener system is proposed to model the nonlinear arterial tree. Along with the channel’s coefficients, the nonlinear functions are estimated using cross-relation and kernel methods. Data-driven machine learning methods are tested to estimate the aortic pressure signals. In many cases, they suffer from underfitting problems. As a remedy, a hybrid machine learning and cross-relation approach is also proposed to add more robustness to the machine learning models. This hybrid approach is implemented by combining the cross-relation with any machine learning method, including deep learning approaches. The various methods are tested using pre-validated virtual databases. The results show that the linear method produces root mean squared errors between 3.40 mmHg and 6.24 mmHg depending on the cross-relation constraint and the equalization tech- nique. On the other hand, the root mean squared errors associated with the nonlinear methods are between 3.76 mmHg and 4.22 mmHg and hence more stable. For the hybrid machine learning and cross-relation approach, applying the cross-relation and the dictionary learning reduce the root mean squared errors up o 67% comparing with the pure machine learning models.