1. A method for continuously and non-invasively monitoring blood pressure of a patient, the method comprising the steps of: positioning a first ultrasound sensor and a second ultrasound sensor aligned with a blood vessel of the patient, the first and second ultrasound sensors being operable to determine the diameter of the blood vessel and the flow rate of blood through the blood vessel; obtaining a first blood flow rate determined from the first ultrasound sensor, a second blood flow rate determined from the second ultrasound sensor, and a blood vessel radius; utilizing a transmission line model to represent the blood vessel, where the voltage at each node of the transmission line model corresponds to the blood pressure, the transmission line model including an input current source and an output current source positioned between an RLC ladder network, wherein the input current source is the first blood flow rate and the output current source is the second blood flow rate; developing a series of state variable equations based on the transmission line model; and inputting the obtained first blood flow rate, the second blood flow rate and the blood vessel radius into a Kalman filter; utilizing the Kalman filter to estimate the state variables of the transmission line model; using a transmission-line-based computation to estimate the blood pressure.