A flight-path reconstruction algorithm for tethered aircraft, which is based on an extended Kalman filter, is presented. The algorithm is fed by the measurements of a set of onboard and ground-based instruments and provides the optimal estimation of the system state-space trajectory, which includes typical aircraft variables such as position and velocity, as well as an estimation of the aerodynamic force and torque. Therefore, it can be applied to closed-loop control in airborne wind energy systems and it is a first step toward aerodynamic parameter identification of tethered aircraft using flight-test data. The performance of the algorithm is investigated by feeding it with real flight data obtained from a low-cost and highly portable experimental setup with a four-line kite. Several flight tests, which include pullup and lateral-directional steering maneuvers with two kites of different areas, are conducted. The coherence of the estimations provided by the filter, such as the kite state-space trajectory and aerodynamic forces and torques, is analyzed. For some standard variables, such as kite Euler angles and position, the results are also compared with a second independent onboard estimator.