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This paper presents a novel system identification framework for small unmanned aerial vehicles (UAVs) by combining an unscented Kalman filter (UKF) estimator with a neural network (NN) identifier. The method is effective for systems with low-cost, erroneous sensors where the sensor outputs cannot be used directly for system identification and control. The UKF state estimator computes error-compensated attitude and velocities by integrating sensor data from an inertial measurement unit (IMU) and a global positioning system (GPS). The NN identifier approximates the nonlinear dynamics of the UAV from the UKF estimated states, hence identifying the system. As an illustration, the UKF-NN system identification framework is applied to fixed-wing as well as rotary-wing 6-DOF multi-input-multi-output (MIMO) nonlinear UAV models.