This paper considers the self-localization of a tethered drone without using a cable-tension force sensor in GPS-denied environments. The original problem is converted to a state-estimation problem, where the cable-tension force and the three-dimensional position of the drone with respect to a ground platform are estimated using an extended Kalman filter (EKF). The proposed approach uses the data reported by the onboard electric motors (i.e., the pulse width modulation (PWM) signals), accelerometers, gyroscopes, and altimeter, embedded in the commercial-of-the-shelf (COTS) inertial measurement units (IMU). A system-identification experiment was conducted to determine the model that computes the drone thrust force using the PWM signals. The proposed approach was compared with an existing work that assumes known cable-tension force. Simulation results show that the proposed approach produces estimates with less than 0.3-m errors when the actual cable-tension force is greater than 1 N.