Industrial robots are increasingly used in industry for contact-based manufacturing processes such as milling and forming. In order to meet part tolerances, it is mandatory to compensate tool deflections caused by the external force-torque vector. However, using a third-party measuring device for sensing the external force-torque vector lowers the cost efficiency. Novel industrial robots are increasingly equipped with double encoders, in order to compensate deviations caused by the gearboxes. This paper proposes a method for the usage of such double encoders to estimate the external force-torque vector acting at the tool centre point of an industrial robot. Therefore, the joint elasticities of a six revolute joint industrial robot are identified in terms of piecewise linear functions based on the angular deviations at the double encoders when an external force-torque vector is applied. Further, initial deviations between the encoder values caused by gravitational forces and friction are modelled with a Gaussian process regression. Combining both methods to a hybrid model enables the estimation of external force-torque vectors solely based on measurements of the joint angles of secondary encoders. Based on the proposed method, additional measurement equipment can be saved, which reduces investment costs and improves robot dynamics.