Recent developments in planetary exploration have shown the potential of Unmanned Aerial Vehicles (UAVs), such as the Ingenuity helicopter that provided valuable mapping data. However, limited payload capabilities constrain the flight times and compute available for localization which restrict their applicability. By providing a tethered connection, issues such as battery and computational constraints are offloaded to the base rover. At the same time, the cable can be exploited for non-drifting localization. This work presents a novel Tether-Inertial Localization approach that uses tether length, and angle measurements to estimate the UAV pose relative to its base. The method combines a computationally efficient analytical catenary model with Gaussian Process (GP) residual error compensation. This accounts for systematic sensor inaccuracies and model limitations under dynamic conditions. Experimental validation across circular, triangular, and figure-eight trajectories with tether lengths up to 4.5 m spanning 41 minutes of flight time with only the tether based estimate as position feedback, demonstrates estimation errors of 0.073 m average RMSE for the analytical model alone and 0.049 m average RMSE with GP-enhancement. With this, we provide an alternative localization method to conventional vision or GNSS-based methods, providing similar accuracies for Tethered UAVs.