Radio-based indoor localization is currently a very vibrant scientific research field with many potential use cases. It offers high value for customers, for example, in the fields of robotics, logistics, and automation, or in context-aware IT services. Especially for autonomous systems, dynamic human-machine interaction, or augmented reality applications, precise localization coupled with a high update rate is a key. In this paper, we present a completely novel localization concept whereby received radio signal phase values that are fed into an extended Kalman filter (EKF) without any preprocessing are evaluated. Standard preprocessing steps, such as angle-of-arrival estimation, beamforming, and time-of-flight or time-differenceof-arrival estimations are not required with this approach. The innovative localization concept benefits from the high sensitivity of radio signals' phase to distance changes and the fast and straightforward recursive computation offered by the EKF. It completely forgoes the computational burden of other phase-based high-precision localization techniques, such as synthetic aperture methods. To verify the proposed method, we use an exemplary setup employing a 24 GHz frequency-modulated continuous-wave (CW) single-input multiple-output secondary radar with 250 MHz bandwidth. A high-precision six-axis robotic arm serves as a 3D positioning reference. The test setup emulates a realistic industrial indoor environment with significant multipath reflections. Despite the challenging conditions and the rather low bandwidth, the results show an outstanding localization 3D RMSE of around 1.7 cm. The proposed method can easily be applied to nearly any type of radio signal with CW carrier and is an attractive alternative to common multilateration and multiangulation localization approaches. We think it is a quantum leap in wireless locating, as it has the potential for precise, simple, and low-cost wireless localization even with standard narrowband communication signals. INDEX TERMS FMCW, radar, localization, extended Kalman filter, near field, indoor.