As radar sensors are being miniaturized, there is a growing interest for using them in indoor sensing applications such as indoor drone obstacle avoidance. In those novel scenarios, radars must perform well in dense scenes with a large number of neighboring scatterers. Central to radar performance is the detection algorithm used to separate targets from the background noise and clutter. Traditionally, most radar systems use conventional CFAR detectors but their performance degrades in indoor scenarios with many reflectors. Inspired by the advances in non-linear target detection, we propose a novel high-performance, yet low-complexity target detector and we experimentally validate our algorithm on a dataset acquired using a radar mounted on a drone. We experimentally show that our proposed algorithm drastically outperforms OS-CFAR (standard detector used in automotive systems) for our specific task of indoor drone navigation with more than 19% higher probability of detection for a given probability of false alarm. We also benchmark our proposed detector against a number of recently proposed multi-target CFAR detectors and show an improvement of 16% in probability of detection compared to CHA-CFAR, with even larger improvements compared to both OR-CFAR and TS-LNCFAR in our particular indoor scenario. To the best of our knowledge, this work improves the state of the art for high-performance yet low-complexity radar detection in critical indoor sensing applications.