With the rapid development of the internet of things (IoT), location-based services are becoming increasingly prominent in various aspects of social life, and accurate location information is crucial. However, RF-based indoor positioning solutions are severely limited in positioning accuracy due to signal transmission losses and directional difficulties, and optical indoor positioning methods require high propagation conditions. To achieve higher accuracy in indoor positioning, we utilize the principle of resonance to design a triangulation-based resonant beam positioning system (TRBPS) in the RF band. The proposed system employs phase-conjugation antenna arrays and resonance mechanism to achieve energy concentration and beam self-alignment, without requiring active signals from the target for positioning and complex beam control algorithms. Numerical evaluations indicate that TRBPS can achieve millimeter-level accuracy within a range of 3.6 m without the need for additional embedded systems.