Since 2010 a 2^nd generation NOAA MF/HF radar, also referred to as the VIPIR ionosonde, has been operated at Hualien, Taiwan (23.8973°N, 121.5503°E). The Hualien VIPIR ionosonde is a modern ionospheric radar, fully digitizing complex signal records and using multiple parallel receiver channels for simultaneous signal measurements from multiple spaced receiving antennas. This paper considers radio direction finding based on interferometric phase measurements from a horizontal antenna array in the Hualien VIPIR ionosonde system. We applied the Hermite normal form method to solve the phase-measurement aliasing and least squares problems and improve the radio angle-of-arrival (AOA) measurements. Backward ray-tracing simulation has been proposed to determine radio transmitter position. This paper presents a numerical, step by step ray-tracing method based on the IGRF superimposed onto a phenomenological ionospheric electron density model, the TaiWan Ionospheric Model (TWIM). The proposed methodology is successfully applied to locate two experimental HF radio transmitters at Longquan and Chungli with distance errors within 5 km and less than 5% of the great circle distances.