The direct position determination (DPD) approach has been shown to be superior to alternative (two-steps) indirect methods for emitter localization in terms of the resulting accuracy. However, its requirement of joint raw data processing from all receiving non-co-located sensor arrays in different base stations results in one of its main drawbacks-that (all the) raw data be transferred to a common processor. To alleviate the communication requirements between the base stations, it has been recently proposed to use a coarsely quantized version of the raw data, specifically with one-bit-per-sample quantized measurements, for which the One-Bit DPD (OBDPD) method was developed. While OBDPD significantly reduces the requirements on the communication links between the base stations, similarly to classical DPD, it typically suffers from (substantially) degraded localization accuracy when multiple emitters are present in the area of interest. To tackle this limitation, we propose high-resolution OBDPD (HROBDPD), which is similar in nature to OBDPD, but with a minimum variance distortionless response approach. Despite the one-bit-per-sample quantization, HROB-DPD yields favorable spatial heat maps for the multiple-emitters case, thus leading to enhanced localization. Simulation results demonstrate the improved performance of HROBDPD relative to OBDPD in a scenario with more than a single emitter.