Efficient Position Determination Using Low-Rank Matrix Completion

In increasingly complex electromagnetic environments, distributed systems are crucial for passive target localization. These systems, consisting of spatially dispersed sensing nodes, collaboratively enhance the localization of target signals. Particularly in blind localization tasks within low signal-to-noise ratio (SNR) settings, distributed passive localization offers improved positioning performance. Traditional passive localization methods typically follow a two-step process: initially extracting parameters, such as the direction of arrivals (DOA), from raw data, followed by localizing the target. This approach often requires a high SNR. In contrast, Direct Position Determination (DPD) methods directly leverage all the received raw data, thus overcoming the constraints of the two-step process. However, DPD methods involve a time-consuming grid search within the area of interest. To address this challenge, we propose a radiation source localization method that utilizes random sampling. This method capitalizes on the low-rank properties of the grid search matrix used in DPD methods. By integrating random sampling with low-rank matrix completion algorithms, our approach efficiently localizes the radiation source. Simulation results demonstrate that this random sampling-based method significantly reduces computational demands while preserving high localization accuracy.