On the Efficient and Accurate One-Step Passive Localization using Sub-Nyquist Sampling Signals Directly

Relying on the reception and analysis of signals already present in the environment, has various applications across different domains, from acoustics to electromagnetics. However, the growing signal bandwidth poses tremendous challenges in data transmission, highlighting the advantages of the compressive sensing (CS) technique. In this study, we investigate the direct position determination (DPD) using sub-Nyquist sampling signals directly without reconstruction the full signal first. Leveraging the Hadamard matrix as the CS measurement matrix, the cost function for emitter source determination is first established with the sub-Nyquist sampled signals. Hence, the full signal recovery error and cumbersome computation are avoided compared with existing passive localization methods with CS signals. In addition, the Carmér-Rao Lower bound (CRLB) is theoretically derived and points out the trade-off between localization accuracy and sparse signal sampling rate. The effectiveness of the proposed method is demonstrated through Monte Carlo simulations and comparisons.