Passive Direct Location Determination for Multiple Sources Based on FRFT

The Direct Position Determination (DPD) method can fully use the information of an observed signal, and it is known to outperform the traditional two-step methods at a low Signal-to-Noise Ratio (SNR). To solve the problem of localizing multiple transmitters with unknown Linear Frequency Modulation (LFM) signals in multi-static passive radar systems, a multi-target positioning algorithm based on DPD algorithm and FRactional Fourier Transform (FRFT) is proposed. First, according to the established signal model, the theoretically optimal high-dimensional maximum likelihood estimator is deduced; Then, to address the high computational complexity of the estimator in jointly estimating high-dimensional signal parameters and positions of sources, we propose a dimensionality reduction strategy based on the FRFT and some basic classification algorithms to transform the multi-target localizing problem to a multiple single-target localizing problem. Through this method, the position and the corresponding signal parameters of each source can be efficiently estimated by a four-dimensional grid search. Simulation results show that the proposed method outperforms the existing DPD algorithm, and it can determine the positions of sources without directly utilizing the transmitted signal information.