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.