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Passive Direct Location Determination for Multiple Sources Based on FRFT
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摘要: 直接定位(DPD)算法能充分利用观测回波信息，在低信噪比条件下其定位精度一般要高于传统的两步定位算法。为解决多基站无源雷达系统中多个未知线性调频(LFM)信号辐射源的定位问题，该文提出一种基于DPD算法和分数傅里叶变换(FRFT)相结合的多目标定位算法。首先，根据建立的信号模型推导了理论上最优的高维最大似然估计器；其次，由于高维信号参数和目标位置联合估计的计算复杂度限制，利用基于FRFT和基本分类算法的降维策略将多目标定位问题转化为多个单目标定位问题；最后，目标的位置及相应信号参数可通过4维网格搜索得到有效估计。仿真结果表明，相比于已存在的忽略发射信号的DPD算法，该文提出算法定位性能更优。Abstract: 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.
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图 4 接收信号的FRFT功率谱3维分布图
Figure 4. Three-dimensional FRFT power spectrum for received signal
表 1 信号参数设置
Table 1. Signal parameter setting
目标信号 信号长度Tp
(μs)初始频率f0
(MHz)调频斜率k
(MHz/μs)目标1信号 20 2 0.10 目标2信号 25 6 –0.05 目标3信号 30 5 0.25 
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