Compressive Sensing Based Multi-target Device-free Passive Localization Algorithm Using Multidimensional Measurement Information
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摘要:
无源被动定位是入侵者检测、环境监测以及智能交通等应用的关键问题之一。现有的无源被动定位方法可通过信道状态信息获取多个维度上的测量信息，但是现有方案未能充分挖掘多个信道上的频率分集以提高定位性能。该文提出一种基于多维测量信息的压缩感知多目标无源被动定位算法，在压缩感知框架下利用多维测量信息的频率分集提高定位精度和鲁棒性。根据鞍面模型建立无源字典，将多目标无源被动定位问题建模成多测量向量联合稀疏恢复问题，并利用多维稀疏贝叶斯学习算法估计目标位置向量。仿真结果表明，该算法能有效利用多维测量信息提高定位性能。
Abstract:Device-free passive localization is a key issue of the intruder detection, environmental monitoring, and intelligent transportation. The existing device-free passive localization method can obtain the multidimensional measurement information by channel state information, but the existing scheme can not fully exploit the frequency diversity on multiple channels to improve the localization performance. This paper proposes a Compressive Sensing (CS) based multi-target device-free passive localization algorithm using multidimensional measurement information. It takes advantage of the frequency diversity of multidimensional measurement information to improve the accuracy and robustness of localization results under the CS framework. The dictionary is built according to the saddle surface model, and the multi-target device-free passive localization problem is modeled as a joint sparse recovery problem based on multiple measurement vectors. The target location vector is estimated based on the multiple sparse Bayesian learning algorithm. Simulation results indicate that the proposed algorithm can make full use of the multidimensional measurement information to improve the localization performance.
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表 1 联合稀疏恢复算法
(1) 令${\gamma _{{\rm{th}}}} = {10^{ - 3}}$, ${\tau _{\max }} = {10^3}$, ${\eta _{{\rm{th}}}} = - 10\ {\rm{dB}}$, $\gamma = \tau = 0$。 (2) while ($\gamma \ge {\gamma _{{\rm{th}}}}$或$\tau \le {\tau _{\max }}$) do (3) 根据式(16)和式(17)，计算${{Σ}}$和${{Π}}$。 (4) 根据式(19)和式(20)，更新参数${\alpha _n}$和${\sigma ^2}$。 (5) 令$\gamma \leftarrow \parallel{Y} - {{Φ}}{{Π}}\parallel $, $\tau \leftarrow \tau + 1$。 (6) end while (7) 选择使$\left\| {{{{y}}^f} - {{Φ}}{{{Π}} _{ \cdot f}}} \right\|$取得最小值的子信道$\hat f$。 (8) $\forall n \in \left\{ {1,2,·\!·\!·,N} \right\}$，若$20\lg ({{{Π}} _{nf}}/\mathop {\max }\limits_i |{{{Π}} _{i\hat f}}|) < {\eta _{{\rm{th}}}}$，则${{{Π}} _{n\hat f}} = 0$。 (9) 令恢复的位置向量$\hat {{θ}} = {{{Π}} _{ \cdot \hat f}}$，目标个数${\widehat K} = |\hat {{θ}}|$。 
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表 2 平均定位误差与定位均方根误差的比较
定位算法 OMP BP GMP BCS VEM 自有算法($F = 5$) 自有算法($F = 10$) 自有算法($F = 20$) 平均定位误差 3.2028 1.3028 2.1795 0.8955 0.6196 0.4631 0.2744 0.2584 定位均方根误差 3.3801 1.5735 2.4543 1.5838 1.0036 0.8392 0.6720 0.4738
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