Dictionary Refinement Method for Compressive Sensing Based Multi-target Device-free Localization
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摘要:
该文针对压缩感知多目标无源定位在无线定位环境中的字典失配问题，提出基于变分期望最大化算法的字典适配方法。该方法首先根据鞍面模型建立无源字典，并将与定位环境相关的字典参数作为可调参数。然后，为目标位置向量建立两层的混合高斯先验模型以诱导其稀疏性。最后，利用变分期望最大化算法估计隐藏变量的后验分布以及优化字典环境参数，实现多目标位置估计和字典适配。仿真结果表明，相较于传统的压缩感知多目标无源定位方法，在变化的无线定位环境下，所提定位方法的性能优势尤为明显。
Abstract:In order to solve the dictionary mismatch problem of Compressive Sensing (CS) based multi-target Device-Free Localization (DFL) under the wireless localization environments, a Variational Expectation Maximization (VEM) based dictionary refinement method is proposed. Firstly, this method builds the dictionary based on the saddle surface model, and models the environment-related dictionary parameters as tunable parameters. Then, a two-layer hierarchical Gaussian prior model is imposed on the location vector to induce its sparsity. Finally, the VEM algorithm is adopted to estimate the posteriors of hidden variables and optimize the environment-related dictionary parameter, thus the estimation of target locations and dictionary refinement can be realized jointly. Compared with the conventional CS based multi-target DFL schemes, the simulation results demonstrate that the performance of the proposed algorithm is especially excellent in changing wireless localization environments.
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表 1 目标位置估计算法
(1) 令${\gamma _{{\text{th}}}} = {10^{ - 3}}$, ${r_{\max }} = {10^3}$, ${\eta _{{\text{th}}}} = - 10\;{\text{dB}}$, $\gamma = \tau = 0$。 (2) while($\gamma \ge {\gamma _{{\text{th}}}}$或$r \le {r_{\max }}$)do (3) 根据式(17)和式(18)，计算${{Σ}} $和${{μ}} $； (4) 根据式(20)和式(21)，更新参数${a^ * }$和${b^ * }$； (5) 根据式(23)和式(24)，更新参数${c^ * }$和$d_n^ * $； (6) while($\tau \le {\tau _{\max }}$)do (7) 根据式(30)更新$\rho $； (8) end while (9) 令$\gamma \leftarrow \parallel {{y}} - {{Φ}} ({\rho ^ * }){{μ}} \parallel_2^2$, $r \leftarrow r + 1$； (10) end while (11) $\forall n \in \{ 1,2, ·\!·\!· , N\} $，若$20\lg ({\mu _n}/\mathop {\max }\nolimits_i |{\mu _i}|) < {\eta _{{\text{th}}}}$，则${\mu _n} \!=\! 0$； (12) 令恢复的位置向量$\hat {{θ}} = {{μ }}$，目标个数$\hat K = |\hat {{θ}} |$。 
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