This article considers distributed estimation of an unknown deterministic parameter vector in a bandwidth constrained multisensor network with a fusion center (FC). Due to the stringent bandwidth requirements, each sensor compresses its observation as a low-dimensional vector via a linear transformation. Then, the FC linearly combines all received compressed data to estimate the deterministic parameter vector based on the best linear unbiased estimator. The problem of interest is to jointly design the dimension assignment (i.e., the compression dimension of each sensor) and the corresponding compression matrix when the total number of compression dimensions is given. Such a joint design problem is formulated as an optimization problem with rank and linear matrix equality constraints, which is shown to be NP-hard for the first time. In addition, penalty decomposition (PD), successive quadratic upper-bound minimization method of multipliers (SQUM-M), and SQUM-M-block coordinate descent (SQUM-M-BCD) are proposed to solve it approximately. Furthermore, we show that any accumulation point of the sequence generated by the PD satisfies the Karush-Kuhn-Tucker conditions of the equivalent formulation of the joint design problem; the SQUM-M admits the same convergence property as the PD under some conditions. Numerical experiments corroborate the merits of PD and SQUM-M-BCD as compared with existing strategies for the heterogeneous scenario, and further illustrate the effectiveness of the proposed algorithms for the correlated noise case.

中文翻译：

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分布式多传感器网络中确定性参数矢量估计的联合维数分配和压缩

本文考虑了在带融合中心（FC）的带宽受限多传感器网络中未知确定性参数矢量的分布式估计。由于严格的带宽要求，每个传感器都通过线性变换将其观察结果压缩为低维向量。然后，FC根据最佳线性无偏估计器将所有接收到的压缩数据进行线性组合，以估计确定性参数矢量。感兴趣的问题是在给出压缩尺寸的总数时，共同设计尺寸分配（即，每个传感器的压缩尺寸）和相应的压缩矩阵。这种联合设计问题被公式化为具有秩和线性矩阵等式约束的优化问题，这首次被证明是NP难的。此外，罚分解（PD），乘数的连续二次上界最小化方法（SQUM-M）和SQUM-M块坐标下降（SQUM-M-BCD）被提出来解决。此外，我们表明，由PD生成的序列的任何累加点都满足联合设计问题等效公式的Karush-Kuhn-Tucker条件；在某些条件下，SQUM-M接受与PD相同的收敛性。数值实验证实了PD和SQUM-M-BCD与针对异构场景的现有策略相比的优点，并进一步说明了所提出算法在相关噪声情况下的有效性。并提出了SQUM-M块坐标下降法（SQUM-M-BCD）来对其进行近似求解。此外，我们表明，由PD生成的序列的任何累加点都满足联合设计问题等效公式的Karush-Kuhn-Tucker条件；在某些条件下，SQUM-M接受与PD相同的收敛性。数值实验证实了PD和SQUM-M-BCD与针对异构场景的现有策略相比的优点，并进一步说明了所提出算法在相关噪声情况下的有效性。并提出了SQUM-M块坐标下降法（SQUM-M-BCD）来对其进行近似求解。此外，我们表明，由PD生成的序列的任何累加点都满足联合设计问题等效公式的Karush-Kuhn-Tucker条件；在某些条件下，SQUM-M接受与PD相同的收敛性。数值实验证实了PD和SQUM-M-BCD与针对异构场景的现有策略相比的优点，并进一步说明了所提出算法在相关噪声情况下的有效性。在某些条件下，SQUM-M接受与PD相同的收敛性。数值实验证实了PD和SQUM-M-BCD与针对异构场景的现有策略相比的优点，并进一步说明了所提出算法在相关噪声情况下的有效性。在某些情况下，SQUM-M接受与PD相同的收敛性。数值实验证实了PD和SQUM-M-BCD与针对异构场景的现有策略相比的优点，并进一步说明了所提出算法在相关噪声情况下的有效性。