线性逆问题的最小特征空间最大投影传感器配置
Sensor placement by maximal projection on minimum eigenspace for linear inverse problems
摘要：
本文提出了两种新的贪婪传感器布局算法，命名为最小非零特征值追踪（MNEP）和最小特征空间上的最大投影（MPME），线性逆问题，更侧重于MPME算法的性能与现有的方法进行比较。我们逐一选择感测位置。以这种方式，可以通过在确定每个感测位置之后检查是否满足估计精度来确定所需传感器的最少数量。最小特征空间被定义为与对偶观测矩阵的最小特征值相关联的特征空间。对于每个感测位置，其观测向量到最小特征空间的投影被证明是单调递减的w.r.t.估计参数的最坏情况误差方差（WCEV）。我们选择的感测位置的观测向量具有最大的投影到当前的对偶观测矩阵的最小特征空间。所提出的MPME被证明是计算效率最高的算法之一。我们的蒙特卡罗模拟表明，MPME在WCEV和估计参数的均方误差（MSE）方面优于凸松弛方法[1]、SparSenSe方法[2]和FrameSense方法[3]，特别是当可用传感器节点的数量非常有限时。
英文摘要：
This paper presents two new greedy sensor placement algorithms, named minimum nonzero eigenvalue pursuit (MNEP) and maximal projection on minimum eigenspace (MPME), for linear inverse problems, with greater emphasis on the MPME algorithm for performance comparison with existing approaches. We select the sensing locations one-by-one. In this way, the least number of required sensors can be determined by checking whether the estimation accuracy is satisfied after each sensing location is determined. The minimum eigenspace is defined as the eigenspace associated with the minimum eigenvalue of the dual observation matrix. For each sensing location, the projection of its observation vector onto the minimum eigenspace is shown to be monotonically decreasing w.r.t. the worst case error variance (WCEV) of the estimated parameters. We select the sensing location whose observation vector has the maximum projection onto the minimum eigenspace of the current dual observation matrix. The proposed MPME is shown to be one of the most computationally efficient algorithms. Our Monte-Carlo simulations showed that MPME outperforms the convex relaxation method [1], the SparSenSe method [2], and the FrameSense method [3] in terms of WCEV and the mean square error (MSE) of the estimated parameters, especially when the number of available sensor nodes is very limited.
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