We consider a sensor selection problem for binary hypothesis testing with cost-constrained measurements. Random outputs related to a parameter vector of interest are assumed to be generated by a linear system corrupted with Gaussian noise. The aim is to decide on the state of the parameter vector based on a set of measurements collected by a limited number of sensors. The cost of each sensor measurement is determined by the number of amplitude levels that can reliably be distinguished. By imposing constraints on the total cost, and the maximum number of sensors that can be employed, a sensor selection problem is formulated in order to maximize the detection performance for binary hypothesis testing. By characterizing the form of the solution corresponding to a relaxed version of the optimization problem, a computationally efficient algorithm with near optimal performance is proposed. In addition to the case of fixed sensor measurement costs, we also consider the case where they are subject to design. In particular, the problem of allocating the total cost budget to a limited number of sensors is addressed by designing the measurement accuracy (i.e., the noise variance) of each sensor to be employed in the detection procedure. The optimal solution is obtained in closed form. Numerical examples are presented to corroborate the proposed methods.

中文翻译：

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存在成本约束的二元假设检验的传感器选择和设计

我们考虑具有成本约束的测量的二元假设检验的传感器选择问题。假定与感兴趣的参数矢量有关的随机输出是由受高斯噪声破坏的线性系统生成的。目的是基于由有限数量的传感器收集的一组测量值来确定参数矢量的状态。每次传感器测量的成本取决于可以可靠地区分的幅度级别数。通过对总成本和可以使用的传感器的最大数量施加限制，提出了传感器选择问题，以最大程度地提高二元假设测试的检测性能。通过描述与优化问题的宽松版本相对应的解决方案的形式，提出了一种具有近乎最优性能的高效计算算法。除了固定的传感器测量成本的情况外，我们还考虑了需要进行设计的情况。特别地，通过设计要在检测过程中使用的每个传感器的测量精度（即，噪声方差）来解决将总成本预算分配给有限数量的传感器的问题。最优解以封闭形式获得。数值例子表明了所提出的方法。检测过程中要使用的每个传感器的噪声方差）。最优解以封闭形式获得。数值例子表明了所提出的方法。检测过程中要使用的每个传感器的噪声方差）。最优解以封闭形式获得。数值例子表明了所提出的方法。