Since the Cramér-Rao lower bounds (CRLB) of target localization depends on the sensor geometry explicitly, sensor placement becomes a crucial issue in many target or source localization applications. In the context of simultaneous time-of-arrival (TOA) based multi-target localization, we consider the sensor placement for multiple sensor clusters in the presence of shared sensors. To minimize the mean squared error (MSE) of target localization, we formulate the sensor placement problem as a minimization of the trace of the Cramér-Rao lower bound (CRLB) matrix (i.e., $A$ -optimal design), subject to the coupling constraints corresponding to the freely-placed shared sensors. For the formulated nonconvex problem, we propose an optimization approach based on the combination of alternating minimization (AM), alternating direction method of multipliers (ADMM) and majorization-minimization (MM), in which the AM alternates between sensor clusters and the integrated ADMM and MM are employed to solve the subproblems. The proposed algorithm monotonically minimizes the joint design criterion and converges to a stationary point of the objective. Unlike the state-of-the-art analytical approaches in the literature, the proposed algorithm can handle both the non-uniform and correlated measurement noise in the simultaneous multi-target case. Through various numerical simulations under different scenario settings, we show the efficiency of the proposed method to design the optimal sensor geometry.

中文翻译：

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基于优化的传感器放置，用于耦合传感器集群的多目标定位

由于目标定位的 Cramér-Rao 下界 (CRLB) 明确取决于传感器几何形状，因此传感器放置成为许多目标或源定位应用中的关键问题。在基于同时到达时间（TOA）的多目标定位的背景下，我们考虑在存在共享传感器的情况下多个传感器集群的传感器放置。为了最小化目标定位的均方误差 (MSE)，我们将传感器放置问题表述为 Cramér-Rao 下界 (CRLB) 矩阵迹线的最小化（即$A$ -优化设计），受到与自由放置的共享传感器相对应的耦合约束。对于公式化的非凸问题，我们提出了一种基于交替最小化（AM）、乘子交替方向法（ADMM）和主要最小化（MM）组合的优化方法，其中AM在传感器集群和集成ADMM之间交替和MM用于解决子问题。所提出的算法单调最小化联合设计标准并收敛到目标的驻点。与文献中最先进的分析方法不同，所提出的算法可以处理同时多目标情况下的非均匀和相关测量噪声。通过不同场景设置下的各种数值模拟，