Fang Xinpeng, He Zhihao, Zhang Shouxu, Li Junbing, Shi Ranjun
School of Aerospace Science and Technology, Xidian University, Xi'an 710071, China.
School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China.
Entropy (Basel). 2022 Dec 23;25(1):32. doi: 10.3390/e25010032.
In addition to various estimation algorithms, the target localization accuracy in wireless sensor networks (WSNs) can also be improved from the perspective of geometry optimization. Note that existing placement strategies are mainly aimed at unconstrained deployment regions, i.e., the positions of sensors are arbitrary. In this paper, considering factors such as terrain, communication, and security, the optimal range-based sensor geometries under circular deployment region and minimum safety distance constraints are proposed. The geometry optimization problem is modeled as a constrained optimization problem, with a D-optimality-based (maximizing the determinant of FIM matrix) scalar function as the objective function and the irregular feasible deployment regions as the constraints. We transform the constrained optimization problem into an equivalent form using the introduced maximum feasible angle and separation angle, and discuss the optimal geometries based on the relationship between the minimum safety distance and the maximum feasible angle. We first consider optimal geometries for two and three sensors in the localization system, and then use their findings to extend the study to scenarios with arbitrary numbers of sensors and arbitrarily shaped feasible regions. Numerical simulation results are included to verify the theoretical conclusions.
除了各种估计算法外，无线传感器网络（WSN）中的目标定位精度还可以从几何优化的角度进行提高。需要注意的是，现有的布局策略主要针对无约束的部署区域，即传感器的位置是任意的。在本文中，考虑地形、通信和安全等因素，提出了在圆形部署区域和最小安全距离约束下基于距离的最优传感器几何形状。将几何优化问题建模为一个约束优化问题，以基于D最优性（最大化费希尔信息矩阵的行列式）的标量函数为目标函数，以不规则可行部署区域为约束条件。我们利用引入的最大可行角度和分离角度将约束优化问题转化为等效形式，并根据最小安全距离与最大可行角度之间的关系讨论最优几何形状。我们首先考虑定位系统中两个和三个传感器的最优几何形状，然后利用这些结果将研究扩展到具有任意数量传感器和任意形状可行区域的场景。文中包含数值模拟结果以验证理论结论。
