Localization accuracy is an important indicator to design, and deploy the wireless sensor network. This article quantitatively investigates the bearing-based localization accuracy (BBLA) from the perspective of network geometric structure. The average geometric dilution of precision (AGDOP) is used to model the geometric structure-based BBLA, and is expressed by the geometry matrix which is based on the bearing measurement. Since geometry matrix is influenced by two factors (the bearing, and link length), these factors will convert to network characteristics such as the network scale, network size, and network symmetry, to perform the interaction on the BBLA. So we consider two cases to deduce the closed-form expression for the BBLA lower bound based on AGDOP by using the method of control variables, and to independently analyze the influence of the network characteristics on the BBLA. Concretely, the impacts of the network scale, and network symmetry on the BBLA are analyzed under the coordinate symmetry assumption in the first case, while the impact of the network size on the BBLA is analyzed in the second case. From these analyses, we find that the network scale, and network symmetry are approximately positively associated with the BBLA, while the network size is negatively associated with the BBLA. Finally, simulations are provided to demonstrate the effectiveness of the calculated lower bounds, and to illustrate validly the correctness of the accuracy analyses.

中文翻译：

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无线传感器网络中基于方位的定位的下界精度

定位精度是设计和部署无线传感器网络的重要指标。本文从网络几何结构的角度定量研究了基于轴承的定位精度（BBLA）。精度的平均几何稀释度（AGDOP）用于对基于几何结构的BBLA建模，并由基于轴承测量的几何矩阵表示。由于几何矩阵受两个因素（方位和链接长度）的影响，这些因素将转换为网络特征，例如网络规模，网络大小和网络对称性，以在BBLA上进行交互。因此，我们考虑两种情况，通过使用控制变量的方法来推导基于AGDOP的BBLA下界的闭式表达式，并独立分析网络特性对BBLA的影响。具体地，在第一种情况下，在坐标对称性假设下分析了网络规模和网络对称性对BBLA的影响，而在第二种情况下，分析了网络规模对BBLA的影响。从这些分析中，我们发现网络规模和网络对称性与BBLA近似正相关，而网络规模与BBLA负相关。最后，提供了仿真以演示计算出的下限的有效性，并有效地说明了精度分析的正确性。在第一种情况下，在坐标对称性假设下分析了BBLA的网络对称性和网络对称性，在第二种情况下，分析了网络大小对BBLA的影响。从这些分析中，我们发现网络规模和网络对称性与BBLA近似正相关，而网络规模与BBLA负相关。最后，提供了仿真以演示计算出的下限的有效性，并有效地说明了精度分析的正确性。在第一种情况下，在坐标对称性假设下分析了BBLA的网络对称性和网络对称性，在第二种情况下，分析了网络大小对BBLA的影响。从这些分析中，我们发现网络规模和网络对称性与BBLA近似正相关，而网络规模与BBLA负相关。最后，提供了仿真以演示计算的下界的有效性，并有效地说明了精度分析的正确性。