The centroid of a set of points can be used by a sensor to compute its location provided that each point represents an anchor with a known location. In this paper, we present mathematical characteristics of centroid based localization in a wireless sensor network. We prove that the centroid of a set of points minimizes an objective function, which is the summation of squares of distances from individual points. We provide a mathematical expression for the minimum value of the summation of the objective function. Also, we provide an expression for the distance between the centroids of a set of k and \((k+1)\) points. We describe a scheme for localization of sensors using the centroid of locations of anchors. Our scheme excludes locations of anchors that may adversely affect localization of a sensor.

传感器可以使用一组点的质心来计算其位置，前提是每个点都代表一个具有已知位置的锚点。在本文中，我们介绍了无线传感器网络中基于质心的定位的数学特征。我们证明一组点的质心最小化了一个目标函数，它是各个点的距离平方的总和。我们提供了目标函数总和的最小值的数学表达式。此外，我们提供了一组k和\((k+1)\)的质心之间的距离的表达式点。我们描述了一种使用锚点位置的质心定位传感器的方案。我们的方案排除了可能对传感器定位产生不利影响的锚点位置。