Establishing relative coordinate system is essential for many applications of sensor networks. This paper proposes a computation scalable scheme for establishing relative coordinate system of sensor networks using distance measurements between sensors. A distributed selection algorithm is proposed to select a small number of nodes from all sensors to serve as virtual grid point and establish the grid relative coordinate system. The grid coordinate system forms the backbone of localization for static and mobile nodes, whereby the non-grid nodes can compute their positions via message exchange with their neighboring grid nodes. This paper shows by both mathematical analysis and simulations that the localization error of the scalable grid approach is upper bounded by half the grid width (i.e., the length of two adjacent grid points). The results also indicate that the precision of grid coordinate system can be adaptively adjusted by the grid width and the density of grid nodes to meet target applications. For those non-grid nodes, the results show that the localization precision of non-grid nodes would be bounded by one grid-cell error.
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