Abstract: According to the error caused by imperfect direct distance ranging technology in static networks, an improved Voronoi graph localization algorithm based on geometric constraint is proposed. The Cayley-Menger determinant is introduced to limit the distance relation, and the constraint equation of distance error is obtained, and then the optimal problem is solved by using the Lagrange multiplier method, the distances between nodes satisfy the true geometric constraints after the optimization. At the same time, the distance information is applied to the location of many anchor nodes. At last, the modified distance is applied to the Voronoi map positioning algorithm to optimize the algorithm. Simulation results show that the proposed algorithm is superior to the traditional positioning algorithm based on Voronoi map, which can effectively improve the success rate of positioning and positioning accuracy, and it has wider application scope.

Key words: Static network, geometry aided, voronoi diagram, lagrange multiplier method, multi anchor node

摘要： 针对静态网络中因测距技术的不完善而形成的直接测距误差，提出了一种基于几何约束辅助的Voronoi图改进定位算法。该算法引进Cayley-Menger行列式对距离关系进行限制，从而得到关于测距误差的约束方程，再利用拉格朗日乘数法对该方程的最优问题进行求解，使得优化后节点间的距离满足真实的几何约束关系，同时把距离信息应用于多锚节点定位中，最后把修正后的距离应用到Voronoi图定位算法中使该算法得到优化。仿真证明该算法优于基于Voronoi图的传统定位算法，可以有效提高定位成功率以及定位精度，具有更广泛的应用前景。

关键词: 静态网络, 几何辅助, 泰森多边形, 拉格朗日乘数法, 多锚节点