The distance vector-hop (DV-hop) is a typical localization algorithm. It estimates sensor nodes location through detecting the hop count between nodes. To enhance the positional precision, the weight is used to estimate position, and the conventional wisdom is that the more hop counts are, the smaller value of weight will be. However, there has been no clear mathematical model among positioning error, hop count, and weight. This paper constructs a mathematical model between the weights and hops and analyzes the convergence of this model. Finally, the genetic algorithm is used to solve this mathematical weighted DV-hop (MW-GADV-hop) positioning model, the simulation results illustrate that the model construction is logical, and the positioning error of the model converges to 1/4R.

距离向量跳（DV-hop）是一种典型的定位算法。它通过检测节点之间的跳数来估计传感器节点的位置。为了提高定位精度，使用权重来估计位置，传统观点认为跳数越多，权重值越小。然而，定位误差、跳数和权重之间一直没有明确的数学模型。本文构建了权重和跳数之间的数学模型，并分析了该模型的收敛性。最后，利用遗传算法对该数学加权DV-hop（MW-GADV-hop）定位模型进行求解，仿真结果表明模型构建合理，模型定位误差收敛到1/ 4R。