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In wireless sensor networks, accurate node localization is essential for ensuring the precision of data collection. The DV-Hop algorithm, a popular range-free localization method, estimates distances between nodes by multiplying hop counts with average hop distances obtained through distance vector routing. However, this algorithm often experiences localization errors in randomly distributed network environments due to considerable inaccuracies in average hop distance calculations and the approximation of actual paths by straight-line paths. This paper introduces an enhanced DV-Hop localization algorithm, which constructs a mathematical model to optimize the mean square error of the average hop distance for any anchor node. This optimization corrects the average hop distance across the network, bringing it closer to the actual value, thus reducing errors and enhancing accuracy. Simulation results indicate that with 150 nodes, a 30% beacon node ratio and a 100-m communication range, the localization error of the improved FuncDV-Hop model decreased from 0.3916 to 0.1705, and the Root Mean Square Error (RMSE) decreased from 24.78m to 14.39m, thereby improving localization accuracy by 56.46%.

The conventional range-free positioning DV-Hop algorithm used in wireless sensor networks experience low positioning accuracy due to several factors. An improved algorithm: HSDV-Hop (Harmony Search DV-Hop) was proposed in this paper which provides high convergence speed and outstanding performance in solving global optimization problems as compared to the original DV-Hop algorithm. The improved algorithm establishes the optimization functions by the information of distance between the nodes and the location of beacon nodes, so the locations of unknown nodes are estimated. The results show that the proposed method can significantly improve positioning accuracy as compared to the original DV-Hop algorithm without increasing the sensor nodes hardware.