Abstract: Aiming at the disadvantages of the traditional 3D DV-Hop positioning algorithm with large positioning errors and heavy calculation of machine learning and bionic algorithms, an improved unconstrained optimization 3D DV-Hop positioning algorithm is proposed. In terms of hop count, a two- communication radius strategy is adopted to calculate the minimum hop value. In terms of hop distance, a square cost function method is proposed to optimize the anchor node hop distance value, and its weighted hop distance value is used as the unknown node hop distance value. Finally, according to the unconstrained solution idea of the constraint problem, the weighted error is minimized and then solved. Through simulation comparison with traditional algorithms and various improved algorithms under three conditions, it is verified that the optimization algorithm can significantly reduce the positioning error under the condition of low calculation amount.

Key words: hop count optimization, hop-size weighting, unconstrained optimization, Lagrangian multiplier