Abstract: The time difference of arrival(TDOA) for radiation source target in the air with unmanned aerial vehicle(UAV) carrying positioning equipment in this paper, which can effectively avoid the influence of ground station geometry factors and errors caused by non-line-of-sight(NLOS) propagation. In this positioning scenario, aiming at the flight path minimization problem with positioning accuracy guarantee, this paper mainly considers the problem of minimizing flight path under the condition of ensuring positioning accuracy. And the lower bound of positioning error expectation is derived, the flight path optimization model in the process of minimizing the lower bound is given, and two numerical approximate optimization algorithms for the model are proposed. At the last of this paper, the simulation experiment compares the performance of the two algorithms in different scenarios on path optimization and the effect on positioning accuracy when the flight distance is limited, both of them have well performance at last