In the sensor networks, the algorithm using range difference of arrival data is one of the passive localization methods for searching the target location. The previous works addressed this problem with a cost function built with a constrained equation. The constraint was defined by the geometrical relation between the sensors to minimize estimation errors. However, the constraint equation may cause a computational burden. We diminish the computational burden with a robust least square algorithm which does not use the constraint. Instead, the proposed method compensates the estimation error with stochastic information. In the simulation, the results shows the compensation effect with the proposed algorithm and the estimation of the moving target position with the recursive formula based on the no additional computation.