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A novel fault-tolerant localization method for low-cost UAVs flying at constant altitude is proposed in this paper, which is based on measuring relative ranges from one UAV to other UAVs. Contrast to the traditional navigation methods of single aerial vehicle, like INS/GPS and SINS/GPS, the proposed method is more suitable for low-cost small-size UAVs because of its low requirement to the navigation device. Furthermore, its localization accuracy is higher than other methods for multi-UAV because the sharable information in multi-UAV network is made full of use. Similar to the principle of GPS, the method takes three other UAVs as the reference points of an UAV whose GPS receiver works improperly due to failure. Thus the UAV's location in 2D horizontal plane can be determined by using the relative ranges from the faulty UAV to the other three UAVs at known location in inertial coordinate system. In order to improve the accuracy of estimated location, a Kalman filter is designed, which can calculate the variance of observations in terms of horizontal dilution of positioning (HDOP) adaptively. Meanwhile, option of the reference points is also optimized in the paper. Simulation results in MatlabSimulink show the effectiveness of the proposed approach.