Ultrasonic signals will be generated when high voltage equipment is partially discharged. In order to de-termine the location of partial discharge, the time difference between ultrasonic signal and sensor can be used. In this paper, Alpha stable distribution is used to model noisy ultrasonic signals collected during actual partial discharge, and a nonlinear transformation-covariant time difference estimation method is proposed. Firstly, the signal-to-noise ratio can be improved to a certain extent by preprocessing the noisy signal based on the arctangent nonlinear transformation. Then, the covariant correlation function is used to measure the similarity of the two signals arriving at the sensor, and according to the position of the peak value of the covariant correlation function, the time difference information of signal arrival is obtained. On the basis of theoretical analysis, the experimental results of computer simulation are discussed and summarized. Com-pared with generalized correlation method and covariant algorithm, the proposed method is more suitable for TDOA estimation of PD ultrasonic signals in low SNR and impulsive noise environment.