In this paper, we introduce a reflectometry which is used as localizing faults in an underground power cable. To increase the resolution and SNR, time-frequency domain reflectometry (TFDR) adopts the Gaussian enveloped linear chirp signal and Wigner-Ville distribution (WVD) based time-frequency cross-correlation (TFCC) method. However, the nonlinearity of WVD and the computational burden of 2D cross-correlation hinder the TFDR from being a field testing implementation. In order to reduce the nonlinearity and computational burden, we derive the second order time-varying AR model of Gaussian enveloped linear chirp signal and estimate the instantaneous frequency (IF) by using the weighted robust least squares (WRLS) estimator. Based on the estimated IF, the fault distance can be calculated. Computer simulations are conducted to verify the proposed method. The simulation result shows that the proposed method reduces the computational burden of time-frequency cross-correlation and the nonlinearity of WVD.