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This paper presents an application of a cable fault localization using an instantaneous frequency (IF) estimation in the Gaussian-enveloped linear chirp (GELC) reflectometry. The GELC reflectometry sends a GELC signal into a cable and measures the reflected signals from the faults. A fault distance is calculated by the estimated time delay between the incident and reflected signals. The cross-correlation method for estimating time delay can be affected by the propagation characteristics of the cable and this results in the time offset in the time delay estimation. To reduce the time offset, we propose an IF-estimation-based fault-localization method. The proposed method uses the statistical-model-based detection with the hidden Markov model and the constrained Kalman filtering for estimating the IF of the GELC. We can obtain the time delay between the incident and reflected signals by calculating the time delay between the center frequencies corresponding to the incident and reflected signals, respectively. Experimental results show that the proposed method estimates the accurate fault distance without the compensation term for the time offset. Therefore, the proposed method is an appropriate method for estimating the fault localization in a cable.