The incipient faults which mainly occur due to the electric arc occurrence in the power cables with insulation defects are hardly detectable by the conventional protective relays, and over time can develop into a permanent fault in the system. Employing Kalman filter, this paper puts forward a method to detect the incipient faults and to discriminate them from other similar incidents in the power system. The proposed method is established on the comparison between the waveform of the measured voltage and fundamental component of the measured voltage, estimated by Kalman filter algorithm in the sending end of the cable during the fault. Employing the difference between the measured and estimated waveforms, the incipient fault detection and discrimination are carried out within two stages. In the first stage, event detection is relegalized by comparing the standard deviation of the obtained error with a certain threshold. The second stage is conducted to find the incipient fault based on the non-attenuating characteristic and quasi-periodic nature of the incipient fault. The feasibility of the proposed method is verified through computer simulation using four different electric arc models and also the acquired experimental data from real incipient faults.