Integrity of the control and instrumental cables in nuclear power plant is important to maintain the stability of the nuclear power plants. In order to diagnose the integrity of the cables, the diagnostic methods based on reflectometry have been studied. The reflectometry is a non-destructive method and it is applicable to diagnose the live cables. We introduce a Gaussian enveloped linear chirp reflectometry to diagnose the cables in the nuclear power plants. In this paper, we estimate the instantaneous frequency of the Gaussian enveloped linear chirp signal by using the weighted robust least squares filtering to localize the impedance discontinuities in the class 1E instrumental cable.