The chaotic spread spectrum time delay estimation is a challenge posed by low peak parameterization when using existing methods. Furthermore, more potential misclassification spots and poor signal-to-noise ratio (SNR) hinders cable fault signal time delay estimation. Therefore, this study proposes a new delay estimation approach that integrate the third-order cumulative one-dimensional slicing with quadratic correlation. In chaotic time delay estimation, this method was used to the Simulink simulation model. The results obtained via the simulation show that the proposed method could obtain good estimation results at lower SNR while suppressing the interference of correlated background and non-Gaussian noise when compared with existing basic intercorrelation and quadratic correlation methods. Its operation increases the absolute value of the primary peak-to-parameter ratio by more than 1.70 dB and decreases the false peak-to-fault point peak ratio by more than 0.133 when compared with the basic intercorrelation operation. This method introduces a novel technical approach for detecting fiber optic cable faults and their cable faults using chaotic spread spectrum detection.