To address the issue of significant time delay estimation errors in pipeline leakage localization, which stem from the low signal-to-noise ratio (SNR) of detection signals and the existence of diverse noise interferences, a cascaded arctangent least mean square (LMS) adaptive time delay estimation method is proposed. First, the arctangent function is incorporated into the LMS adaptive filter to improve the filter’s robustness against non-Gaussian noise. Next, two channels of leakage signals are fed into the first stage adaptive filter to suppress correlated Gaussian noise. Subsequently, the two output signals from the first stage filter serve as the input and desired signals for the second stage filter to further eliminate noise. Finally, the time delay estimation is obtained by analyzing the weight coefficient curve of the second stage filter. In the simulation, under the influence of correlated Gaussian noise and non-Gaussian noise with three distinct distributions, when compared with the cross-correlation method, the arctangent LMS method, and the cascaded LMS method, the proposed method exhibits the optimal noise suppression performance, and the signal correlation peak is the most pronounced. As the SNR gradually declines, this method can attain superior time delay estimation accuracy at a lower SNR. Finally, the effectiveness and practicality of the proposed method are further validated through an actual pipeline leakage location experiment. Under the influence of noise, the method can precisely locate the leakage point, with an average relative location error of 2.31% and a standard deviation of 2.08%.