Due to the short-term large value characteristics of impulsive noise, the signals parameter estimation method based on Gaussian hypothesis cannot effectively estimate parameters in impulsive noise environment. To solve this problem, this paper proposes an LFM signals parameter estimation method based on Sigmoid-CFRFT by using alpha stable distribution to simulate random impulsive noise. Firstly, an improved Sigmoid function is established to prove that after this nonlinear transformation, the 2nd moment of the signal changes from unbounded to bounded, and the phase information of the signal remains unchanged. Secondly, the transformed signal is discrete-time CFRFT, a mathematical optimization model for LFM signals parameter estimation is established, and the water cycle algorithm is used to search for the optimal value point. Finally, a correction method for non-standard SαS distribution noise is used, and the performance of parameter estimation under standard and non-standard distribution is analyzed. The simulation results show that the proposed method can not only effectively suppress the influence of impulsive noise on the fractional spectral characteristics of LFM signals, but also achieve high-precision estimation of signals parameters with low signal-to-noise ratio. Compared with the existing parameter estimation methods based on nonlinear transformation, the proposed method has better accuracy, stability and noise robustness.