Characterized by its impulsive features, high intensity, and non-Gaussian properties, impulsive noise disrupts the peak characteristics of linear frequency modulated signals in the fractional Fourier domain. This degrades the performance of parameter estimation algorithms based on the fractional Fourier transform, causing significant estimated biases in non-Gaussian noise environments. To address this issue, a tensor-based parameter estimation method for LFM signals was proposed in impulsive noise environments. First, the noisy LFM signal is segmented by a sliding window along the time dimension to construct a three-dimensional tensor representation. Next, a denoising model is developed via higher-order singular value decomposition, where core tensor components are extracted from tensor signals by applying an energy thresholding criterion. Subsequently, an FRFT-based LFM parameter estimation model is established and solved by the dream optimization algorithm (DOA). Furthermore, the DOA optimization process is iteratively alternated with the tensor denoising procedure. Finally, the chirp rate and initial frequency are estimated by locating the peak position in the FRFT domain. Experimental results demonstrate that tensor representation effectively suppresses impulsive noise compared to the baseline FRFT method. Experimental results demonstrate that when the stability parameter α≥0.8 and GSNR=-4 dB, the RMSE of chirp rate estimated by the proposed method remains stably below 0.1, significantly outperforming other comparative methods. This validates the stronger noise resistance and superior generalization capability of the tensor representation method on both simulated and real-world data.