Accurate measurement of line-of-sight angle rate with a strapdown seeker is not achievable, and the presence of measurement outliers can degrade the accuracy of estimation techniques based on Kalman filters. To address this challenge, we propose a robust iterative cubature filtering framework that incorporates a linear regression model to mitigate the impact of wide-field disturbances and target surface reflections, which introduce strong non-Gaussian noise in the observation system. Specifically, for line-of-sight angular rate estimation, we employ a Kalman filter and replace the Huber function with the Cauchy function. Numerical simulations are conducted to evaluate the performance of the proposed method, the Huber-based robust iterative cubature filter, and the cubature Kalman filter under identical conditions. The simulation results demonstrate the effectiveness of the proposed method in accurately estimating the line-of-sight angular rate under Gaussian noise. Even when faced with strong non-Gaussian noise, our suggested method shows exceptional resilience by retaining high estimate accuracy.