<p>In recent years, significant progress has been made in the study of hyperbolic functions. Based on this research framework, a new cost function has been designed by integrating it with the standard cost function, and relevant quantization algorithms have been introduced. By combining the exponential function with the hyperbolic sine function, a robust adaptive filtering algorithm has been proposed. The nonlinear saturation characteristic of the output error is used to update the weight by the stochastic gradient descent method. At the same time, the characteristics of the hyperbolic sine function are used to ensure that the exponential hyperbolic sine robust adaptive filtering algorithm has good anti-impulse interference performance and improves the convergence speed. Building on this foundation, vector quantization is introduced to process input space data, leading to the development of a quantized exponential hyperbolic sine-based adaptive filtering algorithm, which effectively suppresses network size growth while maintaining robustness. The algorithm effectively suppresses the linear growth of the network and reduces the computational complexity. The simulation results show that the proposed algorithm has certain advantages in convergence speed, robustness and computational complexity in Mackey–Glass short-term chaotic time series prediction and unknown system identification.</p>