<p>The Hyperbolic secant function in adaptive filtering can enhance the robustness of the algorithm, similar to the filtering effects of the Gaussian function and Versoria function. Specifically, it suppresses updates of the weight vector when system errors are large, thereby effectively resisting impulse signal interference. Inspired by the above, this paper introduces the hyperbolic secant function into the kernel space, establishes the maximum hyperbolic secant metric criterion using the generalized hyperbolic secant function, then leverages the standard versoria function to develop a variable scale factor structure in an error-weighted manner, and proposes the kernel maximum hyperbolic secant algorithm. The algorithm innovatively combines the nonlinear processing capability of the kernel method with the impulse suppression property of the hyperbolic secant function, and balances the convergence speed and steady-state performance via an adaptive parameter adjustment mechanism. Experimental results in nonlinear system identification, acoustic echo cancellation, and Mackey-Glass time series prediction demonstrate that the kernel maximum hyperbolic secant adaptive filtering algorithm exhibits better robustness than other algorithms.</p>