In this brief, a kernel adaptive filter based on the Student’s ${t}$ distribution in the reproducing kernel Hilbert space (RKHS) is presented, which is distinct from the traditional kernel adaptive filtering algorithms as follows: first, a Student’s ${t}$ reproducing kernel function is proposed to fight against the abrupt noise together with Gaussian noise depicted by the impulsive-Gaussian mixed noise model; and second, a Strengthened Surprise Criterion (SSC) is devised to reduce the size of the neural networks, which is utilized to implement the proposed Student’s ${t}$ -based kernel filter. The proposed algorithms are compared with the widely used KLMS and recently proposed KRLS-type filters in terms of the accuracy error under both Gaussian and abrupt noise. Experimental results show that the proposed Student’s ${t}$ -based kernel adaptive filter can improve the estimation accuracy at least by 20% while having more compact size of neural networks compared with the existed kernel adaptive algorithms.