This paper is a continuation and extension of our previ- ous research where kernel normalized mixed-norm (KNMN) algorithm, a combination of the kernel trick with the mixed-norm strategy, was proposed to demonstrate superior performance for system identification under non-Gaussian environment. Meanwhile, we also introduced a naive adaptive mixing parameter (AMP) updating mechanism to make KNMN more robust under nonstationary scenarios. The main contributions of this paper are threefold: firstly, the p-norm is substituted for the 4- norm in the cost function, which can be viewed as a generalized version to the form of mixed-norms; secondly, instead of using the original AMP proposed in our previous work, a novel time-varying AMP is employed to provide better tracking behavior to the nonstationarity; and thirdly, the mean square convergence analysis is conducted, where the second moment behavior of weight error vector is elaborately studied. Simulations are conducted on two benchmark system identification problems, and different kinds of additive noises are added respectively to verify the effectiveness of improvements. © Springer International Publishing Switzerland 2015.