Generalized Kernel Normalized Mixed-Norm Algorithm: Analysis and Simulations
This paper is a continuation and extension of our previous 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 \(\ell _p\)-norm is substituted for the \(\ell _4\)-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.
KeywordsKNMN algorithm Generalized KNMN algorithm Adaptive mixing parameter System identification
This work is supported partially by the National Natural Science Foundation of China (no.61402122) and the 2014 Ph.D. Recruitment Program of Guizhou Normal University.
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