Set-membership kernel adaptive algorithms

Abstract

In the last decade, a considerable research effort has been devoted to developing adaptive algorithms based on kernel functions. One of the main features of these algorithms is that they form a family of universal approximation techniques, solving problems with nonlinearities elegantly. In this paper, we present data-selective adaptive kernel normalized least-mean square (KNLMS) algorithms that can increase their learning rate and reduce their computational complexity. In fact, these methods deal with kernel expansions, creating a growing structure also known as the dictionary, whose size depends on the number of observations and their innovation. The algorithms described herein use an adaptive step-size to accelerate the learning and can offer an excellent tradeoff between convergence speed and steady state, which allows them to solve nonlinear filtering and estimation problems with a large number of parameters without requiring a large computational cost. The data-selective update scheme also limits the number of operations performed and the size of the dictionary created by the kernel expansion, saving computational resources and dealing with one of the major problems of kernel adaptive algorithms. A statistical analysis is carried out along with a computational complexity analysis of the proposed algorithms. Simulations show that the proposed KNLMS algorithms outperform existing algorithms in examples of nonlinear system identification and prediction of a time series originating from a nonlinear difference equation.

Variable-mixing parameter quantized kernel robust mixed-norm algorithms for combating impulsive interference

“…Although the above-mentioned kernel adaptive filters achieve improved performance, they are not suitable for online applications, as their structures grow linearly with the number of processed patterns. In the past years, some sparsification techniques that constrain the growth of the network size were proposed [5,6,16,17,18,19,20]. In 2012, the quantized KLMS (QKLMS) algorithm has been successfully applied to static function estimation and time series prediction [17].…”

Set-membership adaptive filtering algorithm based on hyperbolic tangent kernel fractional p-power method

“…In order to improve and perfect the performance of kernel adaptive filtering algorithm, SM theory can be used for reference. In fact, the set membership theory has been applied in the traditional adaptive filter [11][12][13][14]. The main purpose of this concept is to reduce the network size of the kernel and to provide adaptive step size for adaptive algorithms.…”