Abstract
Nowadays, the kernel methods are increasingly developed, they are a significant source of advances, not only in terms of computational cost but also in terms of the obtained efficiencies in solving complex tasks, they are founded on the theory of reproducing kernel Hilbert spaces (RKHS). In this paper, we propose an algorithm for recursive identification of finite impulse response (FIR) nonlinear systems, whose outputs are detected by binary value sensors. This algorithm is based on a nonlinear transformation of the data using a kernel function. This transformation performs a basic change that allows the data to be projected into a new space where the relationships between the variables are linear. To test the accuracy of the proposed algorithm, we have compared it with another algorithm proposed in the literature, for that, we employ the practical frequency selective fading channel, called Broadband Radio Access Network (BRAN). Monte Carlo simulation results, in noisy environment and for various data length, demonstrate that the proposed algorithm can give better precision.
Highlights
The field of systems identification has recently become an active area of research that has attracted the attention of a considerable number of researchers [1,2,3,4,5]
The kernel methods are increasingly developed, they are a significant source of advances, in terms of computational cost and in terms of the obtained efficiencies in solving complex tasks, they are founded on the theory of reproducing kernel Hilbert spaces (RKHS)
We propose an algorithm for recursive identification of finite impulse response (FIR) nonlinear systems, whose outputs are detected by binary value sensors
Summary
The field of systems identification has recently become an active area of research that has attracted the attention of a considerable number of researchers [1,2,3,4,5]. Kernel methods are increasingly developed, they are a significant source of advances, in terms of computational cost and in terms of the obtained efficiencies in solving complex tasks. As these methods largely determine the efficiency of the treatments, by their ability to reveal existing similarities in the processed data. They are based on a central principle called “kernel trick”, exploited for the first time with the Support Vector Machine (SVM)[6, 7], used to transform numerous linear dimensionality reduction algorithms into non-linear algorithms [8]. Some simulations to assess the performance of the proposed algorithm are shown in Section 6 and, Section 7 concludes the paper
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