Análise do Comportamento Estocástico do Algoritmo KLMS para um Sinal de Entrada Correlacionado

The Kernel Least-Mean-Square (KLMS) algorithm is a popular algorithm for adaptive nonlinear filtering due to its simplicity and robustness. In kernel-based adaptive filtering with finite order models, the statistics of the linear filter depend on the kernel and its parameters, as well as, on the input vector dictionary update rule that defines the Hilbert space in which the filter operates. The existence of the highly nonlinear relationships between the adaptive filter parameters and the performance criteria makes the design of these filters an almost impossible task without the help of analytical models that predict their performance. Theoretical analyses of the stochastic behavior of the KLMS have already been performed assuming fixed dictionaries and variable dictionaries under the consideration that the temporal sequence of the input vectors is statistically independent. This paper studies the KLMS mean-weight be- havior with Gaussian kernel for variable dictionaries and time- correlated input vectors.