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In this paper the algorithm KSCP (KLMS with Surprise Criterion and Parallel Hyperslab Projection Along Affine Subspaces) for adaptive estimation of nonlinear systems is proposed. It is based on the combination of: the reproducing kernel to deal with the high complexity of nonlinear systems; -the parallel hyperslab projection along affine subspace learning algorithm, to deal with adaptive nonlinear estimation problem; the kernel least mean square with surprise criterion that uses concepts of likelihood and bayesian inference to predict the posterior distribution of data, guaranteeing an appropriate selection of data to the dictionary at low computational cost, to deal with the exponential growth of the dictionary, as new data arrives. The proposed algorithm offers high accuracy estimation and high velocity of computation, characteristics that are very important in estimation and tracking online applications.

Nonlinear Adaptive Estimation by Kernel Least Mean Square with Surprise Criterion and Parallel Hyperslab Projection along Affine Subspaces Algorithm