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The performance of adaptive estimators that employ embedding in reproducingkernel Hilbert spaces (RKHS) depends on the choice of the location of basiskernel centers. Parameter convergence and error approximation rates depend onwhere and how the kernel centers are distributed in the state-space. In thispaper, we develop the theory that relates parameter convergence andapproximation rates to the position of kernel centers. We develop criteria forchoosing kernel centers in a specific class of systems - ones in which thestate trajectory regularly visits the neighborhood of the positive limit set.Two algorithms, based on centroidal Voronoi tessellations and Kohonenself-organizing maps, are derived to choose kernel centers in the RKHSembedding method. Finally, we implement these methods on two practical examplesand test their effectiveness.

Kernel Center Adaptation in the Reproducing Kernel Hilbert Space Embedding Method