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This paper presents a kernelized version of the extended recursive least squares (EX-KRLS) algorithm which implements for the first time a general linear state model in reproducing kernel Hilbert spaces (RKHS), or equivalently a general nonlinear state model in the input space. The center piece of this development is a reformulation of the well known extended recursive least squares (EX-RLS) algorithm in RKHS which only requires inner product operations between input vectors, thus enabling thedoi:10.1109/tsp.2009.2022007 fatcat:kupa7zogrzcnbn5jwx2dsg256y