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In this paper we present a novel algorithm to identify LPV systems with affine parameter dependence. Ideas from closed-loop LTI subspace identification are used to formulate the input-output behavior of an LPV system. From this input-output behavior the LPV equivalent of the Markov parameters can be estimated. We show that with this estimate the product between the observability matrix and state sequence can be reconstructed and an SVD can be used to estimate the state sequence and consequently the system matrices. The curse of dimensionality in subspace LPV identification will appear and the kernel method is proposed as a partial remedy. The working of the algorithm is illustrated with two simulation examples.