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Two approaches for on-line Gaussian process regression with low computational and memory demands are proposed. The first approach assumes known hyperparameters and performs regression on a set of basis vectors that stores mean and covariance estimates of the latent function. The second approach additionally learns the hyperparameters on-line. For this purpose, techniques from nonlinear Gaussian state estimation are exploited. The proposed approaches are compared to state-of-the-art sparse Gaussian process algorithms.