An inference method for Gaussian process augmented state-space models are\npresented. This class of grey-box models enables domain knowledge to be\nincorporated in the inference process to guarantee a minimum of performance,\nstill they are flexible enough to permit learning of partially unknown model\ndynamics and inputs. To facilitate online (recursive) inference of the model a\nsparse approximation of the Gaussian process based upon inducing points is\npresented. To illustrate the application of the model and the inference method,\nan example where it is used to track the position and learn the behavior of a\nset of cars passing through an intersection, is presented. Compared to the case\nwhen only the state-space model is used, the use of the augmented state-space\nmodel gives both a reduced estimation error and bias.\n