  We consider the problem of sequential estimation of the unknowns of
state-space and deep state-space models that include estimation of functions
and latent processes of the models. The proposed approach relies on Gaussian
and deep Gaussian processes that are implemented via random feature-based
Gaussian processes. In these models, we have two sets of unknowns, highly
nonlinear unknowns (the values of the latent processes) and conditionally
linear unknowns (the constant parameters of the random feature-based Gaussian
processes). We present a method based on particle filtering where the
parameters of the random feature-based Gaussian processes are integrated out in
obtaining the predictive density of the states and do not need particles. We
also propose an ensemble version of the method, with each member of the
ensemble having its own set of features. With several experiments, we show that
the method can track the latent processes up to a scale and rotation.
