  A different route to identification of time-invariant linear systems has been
recently proposed which does not require committing to a specific parametric
model structure. Impulse responses are described in a nonparametric Bayesian
framework as zero-mean Gaussian processes. Their covariances are given by the
so-called stable spline kernels encoding information on regularity and BIBO
stability. In this paper, we demonstrate that these kernels also lead to a new
family of radial basis functions kernels suitable to model system components
subject to disturbances given by filtered white noise. This novel class, in
cooperation with the stable spline kernels, paves the way to a new approach to
solve missing data problems in both discrete and continuous-time settings.
Numerical experiments show that the new technique may return models more
predictive than those obtained by standard parametric Prediction Error Methods,
also when these latter exploit the full data set.
