Efficient algorithms for large scale linear system identification using stable spline estimators

A new nonparametric approach for system identification has been recently proposed where, in place of postulating parametric classes of impulse responses, the estimation process starts from an infinite-dimensional space. In particular, the impulse response is seen as the realization of a zero-mean Gaussian process. Its covariance, the so called stable spline kernel, encodes information on system stability and depends on few hyperparameters estimated from data via marginal likelihood optimization. This approach has been proved to compare much favorably with classical parametric methods but, in data rich situations, a possible drawback may be represented by its computational complexity which scales with the cube of the number of available samples. In this work we design a new computational strategy which may reduce significantly the computational load required by the stable spline estimator, thus extending its practical applicability also to large-scale scenarios.