Constructive state space model induced kernels for regularized system identification ?

There are two key issues for the kernel-based regularization method: the kernel structure design and the hyper-parameter estimation. In this contribution, we introduce a new family of kernel structures based on state space models. It has more flexible and more general structure, and includes some of stable spline kernels and diagonal correlated kernels as special cases. We also tested a different method for the hyper-parameter estimation by maximizing a profile marginal likelihood and examined three methods dealing with the initialization. Monte Carlo simulations show that the tested kernels are on the average a bit better than the tuned correlated kernel and the profile marginal likelihood maximization and the pre-windowing method work well for hyper-parameter estimation and initialization.