  In order to identify one system (module) in an interconnected dynamic
network, one typically has to solve a Multi-Input-Single-Output (MISO)
identification problem that requires identification of all modules in the MISO
setup. For application of a parametric identification method this would require
estimating a large number of parameters, as well as an appropriate model order
selection step for a possibly large scale MISO problem, thereby increasing the
computational complexity of the identification algorithm to levels that are
beyond feasibility. An alternative identification approach is presented
employing regularized kernel-based methods. Keeping a parametric model for the
module of interest, we model the impulse response of the remaining modules in
the MISO structure as zero mean Gaussian processes (GP) with a covariance
matrix (kernel) given by the first-order stable spline kernel, accounting for
the noise model affecting the output of the target module and also for possible
instability of systems in the MISO setup. Using an Empirical Bayes (EB)
approach the target module parameters are estimated through an
Expectation-Maximization (EM) algorithm with a substantially reduced
computational complexity, while avoiding extensive model structure selection.
Numerical simulations illustrate the potentials of the introduced method in
comparison with the state-of-the-art techniques for local module
identification.
