Local module identification in dynamic networks using regularized kernel-based methods

In order to identify a specific system (module) of interest embedded in a dynamic network, one typically has to formulate a multi-input single-output (MISO) identification problem which requires to identify all modules in the MISO structure, and determine their model order. While the former task poses the problem of estimating a large number of parameters that are of no interest to the experimenter, the latter task may result computationally challenging in large-size networks. To avoid these issues and increase the accuracy of the identified module of interest, we use 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 vectors with covariance matrix (kernel) given by the first-order stable spline kernel, accounting also for the noise model affecting the output of the target model. Using an Empirical Bayes (EB) approach, the target-module parameters are estimated by maximizing the marginal likelihood of the module output. The related optimization problem is solved using the Expectation-Maximization (EM) algorithm. Numerical experiments illustrate the potentials of the introduced method in comparison with the state-of-the-art techniques for local identification.