Handling of time delays in system identification with regularized FIR models

Abstract System identification with finite impulse response (FIR) models has been recently revised by introducing specific forms of regularization in the estimation. By utilizing prior knowledge of the dynamic process under investigation different kernels for regularization can be derived. However, the dynamical processes considered are mainly restricted to time-delay free systems. Therefore, in this paper we propose two novel methods to handle the time-delay case. Both methods incorporate the time-delay estimation in the hyperparameter optimization of the regularized FIR models. The first method is built on a single kernel (SK) and the second utilizes a multiple kernel (MK) approach. Simulations on different dynamical systems show the superior behavior of both methods in comparison to standard regularization methods, whereupon the MK outperforms the SK approach.