Linking regularization and low-rank approximation for impulse response modeling

In the last years, nonparametric linear dynamical systems modeling has regained attention in the system identification world. In particular, the application of regularization techniques that were already widely used in statistics and machine learning, has proven beneficial for the estimation of the impulse response of linear systems. The low-rank approximation of the impulse response obtained by the truncated singular value decomposition (SVD) also leads to reduced complexity estimates. In this paper, the link between regularization and SVD truncation for finite impulse response (FIR) model estimation is made explicit. The SVD truncation is reformulated as a regularization problem with a specific choice of the regularization matrix. Both approaches regularization and SVD truncation) are applied on a FIR modeling example and compared with the classic prediction error method/maximum likelihood approach. The results show the advantage of these techniques for impulse response estimation.