Adaptive System Identification with Regularized FIR Models

Abstract

Recent developments propose regularized FIR models as superior to other linear model identification methods. Different kernels exist to incorporate prior knowledge in form of regularization. In this work, we use the impulse response preserving (IRP) kernel which applies prior knowledge of the process pole(s) to the model estimation, yielding a gray-box approach. This concept is extended to deal with time-variant systems in an online manner. Leaky recursive least squares (LRLS), leaky least mean squares (LLMS) and non-fading regularized recursive least squares (NFRA-RLS) are used for this purpose. To increase the interpretability of the regularization strength a new scaling factor is proposed including knowledge about the effective number of data points. A simulation study of a linear time-variant process shows that only the LRLS and LLMS algorithm are able to perform the intended gray-box approach.