An insightful overview of the wiener filter for system identification

Abstract

Efficiently solving a system identification problem represents an important step in nu-merous important applications. In this framework, some of the most popular solutions rely on the Wiener filter, which is widely used in practice. Moreover, it also represents a benchmark for other related optimization problems. In this paper, new insights into the regularization of the Wiener filter are provided, which is a must in real-world scenarios. A proper regularization technique is of great importance, especially in challenging conditions, e.g., when operating in noisy environments and/or when only a low quantity of data is available for the estimation of the statistics. Different regular-ization methods are investigated in this paper, including several new solutions that fit very well for the identification of sparse and low-rank systems. Experimental results support the theoretical developments and indicate the efficiency of the proposed techniques.