Abstract
System identification problems are always challenging to address in applications that involve long impulse responses, especially in the framework of multichannel systems. In this context, the main goal of this review paper is to promote some recent developments that exploit decomposition-based approaches to multiple-input/single-output (MISO) system identification problems, which can be efficiently solved as combinations of low-dimension solutions. The basic idea is to reformulate such a high-dimension problem in the framework of bilinear forms, and to then take advantage of the Kronecker product decomposition and low-rank approximation of the spatiotemporal impulse response of the system. The validity of this approach is addressed in terms of the celebrated Wiener filter, by developing an iterative version with improved performance features (related to the accuracy and robustness of the solution). Simulation results support the main theoretical findings and indicate the appealing performance of these developments.
Highlights
Solving a system identification problem represents a key step in many important real-world applications [1,2]
A useful topic is related to bilinear forms, which have been addressed in the literature in different ways and contexts [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]; most often they are related to approximating nonlinear systems
We focus on a different approach by defining the bilinear term with respect to the impulse responses of a spatiotemporal model, in the context of MISO systems
Summary
Solving a system identification problem represents a key step in many important real-world applications [1,2]. We focus on a different approach by defining the bilinear term with respect to the impulse responses of a spatiotemporal model, in the context of MISO systems. An iterative Wiener filter for such bilinear forms was developed in the framework of a MISO system identification problem [24]. In the previously mentioned approaches, the spatiotemporal impulse response of the MISO system is considered perfectly separable, and its components are combined using the Kronecker product The identification of such linearly separable systems can be efficiently exploited in the frameworks of different applications, such as source separation [31,32], array beamforming [33,34], and object recognition [35,36].
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