An RLS algorithm for the identification of bilinear forms

Bilinear systems are involved in many interesting applications, especially related to the approximation of nonlinear systems. In this context, the bilinear term is usually defined in terms of an input-output relation (i.e., with respect to the data). Recently, a different approach has been introduced, by defining the bilinear term with respect to the impulse responses of a spatiotemporal model, which resembles a multiple-input/single-output (MISO) system. Also, in this framework, the Wiener filter has been involved to address the identification problem of these bilinear forms. Since the Wiener filter may not be always very efficient or convenient to use in practice, we propose in this paper an adaptive filtering approach based on the recursive least-squares (RLS) algorithm. Simulations performed in the context of system identification (based on the MISO system approach) indicate the appealing performance of this algorithm.