Improved Affine Projection Algorithm for the Identification of Multilinear Forms

In this paper, we address the multilinear system identification problem in the framework of multiple-input single-output (MISO) systems. The large parameter space of such systems can be reshaped into a tensorial form. In this context, the affine projection algorithm (APA) is an appealing solution, especially with correlated input signals. The recently developed tensor-based APA (APA-T) combines the solutions provided by the individual (shorter) filters, thus reformulating a high-dimension system identification problem based on low-dimension problems. Following the development of the APA-T, we propose in this paper an improved version of this algorithm, where different projection orders are used for the individual filters. This approach leads to a better compromise between performance and complexity.