Identification of Multilinear Forms with the Tensorial Kalman Filter

The multilinear system identification problem is usually approached with tensors. Recent works have addressed this problem using the well-known Wiener filter, as well as some conventional adaptive algorithms, such as the least-mean-square and recursive least-squares. In this paper, we derive a tensorial Kalman filter designed for the identification of multilinear forms. Furthermore, based on steady-state approximations, we also develop a simplified version of this algorithm, with lower computational complexity. Experimental results support the theoretical findings, highlighting the good performance of the proposed solutions.