Kalman Filter Using a Third-Order Tensorial Decomposition of the Impulse Response

For system identification problems associated with long-length impulse responses, the recently developed decomposition-based technique that relies on a third-order tensor (TOT) framework represents a reliable choice. It is based on a combination of three shorter filters, which merge their estimates in tandem with the Kronecker product. In this way, the global impulse response is modeled in a more efficient manner, with a significantly reduced parameter space (i.e., fewer coefficients). In this paper, we further develop a Kalman filter based on the TOT decomposition method. As compared to the recently designed recursive least-squares (RLS) counterpart, the proposed Kalman filter achieves superior performance in terms of the main criteria (e.g., tracking and accuracy). In addition, it significantly outperforms the conventional Kalman filter, while also having a lower computational complexity. Simulation results obtained in the context of echo cancellation support the theoretical framework and the related advantages.