A Decomposition-Based Kalman Filter for the Identification of Acoustic Impulse Responses

The identification of acoustic impulse responses usually involves long length adaptive filters, with hundreds or even thousands of coefficients. This issue raises significant challenges in terms of both the computational complexity and convergence features. Recently, a decomposition-based solution using the Kronecker product and low-rank approximations was proposed in this context, by exploiting the intrinsic nature of the acoustic impulse responses. These systems are characterized by early reflections and late reverberation, each of these components having different characteristics that should be considered. In this paper, we propose a Kalman filter following this approach, which outperforms the previously developed solution based on the recursive least-squares algorithm. Simulations performed in the framework of acoustic echo cancellation support the performance features of the proposed algorithm.