Hybrid-Frequency-Resolution Adaptive Kalman Filter for Online Identification of Long Acoustic Responses With Low Input-Output Latency

Online acoustic system identification is one of the most challenging tasks for adaptive filters. Along with the desired accuracy in applications such as acoustic echo cancellation, it bears requirements of accommodating high-order systems (i.e., long acoustic impulse responses) while maintaining low input-output latency. These simultaneous requirements by now have been frequently addressed by multi-delay filters (MDF) a.k.a. partitioned-block frequency-domain adaptive filters (PBFDAF) with sectioned filter representation. In this paper, on the contrary, we consider a monolithic representation of high-order acoustic systems and yet constrain to identification with low input-output latency. For block-frequency-domain processing this approach therefore entails a hybrid frequency resolution with respect to system input and output. Further considering a first-order state-space temporal evolution of the acoustic system, we can rely on the Kalman filter framework for derivation of a hybrid-frequency-resolution adaptive Kalman filter (HyKF) algorithm for acoustic system identification with inherent robustness to double-talk and acoustic noise. Given the broad landscape of existing adaptive filter algorithms, the HyKF here turns out to be an entity of its own. Experimentally, it is demonstrated that the HyKF solution considerably improves rate of convergence and system accuracy over former MDF and former frequency-domain adaptive Kalman filters (FDKF). This development is motivated by recently increased attention for employing adaptive filters in deep learning frameworks for acoustic echo control.