System identification is instrumental in various tasks of acoustics, including acoustic measurement and acoustic echo cancellation. Adaptive filtering is proven to be successful for the identification of linear parts with variable impulse responses. Neural network frameworks are recently considered for nonlinear modeling, but the desire for variable system identification on individual sequences may be incompatible with the general concept of training across batch data. This paper therefore pursues architectures mixed from trainable and non-trainable adaptive sections. By seamlessly integrating adaptive FIR filters into end-to-end neural network architectures, the desired flexibility in the network is achieved. In-network adaptivity is here implemented as a recurrent computational layer according to the normalized least mean-square (NLMS) algorithm. Altogether six architectures are explored in order to study what part of a system better relies on training or adaptation. The proposed implementations are thus verified on synthetic data with dedicated variations of speech or noise input, linear or nonlinear system components, and fixed or variant acoustic impulse responses.

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.