The identification of long-length impulse responses represents a challenge in the context of many applications, like echo cancellation. Recently, the problem has been addressed in the framework of low-rank systems, using a decomposition of the impulse response based on the nearest Kronecker product and low-rank approximations. As a result, the original system identification problem that involves a long-length finite impulse response filter is reshaped as a combination of two (much) shorter filters, which leads to significant advantages. In this context, the benchmark Wiener filter can be formulated in terms of an iterative algorithm, where the estimates of the two component filters are sequently updated. However, matrix inversion operations are required within this algorithm. In this article, we develop a new version of the decomposition-based iterative Wiener filter, which relies on the conjugate gradient (CG) method and avoids matrix inversion. Simulations performed in the framework of echo cancellation indicate the good performance of the proposed solution, which outperforms the conventional Wiener filter (implemented using CG updates) and inherits the advantages of the decomposition-based approach.

The identification of room acoustic impulse responses represents a challenging problem in the framework of many important applications related to the acoustic environment, like echo cancellation, noise reduction, and microphone arrays, among others. In this context, the main issues are related to the long length of such impulse responses and their time-variant nature. These raise significant difficulties in terms of the convergence rate, computational complexity, and accuracy of the solution. Recently, a decomposition-based approach was developed for the identification of low-rank systems, which can also be applied (to some extent) for the identification of acoustic impulse responses. This approach exploits the nearest Kronecker product decomposition of the impulse response and solves a high-dimension system identification problem using a combination of low-dimension solutions (provided by shorter filters), thus gaining in terms of both performance and complexity. Nevertheless, it does not consider the intrinsic nature of the room acoustic impulse responses, which contain specific components (e.g., early reflections and late reverberation) that can be very different in nature. In this paper, we propose an improved decomposition-based method (via the Kronecker product) that takes into account these specific components and processes them separately, in order to better exploit their important low-rank features. Following this approach, an iterative Wiener filter is firstly developed, followed by a recursive least-squares (RLS) algorithm designed in the same framework. Both solutions outperform the conventional benchmarks, i.e., the conventional Wiener filter and the RLS algorithm, respectively. Moreover, they achieve superior performances as compared to the recently developed versions based on the nearest Kronecker product decomposition, also owning lower computational complexities than their previous counterparts. Simulations are performed in the framework of acoustic echo cancellation and the obtained results support the performance features of the proposed algorithms.

In this paper, we develop the Kalman filter for the identification of bilinear forms. In this framework, the bilinear term is defined with respect to the impulse responses of a spatiotemporal model, which resembles a multiple-input/single-output system. Recently, the identification of such bilinear forms was addressed in terms of the Wiener filter and conventional adaptive algorithms, i.e., least-mean-square and recursive least-squares. In this work, apart from the derivation of the Kalman filter tailored for the identification of bilinear forms, a simplified (i.e., low complexity) version of the algorithm is also presented. Simulation results support the theoretical findings and indicate the good performance of the proposed solutions.