Online Acoustic System Identification Exploiting Kalman Filtering and an Adaptive Impulse Response Subspace Model

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We introduce a novel algorithm for online estimation of Acoustic Impulse Responses (AIRs) which allows for fast convergence by exploiting prior knowledge about the fundamental structure of AIRs. The proposed method assumes that the variability of AIRs of an acoustic scene is confined to a low-dimensional manifold which is embedded in a high-dimensional space of possible AIR estimates. We discuss various approaches which exploit a training data set of AIRs, e.g., high-accuracy AIR estimates from the acoustic scene, to learn a local affine subspace approximation of the AIR manifold. The model is motivated by the idea of describing the generally nonlinear AIR manifold locally by tangential hyperplanes and its validity is verified for simulated data. Subsequently, we describe how the manifold assumption can be used to enhance online AIR estimates by projecting them onto an adaptively estimated subspace. Motivated by the assumption of manifolds being locally Euclidean, the parameters determining the adaptive subspace are learned from the nearest neighbor AIR training samples to the current AIR estimate. To assess the proximity of training data AIRs to the current AIR estimate, we introduce a probabilistic extension of the Euclidean distance which improves the performance for applications with non-white excitation signals. Furthermore, we describe how model imperfections can be tackled by a soft projection of the AIR estimates. The proposed algorithm exhibits significantly faster convergence properties in comparison to a high-performance state-of-the-art algorithm. Furthermore, we show an improved steady-state performance for speech-excited system identification scenarios suffering from high-level interfering noise and nonunique solutions.