Online Supervised Acoustic System Identification Exploiting Prelearned Local Affine Subspace Models

Abstract

In this paper we present a novel algorithm for improved block-online supervised acoustic system identification in adverse noise scenarios by exploiting prior knowledge about the space of Room Impulse Responses (RIRs). The method is based on the assumption that the variability of the unknown RIRs is controlled by only few physical parameters, describing, e.g., source position movements, and thus is confined to a low-dimensional manifold which is modelled by a union of affine subspaces. The offsets and bases of the affine subspaces are learned in advance from training data by unsupervised clustering followed by Principal Component Analysis. We suggest to denoise the parameter update of any supervised adaptive filter by projecting it onto an optimal affine subspace which is selected based on a novel computationally efficient approximation of the associated evidence. The proposed method significantly improves the system identification performance of state-of-the-art algorithms in adverse noise scenarios.

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

“…Finally, we discuss various affine subspace-based approaches to locally approximate the manifold. Note that a straightforward extension of the subsequently described MISO AIR models to Multiple-Input Multiple-Output (MIMO) systems is obtained by stacking the respective MISO AIR vectors to an extended vector [21].…”

“…In [21] it is proposed to cluster the training data into I disjoint local data sets U i by the k-means algorithm [31,32]. Subsequently, each local training data set U i is used to compute a local affine subspace M i by the PCA approach described in Sec.…”

“…We suspect that the NN model generalizes poorly to AIRs in between the training samples as the respective subspace is zero-dimensional, i.e., condensed to a single element. To remedy this limitation we suggest to remove the condition of non-overlapping local training data sets U i as used in [21]. In particular we propose to estimate the affine subspace parameters from the K NN training samples tr to the optimum AIR vector .…”

“…Recently, besides adaptation control, the exploitation of prior knowledge about the structure of AIRs has been successfully used to deal with slow convergence and nonrobust steady-state performance [18][19][20][21]. These algorithms rely on the assumption that not all possible AIR estimates, i.e., Finite Impulse Response (FIR) filters of fixed length, are equally likely, i.e., certain regions exhibit a higher probability of representing a valid AIR.…”

“…3.4). Local affine subspace models have been exploited for sound field reconstruction by sparse dictionary learning [25] and also local PCA-supported system identification algorithms [19,21]. Besides the affine subspace-based approaches, a globally nonlinear manifold model has been proposed in [20] and was used in an offline least-squares system identification task.…”