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Master-Vortrag: Investigations on Autoencoder Models for Online System Identification

Maximilian Tillmann
Mittwoch, 8. März 2023

11:00 Uhr

Speech communication devices are indispensable in our daily work and personal lives. Using them in hands free mode can create an echo signal, which, if no action is taken, would disturb the speaker. However, the echo signal can be predicted, when the impulse response between loudspeaker and microphone is known. For this task, system identification algorithms exist, such as the Least-Mean-Square (LMS ) algorithm, the Normalized-Least-Mean-Square (NLMS ) algorithm, and the Kalman filter. They work well in general, but face difficulties when confronted with high correlation input signals, high noise levels, or rapidly changing impulse responses over time.

This thesis aims to explore whether prior knowledge about the impulse response can improve system identification. The key approach is to utilize the manifold hypothesis, which has shown promising results in previous works in mapping acoustic room impulse responses to a lower dimensional subspace. These approaches require training data of impulse responses. This thesis investigates how well affine subspace models can represent impulse response with a limited number of subspace components compared to the same number of components in the time domain. One well known way to find an optimal affine subspace is by Principal- Component-Analysis (PCA). It is shown that the affine subspace model can have the same achievable system mismatch with significantly less number of subspace components, when the loudspeaker and the microphone are constrained in their positions.

The manifold LMS algorithm, the manifold NLMS algorithm and the manifold Kalman filter are proposed in this thesis, which can utilise general non linear manifolds for the acoustic echo compensation task. For the manifold LMS and NLMS algorithm in the case of white noise excitation and an affine manifold, the expected convergence speed and the expected steady state system mismatch are derived theoretically and are shown to accurately describe the algorithms behaviour in simulations. For scenarios with constrained loudspeaker and microphone positions it is shown that the manifold NLMS algorithm significantly outperforms the time domain NLMS algorithm. The manifold Kalman filter is compared to the time domain Kalman filter and another subspace approach from literature.