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Master-Vortrag: Parameterschätzung in der adaptiven akustischen Systemidentifikation

Jan Schneider
Donnerstag, 10. Juli 2025

14:00 Uhr
IKS 4G | zoom

Hands-free communication is becoming more and more popular by the day. The ability to communicate without holding a phone directly against ones head provides higher comfort to the user, allows simultaneous video streaming from the same device and enables communication where it was previously impossible such as while driving. To avoid the acoustic echo that is generated when the microphone picks up the sound waves that were generated by the loudspeaker, Acoustic Echo Cancellation (AEC) can be used, which requires the identification of the acoustic system between the loudspeaker and microphone.

A popular method for Acoustic System Identification (ASI) is to formulate the system identification problem as a state-space system and use a Kalman filter to estimate the impulse response. The Kalman filter relies on second order moments that are known in other applications but not in ASI. These process parameters must therefore be estimated alongside the primary estimation of the acoustic system. There exist a number of proposals for this estimation, but most of them are formulated for the Frequency Domain Kalman Filter (FDKF) and most do not take into account the transition matrix.

This thesis investigates different estimators for all three process parameters of a Time Domain Kalman Filter (TDKF): the measurement noise covariance, the process noise covariance and the transition matrix. The basis therefore is a maximum likelihood approach. This thesis shows that existing estimator proposals comply with this approach and particularly process noise covariance estimators can be interpreted as a variant of this solution using mathematically meaningful simplifications. Based on this approach, other simplifications are used to derive a wide range of possible process noise estimators that show a similar performance but have other unique properties.

For the measurement noise covariance, a novel estimator is proposed that imposes a Toeplitz structure on the covariance matrix, which can be shown to improve the estimation performance significantly but has negative impacts on the estimators stability. Although the estimation of the transition matrix from the derived solution is shown to be challenging, this thesis shows that a transition matrix estimation is still worthwhile and proposes a new estimator. By interpreting the problem as a least squares problem and estimating the transition matrix directly from the previously estimated impulse responses, performance improvements can be generated. All proposed estimators were evaluated through exhaustive tests where the estimators were tested for different conditions and scenarios, both in isolation and in conjunction with estimators for the other process parameters.

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