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Master-Presentation: Parameter Estimation in Adaptive Acoustic System Identification
Jan Alexander Schneider
Thursday, July 10, 2025
02:00 PM
IKS 4G | zoom
Hands-free communication is becoming more and more popular by the day. The ability to communicate without holding a phone against ones head enables communication where it was previously impossible. To avoid the acoustic echo that is generated, Acoustic Echo Cancellation can be used, which requires the identification of the acoustic system between the loudspeaker and microphone.
A popular method for Acoustic System Identification is to use a Kalman filter. The Kalman filter relies on second order moments that are not known beforehand. These so called process parameters must therefore be estimated alongside the estimation of the actual acoustic system.
This thesis investigates different estimators for all three process parameters of a Time Domain Kalman Filter: the measurement noise covariance, the process noise covariance and the transition matrix, all based on a maximum likelihood approach. This thesis shows that existing proposals comply with this approach and particularly process noise covariance estimators can be interpreted as a variant of this solution using 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. 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. All proposed estimators were evaluated through exhaustive tests considering different conditions and scenarios.
