Maximum Likelihood Measurement Noise Estimation for Block-Time Domain Kalman Filters

Authors:

Hardenbicker, T. ,  Schneider, J. ,  Jax, P.

Book Title:

Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

Organization:

IEEE

Publisher:

IEEE

Status:

accepted for publication

Date:

May. 2026

Language:

English

Abstract

The performance of Kalman filters in acoustic
system identification depends on an accurate estimation of the
(co)variance of the measurement noise. When no prior knowledge
on the noise is available, it needs to be estimated online, which
is well researched for the Frequency Domain Kalman Filter
(FDKF). Recent publications however, rely on the fast convergence
and tracking performance of the Block-Time Domain Kalman
Filter (BTKF). Hence, this paper addresses the online estimation
of the measurement noise covariance for the BTKF. Although
online maximum likelihood estimation relies on the error vector’s
outer product, a Toeplitz structure is imposed onto the noise
covariance matrix which makes its inversion more stable and is
motivated by short-time stationarity of the measurement noise. An
additional onset detection mechanism enhances robustness against
non-stationary near-end noise levels. Our exemplary evaluation
on using real-world test signals from the ICASSP Acoustic Echo
Cancellation challenge data set demonstrates that the proposed
approach shows the same steady-state performance like the FDKF
but allows to use the BTKFs faster convergence. Compared to the
straightforward maximum likelihood approach, the performance
is significantly improved.

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