Efficient improvement of frequency-domain Kalman filter

TL;DR

This paper analyzes the steady-state behavior of the frequency-domain Kalman filter and proposes two efficient improvements to address under-modeling issues, enhancing robustness with minimal additional computational cost.

Contribution

It introduces two novel FKF improvements that guarantee optimal steady-state performance in under-modeling scenarios.

Findings

Improved FKF algorithms achieve unbiased steady-state solutions.

Proposed methods demonstrate faster convergence and robustness in simulations.

Minimal increase in computational burden compared to standard FKF.

Abstract

The frequency-domain Kalman filter (FKF) has been utilized in many audio signal processing applications due to its fast convergence speed and robustness. However, the performance of the FKF in under-modeling situations has not been investigated. This paper presents an analysis of the steady-state behavior of the commonly used diagonalized FKF and reveals that it suffers from a biased solution in under-modeling scenarios. Two efficient improvements of the FKF are proposed, both having the benefits of the guaranteed optimal steady-state behavior at the cost of a very limited increase of the computational burden. The convergence behavior of the proposed algorithms is also compared analytically. Computer simulations are conducted to validate the improved performance of the proposed methods.