New Insights into the Kalman Filter Beamformer: Applications to Speech and Robustness

Statistically optimal spatial processors (also referred to as data-dependent beamformers) are widely-used spatial focusing techniques for desired source extraction. The Kalman filterbased beamformer (KFB) [1] is a recursive Bayesian method for implementing the beamformer. This letter provides new insights into the KFB. Specifically, we adopt the KFB framework to the task of speech extraction. We formalize the KFB with a set of linear constraints and present its equivalence to the linearly constrained minimum power (LCMP) beamformer. We further show that the optimal output power, required for implementing the KFB, is merely controlling the white noise gain (WNG) of the beamformer. We also show, that in static scenarios, the adaptation rule of the KFB reduces to the simpler affine projection algorithm (APA). The analytically derived results are verified and exemplified by a simulation study.