In this work, a splitting and weighting scheme that allows for splitting a Gaussian density into a Gaussian mixture density (GMM) is extended to allow the mixture components to be arranged along arbitrary directions. The parameters of the Gaussian mixture are chosen such that the GMM and the original Gaussian still exhibit equal central moments up to an order of four. The resulting mixtures' covariances will have eigenvalues that are smaller than those of the covariance of the original distribution, which is a desirable property in the context of nonlinear state estimation, since the underlying assumptions of the extended Kalman filter are better justified in this case. Application to speech feature enhancement in the context of noise-robust automatic speech recognition reveals the beneficial properties of the proposed approach in terms of a reduced word error rate on the Aurora 2 recognition task.
Bibliographic reference. Leutnant, Volker / Krueger, Alexander / Haeb-Umbach, Reinhold (2011): "A versatile Gaussian splitting approach to non-linear state estimation and its application to noise-robust ASR", In INTERSPEECH-2011, 1641-1644.