Speech Modelling Using Subspace and EM Techniques
The speech waveform can be modelled as a piecewise-stationary linear stochastic state space system, and its parameters can be estimated using an expectation-maximisation (EM) algorithm. One problem is the initialisation of the EM algorithm. Standard initialisation schemes can lead to poor formant trajectories. But these trajectories however are important for vowel intelligibility. The aim of this paper is to investigate the suitability of subspace identification methods to initialise EM. 
 
The paper compares the subspace state space system identification (4SID) method with the EM algorithm. The 4SID and EM methods are similar in that they both estimate a state sequence (but using Kalman filters and Kalman smoothers respectively), and then estimate parameters (but using least-squares and maximum likelihood respectively). The similarity of 4SID and EM motivates the use of 4SID to initialise EM. Also, 4SID is non-iterative and requires no initialisation, whereas EM is iterative and requires initialisation. However 4SID is sub-optimal compared to EM in a probabilistic sense. During experiments on real speech, 4SID methods compare favourably with conventional initialisation techniques. They produce smoother formant trajectories, have greater frequency resolution, and produce higher likelihoods.