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Abstract:
This paper concerns modelling using a piecewise-stationary
discrete-time linear stochastic state space model, with
applications to speech modelling. The purpose of the paper is to
compare two algorithms for model parameter estimation: subspace
state space system identification (4SID) and
expectation-maximisation (EM). Both algorithms estimate state
sequence and parameters jointly. EM is related to Kalman smoothing,
maximises likelihoods, is iterative and requires parameter
initialisation. Whereas 4SID is related to Kalman filtering,
minimises a criterion involving both short and long-term prediction
errors using least-squares, is closed-form and requires no
parameter initialisation. Therefore 4SID has the advantage that it
avoids iterative algorithm problems and requires less a priori
knowledge because initialisation parameters are not needed. 4SID
and EM methods are compared through experiments on real speech
data. EM is sensitive to initialisation. Different initialisation
methods are discussed and compared.
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