Speech and Audio Processing for Coding, Enhancement and Recognition by Tokunbo Ogunfunmi Roberto Togneri & Madihally (Sim) Narasimha

Author:Tokunbo Ogunfunmi, Roberto Togneri & Madihally (Sim) Narasimha
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

6.3.1 Learning a Hidden Dynamic Model Using the Extended Kalman Filter

The estimation problem that we investigate is as follows. Given multiple sets of observation sequences, o(k), for each distinct phone regime, we seek to determine the optimal estimates for the unknown values of the state-equation parameters and T, and the observation-equation parameters, W, which is the MLP weight vector of the nonlinear mapping function h(z(k)). For clarity of notation we will drop the s and r subscripts since it is understood the estimation equations only apply for observations taken over a particular phone regime segment.

The expectation-maximization (EM) algorithm is a widely used algorithm for the estimation of the parameters in general state-space models and in the current research on the HDM [34, 35]. The EM algorithm provides new estimates of the parameters after the set of all available N observation vectors have been presented. The EM algorithm can be considered a batch or off-line estimation method most suited to applications where all of the data is available. We now present the EM algorithm for the specific type of model given by (6.8) and (6.9) following [101, 102].

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