Joint State and Parameter Estimation for a Target-Directed Nonlinear Dynamic System Model

R. Togneri and Li Deng


In this paper, we present a new approach to joint

state and parameter estimation for a target-directed, nonlinear

dynamic system model with switching states. The model, which

was recently proposed for representing speech dynamics, is also

called the hidden dynamic model (HDM). The model parameters

subject to statistical estimation consist of the target vector and

the system matrix (also called the “time-constants”), as well as

the parameters characterizing the nonlinear mapping from the

hidden state to the observation. These latter parameters are

implemented in the current work as the weights of a three-layer

feedforward multilayer perceptron (MLP) network. The new estimation

approach presented in this paper is based on the extended

Kalman filter (EKF), and its performance is compared with the

more traditional approach based on the expectation-maximization

(EM) algorithm. Extensive simulation experiment results are

presented using the proposed EKF-based and the EM algorithms

and under the typical conditions for employing the HDM for

speech modeling. The results demonstrate superior convergence

performance of the EKF-based algorithm compared with the EM

algorithm, but the former suffers from excessive computational

loads when adopted for training the MLP weights. In all cases, the

simulation results show that the simulated model output converges

to the given observation sequence. However, only in the case

where the MLP weights or the target vector are assumed known

do the time-constant parameters converge to their true values.

We also show that the MLP weights never converge to their true

values, thus demonstrating the many-to-one mapping property

of the feedforward MLP. We conclude from these simulation

experiments that for the system to be identifiable, restrictions on

the parameter space are needed.


Publication typeArticle
Published inIEEE Trans. on Signal Processing
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