doi:10.1016/S0165-1684(00)00276-0
Copyright © 2001 Elsevier Science B.V. All rights reserved.
Parameter estimation of a target-directed dynamic system model with switching states
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Roberto Togneri
, 
, a, Jeff Mab and Li Deng1, , , b
a Centre for Intelligent Information Processing Systems, Department of Electrical and Electronic Engineering, The University of Western Australia, Nedlands, WA, Perth 6907, Australia
b Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ont., Canada N2L 3G1
Received 16 December 1999;
revised 28 November 2000.
Available online 7 May 2001.
Abstract
In this paper, we describe an implementation of the extended Kalman filter (EKF) for joint state and parameter estimation for a target-directed, switching state-space nonlinear system model and compare its performance with a maximum-likelihood parameter estimation procedure based on the expectation–maximisation (EM) algorithm. The model parameters consist of the target one and the time-constant one. Simulation experimental results are presented for individual and joint estimation of all model parameters for both algorithms. The results show that both algorithms are able to converge to the true target parameter in the model, with the EKF algorithm exhibiting faster convergence. This is true even under the target-undershoot condition when the observation sequence is relatively short. However, convergence to the true time-constant parameter is not evident, possibly due to the non-unique nature of the parameter estimation problem. We also show empirically that in the case of joint estimation of the parameters, the EM algorithm diverges shortly after a small number of iterations whereas the EKF algorithm gives more desirable convergence properties.
Author Keywords: Maximum likelihood; Extended Kalman filter; Target-directed dynamical system
Fig. 1. Simulation of hidden state sequence.
Fig. 2. Observation sequence for the seventh component with different noise levels.
Fig. 3. Simulation of hidden state dynamic (component 2) with the true T and Φ, and true T and estimated Φ after 100 iterations of the EM and EKF algorithms under no noise conditions.
Fig. 4. Simulation of hidden state dynamic (component 2) with the true T and Φ, and true Φ and estimated T after 100 iterations of the EM and EKF algorithms under no noise conditions.
Fig. 5. Simulation of hidden state dynamic (component 2) with the true T and Φ, and true T and estimated Φ after 100 iterations of the EM and EKF algorithms under medium noise conditions.
Fig. 6. Simulation of hidden state dynamic (component 2) with the true T and Φ, and true Φ and estimated T after 100 iterations of the EM and EKF algorithms under medium noise conditions.
Fig. 7. Simulation of hidden state dynamic (component 2) with the true T and Φ, and true T and estimated Φ after 100 iterations of the EM and EKF algorithms under high noise conditions.
Fig. 8. Simulation of hidden state dynamic (component 2) with the true T and Φ, and true Φ and estimated T after 100 iterations of the EM and EKF algorithms under high noise conditions.
Fig. 9. Simulation of hidden state dynamic (component 2) with the true Φ and T, and jointly estimated Φ and T after 100 iterations of the EKF algorithm under medium noise conditions.
Table 1. Estimated T parameter for each phone model after 100 iterations of the EM-T, EKF-T and EKF-PhiT algorithms in medium noise
Table 2. Estimated Φ parameter for each phone model after 100 iterations of the EM-Phi, EKF-Phi and EKF-PhiT algorithms in medium noise
1 Current address: Microsoft Research, One microsoft Way, Redmond, WA 98052, USA.
Corresponding author. Tel.: +61-8-9380-2535; fax: +61-8-9380-1065; email: roberto@ee.uwa.edu.au
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