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.