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The Unscented Kalman filter (UKF) is the popular approach to estimate the recursive parameter of nonlinear dynamical system corrupted with Gaussian and white noises. Also, it has been applied to train the weights of the multi-layered neural network (MNN) models. The Group method of data handling (GMDH)-type neural network is one of the most widely used neural networks which has high capacity in modeling of the complex data. In many researches, different approaches are used in training of neural networks in terms of associated weights or coefficients, such as singular value decomposition, and genetic algorithms. In this paper, the unscented Kalman filter is used to train the parameters of GMDH-type neural network when the experimental data are deterministic. The effectiveness of GMDH-type neural network with UKF algorithm is demonstrated by the modeling of the using a table of the multi input-single output experimental data. The simulation result shows that the UKF-based GMDH algorithm perform well in modeling of nonlinear systems in comparison with the results of using traditional GMDH-type neural network and is more robust against the model and measurement uncertainty.

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A nonlinear model for Autonomous Underwater Vehicles is proposed. In order to describe a more precise dynamic behavior, the nonlinear model for both Lateral and Longitudinal subsystems is derived based on all applied forces and moments. The proposed model can be explained as an extended linear model for AUV in depth and azimuth motions where some nonlinearities are taken into account. Due to some practical issues as well as the form of proposed model, the identification problem based on Least Square method is formulated to achieve the system parameters. By considering unstable dynamic of system, the open loop system cannot be excited. In this case, the PID regulators with simple tuning parameters are proposed in both Lateral and Longitudinal subsystems and the identification problem by utilizing sinusoidal inputs is followed within a feedback loop. Based on measurable variables i.e. linear moments, angular velocities and Euler angles, and utilizing some dynamic filters, the Least Square method is then applied to estimate the model parameters. The effectiveness of proposed nonlinear model as well as the parameter identification approach are finally demonstrated through some numerical simulations.