## 1 Introduction
To solve the estimation problem in three-dimensional space, the quaternion Kalman filter is developed by [PERSON] et al. in [19] for quaternion-valued signals using the well-known minimum mean square error criterion under the Gaussian assumption. In other fields, system identification is also widely used. The development of a real-time vehicle state estimator based on can bus data is presented, which considers suspension kinematics and tire dynamics while also estimating road slope and tire-road interaction characteristics in [20]. In [21], the hybrid models of the Kalman filter and neural networks for state estimation are reviewed, highlighting their academic advancements and demonstrating that these models outperform single models in terms of accuracy and generalization. Through analysis of the above literature, it can be seen that many studies simulate disturbances such as wind, waves, and currents in maneuvering simulations, add sensor noise to mimic real operational conditions, and obtain much of the experimental data from model tests [8; 9; 10; 11]. The data acquired through such simulations cannot accurately reflect the various physical effects involved in the motion of the USV, including the influence of its navigational state and external environmental factors. The dynamic changes in the motion data are critical for the accuracy of the final model that is constructed. Additionally, the parameter identification algorithms proposed in [12; 13; 14; 15] fail to effectively smooth the data. They are highly susceptible to noise and outliers, which results in inaccurate parameter estimation, and these algorithms do not adequately account for the nonlinear characteristics of the data, leading to poor model fitting and compromised identification accuracy. Many studies on the KF algorithm [16; 17; 18; 19] assume the system is linear, which makes it significantly less effective in dealing with nonlinear dynamics. Since KF relies on an exact linear system model, it is less adaptable to nonlinear systems and cannot directly handle nonlinear state transfer and observation models, and the accuracy of the filtering estimation will be affected if the model has errors or is incomplete, which may lead to biased estimation results in practical applications. Motivated by the above analysis, a parameter identification algorithm of the USV Nomoto model based on improved EKF is presented in this paper. The full-scale vessel data are utilized to accurately reflect the various state variables involved in USV motion, including its navigational states and the influence of external environmental factors. In order to fit a local model around each data point, the LWR algorithm is proposed by applying weighted least squares (WLS), providing a smooth estimate of the data to ensure the stability of the identification results. Additionally, the EKF is proposed by performing a first-order Taylor expansion of the nonlinear system based on the current state estimate values, which provides a linear approximation for the prediction and parameter updates. In comparison to previous studies, the key contributions of this research are outlined as follows:  
(1) Full-scale vessel data are employed to more accurately capture the state variables involved in USV motion, including both navigational states and the complex influences of external environmental factors such as wind, waves, and currents. (2) The LWR algorithm is proposed to fit a local model around each data point using weighted least squares, effectively smoothing the data and ensuring stable, reliable parameter estimates to enhance the accuracy and robustness of the identification process. (3) The EKF is designed to approximate the nonlinear system by performing a first-order Taylor expansion based on the current state estimate values, allowing for accurate prediction of system states and efficient parameter updates, thereby improving the model's adaptability and estimation accuracy in dynamic environments.