Single beacon navigation methods with unknown effective sound velocity (ESV) have recently been proposed to solve the performance degeneration induced by ESV setting error. In these methods, a local linearization-based state estimator, which only exhibits local convergence, is adopted to estimate the navigation state. When the initial ESV setting error or vehicle initial position error is large, the local linearization-based state estimators have difficulty guaranteeing the filtering convergence. With this background, this paper proposes a linear time-varying single beacon navigation model with an unknown ESV that can realize global convergence under the condition of system observability. A Kalman filter is adopted to estimate the model state, and the corresponding stochastic model is inferred for the application of the Kalman filter. Numerical simulation confirms that the proposed linear time-varying single beacon navigation model can realize fast convergence in the case of a large initial error, and has superior steady-state performance compared with the existing methods.

最近提出了一种未知有效音速（ESV）的单信标导航方法，以解决由ESV设置错误引起的性能退化。在这些方法中，采用仅表现出局部收敛性的基于局部线性化的状态估计器来估计导航状态。当初始ESV设置误差或车辆初始位置误差较大时，基于局部线性化的状态估计器很难保证滤波收敛。在此背景下，本文提出了一种具有未知ESV的线性时变单信标导航模型，该模型可以在系统可观察性的条件下实现全局收敛。采用卡尔曼滤波器估计模型状态，并推导相应的随机模型用于卡尔曼滤波器的应用。