The Fine Calibration of the Ultra-Short Baseline System With Inaccurate Measurement Noise Covariance Matrix

The ultra-short baseline (USBL) system has been widely applied in marine positioning fields because of its small size and high positioning accuracy. However, there are particular position and angle deviations between the body frame and the USBL frame in a realistic environment. The presence of range-measuring error in the USBL system is also a non-negligible problem. Besides, the measurement noise covariance matrix may change due to the complicated underwater environment. These factors lead to the reduction in positioning accuracy. Therefore, an improved adaptive Kalman filter for fine calibration of the USBL system is proposed to deal with the problems mentioned above. First, the state model of the fine calibration is established based on installation error angles, lever arms, and range-measuring error. For the first time, the system error is included in the calibration model, thereby reducing the influence of system error on positioning accuracy. A modified nonlinear measurement model based on azimuth and slant range is presented. Second, based on the variational Bayesian method, an adaptive filter is proposed to do with the unknown and time-varying measurement noise. Finally, the numerical simulation and field trial are carried out to verify the effectiveness of the proposed algorithm. The advantage of this algorithm is that the system error and installation errors can be estimated simultaneously and the system adjusts the measurement noise covariance matrix adaptively to improve the positioning accuracy.