基于Student’s T分布的SINS/USBL安装误差标定算法
Calibration algorithm for SINS/USBL installation misalignment errors based on Student’s T-distribution
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摘要: 针对水下环境中声学量测不确定性引发的安装误差角标定精度下降问题,提出一种基于变分贝叶斯(variational Bayesian, VB)框架的鲁棒捷联式惯性导航(strapdown inertial navigationsystem, SINS)/超短基线(ultra-short base line, USBL)标定方法. 通过构建安装误差标定的几何模型,推导了状态空间方程与非线性量测方程,将Student’s T分布嵌入VB滤波框架这一算法创新性地应用在安装误差标定中. 针对声学定位中的野值干扰问题,利用Student’s T分布的重尾特性对量测噪声进行建模,结合VB推断对噪声协方差矩阵和辅助变量进行动态联合估计,有效抑制异常量测对状态更新的影响. 仿真实验表明:与传统高斯假设的卡尔曼滤波(Kalman filter, KF)方法相比,所提方法在仿真野值污染环境下将安装误差角估计精度提升了64.6%,在江试实验中经所提算法标定后在不同方向上定位精度均有提升,提高了复杂水下环境下标定算法的鲁棒性.Abstract: In this paper, the reduced calibration accuracy of installation misalignment angles in underwater environments is addressed due to acoustic measurement uncertainties. A robust SINS/USBL calibration method is proposed based on a variational Bayesian framework. A geometric model for installation misalignment calibration is first established. State-space equations and nonlinear measurement equations are derived. The algorithm innovatively integrates Student’s T-distribution into the variational Bayesian filtering framework. To mitigate outlier interference in acoustic positioning, the heavy-tailed properties of Student’s T-distribution are adopted for noise modeling. The noise covariance matrix and auxiliary variables are dynamically co-estimated through variational Bayesian inference, effectively suppressing anomalous measurements during state updates. Variational iterative optimization ensures adaptive matching between noise models and state estimates while maintaining calibration accuracy. Simulations compare the proposed method with traditional Gaussian-based Kalman filter. The proposed method improves the installation angle estimation accuracy by 64.6% in outlier-contaminated simulation environments. Furthermore, field river experiments demonstrate enhanced positioning accuracy across all axes after calibration with the proposed algorithm. The enhanced robustness demonstrates significant potential for complex underwater calibration tasks.