基于鲁棒迭代卡尔曼滤波的惯性/偏振组合定向方法

The inertial/polarization integrated orientation method based on robust iterative Kalman filter

关键词:  迭代扩展卡尔曼滤波  惯性导航系统  偏振罗盘  组合导航  非高斯噪声  异常值

Key words:  Iterative extended Kalman filter (IEKF)  Inertial navigation system (INS)  Polarization compass (PC)  Integrated navigation  Non-Gaussian noise  Outlier

摘要:

偏振罗盘（PC）在复杂环境中（如遮挡或载体高速机动情况下），易受到非高斯测量噪声和大异常值的影响，从而导致惯性导航系统（INS）/PC组合导航系统性能下降。为解决这一问题，基于非线性回归公式，提出了一种以Huber函数作为鲁棒代价函数的鲁棒迭代扩展卡尔曼滤波（Huber-RIEKF）方法，通过引入鲁棒优化框架，重新构建卡尔曼滤波更新步骤，使其具备对预测协方差和观测噪声协方差进行自适应加权的能力，从而有效处理由未知噪声引起的观测量中的大离群值。此外，为克服Huber代价函数的影响函数无法回降的局限性，进一步设计了一种基于Mahalanobis度量的数据关联方法，用于识别异常值，并确保仅将非异常测量值纳入滤波更新过程。在校园内使用无人车进行了２次实测实验，数据采集时长分别持续45 min和30 min。实验结果表明，与IEKF算法相比，所提出算法的航向精度在2组实验中分别提升了35.58%和48.43%，表明所提出的方法显著提高了状态估计对非高斯重尾观测噪声的鲁棒性，有效地提升了INS/PC组合导航系统在复杂环境下的适应能力。

Abstract:

The polarized compass (PC) is highly sensitive to non-Gaussian measurement noise and significant outliers in complex environments, such as occlusion scenarios or high-speed maneuver-ing platforms, leading to a decline in the performance of the integrated inertial navigation system (INS)/PC navigation system. To address this problem, a Huber-robust iterative extended Kalman filter (Huber-RIEKF) method is proposed, which uses the Huber function as a robust cost function within a nonlinear regression framework. By incorporating a robust optimization framework, a novel update step for the Kalman filter is constructed that allows adaptive reweighting of the prediction covariance and the observation noise covariance, effectively mitigating the impact of large outliers in the observations caused by unknown noise. Furthermore, to overcome the limitation of the Huber cost function‘s inability to handle descending influence functions, a data association method based on Mahalanobis distance is developed. This method identifies outliers and ensures that only non-outlier measurements are included in the updating process. Two practical tests are conducted using unmanned vehicles within the campus, with data collection durations of 45 minutes and 30 minutes, respectively. The results of the experiments show that, compared to the IEKF algorithm, the heading accuracy of the proposed algorithm is increased by 35.58% and 48.43% in the two sets of experiments, respectively. This shows that the proposed method significantly enhances the robustness of state estimation against non-Gaussian heavy-tailed observation noise and effectively improves the adaptability of the integrated INS/PC navigation system in complex environments.