基于矩阵李群表示及容积卡尔曼滤波的视觉惯导里程计新方法

针对滤波方法实现的视觉—惯导里程计 (VIO) 问题，为更准确传递旋转运动的不确定性并降低系统线性化误差，提高位姿估计的精度，设计并实现了一种高维矩阵李群表示的采用容积卡尔曼滤波框架实现的VIO算法，算法将状态变量构建为一个高维李群矩阵，并定义了李群变量在容积点采样过程中的‘加法’运算，将容积点和状态均值、方差等概念由欧氏空间扩展到流形空间；采用容积变换传递状态均值及方差，避免了旋转运动复杂的雅克比矩阵计算过程，降低了模型线性化误差。最后，使用EuRoc MAV数据集进行算法验证，结果表明所提出算法在提高位姿估计精度方面是有效的。

Considering robotic visual inertial odometry (VIO) using filtering methods, a VIO algorithm is proposed in order to improve estimation accuracy. This algorithm uses cubature Kalman filter on matrix Lie group to realize it, which can accurately describe system uncertainty in rotation and reduce the linearization error of systems. The characters of the proposed algorithm are that: 1) the state is built by an high dimensional Lie group matrix and the definition of the additional operation for Lie group variant is proposed in cubature point sampling, which can extend the concept of cubature point, state mean and covariance from Euclidean space to manifold; 2) the state mean and covariance are propagated by cubature transformation, which avoids calculating complicated Jacobi matrixes and reduces the linearization error of the system. The performance of the proposed algorithm is tested in the EuRoc MAV dataset, and the results show the effectiveness of the proposed algorithm in improving estimation accuracy.