论文标题
LIKE代数无气体Kalman滤波器进行姿势估计
Lie Algebraic Unscented Kalman Filter for Pose Estimation
论文作者
论文摘要
提出了一个用于基质谎言基团的无味的卡尔曼滤波器，其中在lie代数上配制了状态的时间传播。这是使用对数的运动学微分方程来完成的，该方程使用了右雅各布的倒数。然后可以将Sigma点表示为矢量形式中的对数，Sigma点的时间传播以及平均值的计算和协方差可以在Lie代数上完成。最终的公式在很大程度上是基于向量形式的对数，因此更接近$ \ mathbb {r}^n $的系统的UKF。这提供了一种优雅且结构良好的配方，可提供对问题的更多见解，并且在计算上是有效的。拟议的方法特别是对矩阵谎言组$ SE（3）$进行了调查和调查。包括对左右雅各布人的讨论，并得出了$ SE（3）$的右Jacobian倒数的新颖封闭式解决方案，这提供了紧凑的表示，涉及较少的矩阵操作。在模拟中验证了所提出的方法。
An unscented Kalman filter for matrix Lie groups is proposed where the time propagation of the state is formulated on the Lie algebra. This is done with the kinematic differential equation of the logarithm, where the inverse of the right Jacobian is used. The sigma points can then be expressed as logarithms in vector form, and time propagation of the sigma points and the computation of the mean and the covariance can be done on the Lie algebra. The resulting formulation is to a large extent based on logarithms in vector form, and is therefore closer to the UKF for systems in $\mathbb{R}^n$. This gives an elegant and well-structured formulation which provides additional insight into the problem, and which is computationally efficient. The proposed method is in particular formulated and investigated on the matrix Lie group $SE(3)$. A discussion on right and left Jacobians is included, and a novel closed form solution for the inverse of the right Jacobian on $SE(3)$ is derived, which gives a compact representation involving fewer matrix operations. The proposed method is validated in simulations.
