论文标题
对数线性误差状态模型推导而无近似INS
Log-linear Error State Model Derivation without Approximation for INS
论文作者
论文摘要
通过将导航参数组装成矩阵lie组状态，相应的惯性导航系统（INS）运动模型具有群体属性。导航状态估计误差的谎言对数满足对数线性自主微分方程的满足。这些对数线性模型仍然适用，即使有任意的初始错误，这对于INS初始对齐非常有吸引力。但是，在现有的作品中，对数线性模型均基于一阶线性化近似来得出，这似乎与他们成功的应用程序在INS初始对准方面的成功应用与较大的未对准有关。在这项工作中，可以证明也可以在没有任何近似值的情况下得出对数线性模型，首次在矩阵lie group se_2（3）中给出了连续时间的左右不变误差的误差动力学。这项工作为对数线性模型的有效性提供了另一个证据，这些模型在任意较大的初始错误的情况下。
Through assembling the navigation parameters as matrix Lie group state, the corresponding inertial navigation system (INS) kinematic model possesses a group-affine property. The Lie logarithm of the navigation state estimation error satisfies a log-linear autonomous differential equation. These log-linear models are still applicable even with arbitrarily large initial errors, which is very attractive for INS initial alignment. However, in existing works, the log-linear models are all derived based on first-order linearization approximation, which seemingly goes against their successful applications in INS initial alignment with large misalignments. In this work, it is shown that the log-linear models can also be derived without any approximation, the error dynamics for both left and right invariant error in continuous time are given in matrix Lie group SE_2 (3) for the first time. This work provides another evidence for the validity of the log-linear model in situations with arbitrarily large initial errors.
