http://udel.edu/~yuyang/downloads/tr_observabilityII.pdf
Aided Inertial Navigation: Unified Feature Representations and Observability Analysis
Yulin Yang，Guoquan Huang
辅助惯性导航：统一的特征表示和可观察性分析
Extending our recent work [1] that focuses on the observability analysis of aided inertial navigation systems (INS) using homogeneous geometric features including points, lines and planes, in this paper, we complete the analysis for the general aided INS using different combinations of geometric features (i.e., points, lines and planes). We analytically show that the linearized aided INS with different feature combinations generally possess the same observability properties as those with same features, i.e., 4 unobservable directions, corresponding to the global yaw rotation and the global position of the sensor platform. During the analysis, we particularly propose a novel minimal representation of line features, i.e., the “closest point” parameterization, which uses a 4D Euclidean vector to describe a line and is proved to preserve the same observability properties. Based on that, for the first time, we provide two sets of unified representations for points, lines and planes, i.e., the quaternion form and the closest point (CP) form, and perform extensive observability analysis with analytically-computed Jacobians for these unified parameterizations. We validate the proposed CP representations and observability analysis with Monte-Carlo simulations, in which EKF-based vision-aided INS (VINS) with combinations of geometrical features in CP form are developed and compared.
扩展我们最近的工作[1]，侧重于使用包括点，线和平面的均匀几何特征的辅助惯性导航系统（INS）的可观测性分析，在本文中，我们使用不同的几何组合完成对一般辅助INS的特征分析 （即点，线和平面）。我们分析地表明，具有不同特征组合的线性化辅助INS通常具有与具有相同特征的那些相同的可观察性，即4个不可观察的方向，对应于全局偏转旋转和传感器平台的全局位置。在分析期间，我们特别提出了线特征的新颖的最小表示，即“最近点”参数化，其使用4D欧几里德矢量来描述线并且被证明保持相同的可观察性属性。在此基础上，我们首次为点，线和平面提供了两组单一表示，即四元数形式和最近点（CP）形式，并对这些单一参数化形式的分析计算雅可比行列式进行了广泛的可观测性分析。我们使用蒙特卡罗模拟验证了所提出的CP表示和可观察性分析，其中开发并比较了具有CP形式的几何特征组合的基于EKF的视觉辅助INS（VINS）。