http://udel.edu/~yuyang/downloads/tr_observabilityII.pdf

Aided Inertial Navigation: Unified Feature Representations and Observability Analysis

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.