Angular Velocity and Covariance Estimates for Rigid Bodies in Near Pure-Spin Using Orientation Measurements

The problem of estimating relative pose and angular velocity for uncooperative space objects has garnered great interest, especially within applications such as asteroid mapping and satellite servicing. This paper provides a batch estimator based on orientation measurements to estimate not only the angular velocity magnitude and spin-axis direction of a target body (either external or oneself) undergoing pure-spin, but also the associated uncertainty bounds for the resulting angular velocity magnitude and spin-axis direction estimates under reasonable assumptions. In addition, this paper derives statistics for the third eigenvalue of the stacked measurement matrix, which enable detection of whether the target body’s spin-axis direction is changing. The statistics of the third eigenvalue are shown to match those of a Monte-Carlo-based Gamma distribution fit. Instead of a recursive filtering methodology, the batch formulation pursued in this paper is well-suited to exploit the geometric properties associated with singular value decomposition techniques and Toeplitz recursion. This batch approach relinquishes the need for an iterative scheme to compute the error bounds upon the estimated spin-axis direction.