Angles-Only Initial Relative Orbit Determination Performance Analysis using Cylindrical Coordinates

Bearings-Only Initial Relative Orbit Determination

“…These travel times correspond to near 180 deg transfers, where an infinite number of initial relative velocity solutions satisfy the given relative position vectors and elapsed time. A similar phenomenon is observed in the traditional Lambert problem, as well as in a relative motion cylindrical coordinate formulation given in [12]. Second, with the exception of these rss values near the half-period, a general trend of decreasing relative velocity rss with increasing travel times is shown.…”

“…It is for these reasons that the CW2 equations are chosen as the fundamental model for the IROD algorithm, and more specifically, the relative Lambert linkage process. Although this study employs dynamics expressed in a Cartesian coordinate system, it should be noted that the approaches taken in this work are amenable to dynamics expressed in curvilinear systems, such as those presented in [12].…”

“…can be approximated by a GM PDF of the form [21] qx X L l1 w l p g x; m l ; P l (12) where L is the total number of components and w l , m l , and P l are the discrete probability, mean, and covariance, respectively, of the lth Gaussian component, and p g x; a; A represents a Gaussian PDF for the random variable x with mean a and covariance A, such that…”

Optical Co-Orbital Measurements in Low Earth Orbit

“…This solution is partially practical for large spacecraft operating in close proximity of <100 m due to the larger offsets which could be utilized by the physical size of the spacecraft, however, it is impractical for smaller satellites such as microsatellites and nanosatellites. The use of a specially designed and constrained cylindrical coordinate frame is possible, where the orbit's angular information is theorized to be better preserved due to the nature of the reference frame [2]. However, this may not be the most effective solution as there are several practical limitations on observation timing in order to obtain a sufficiently accurate orbit estimate.…”

“…It is theorized that it may even be possible to uniquely determine range to the target spacecraft for the leader-follower pair in contrast to Woffinden's dilemma. It is also important to note that Geller and Lovell's work acknowledges that this coordinate system may be able to provide observability while using the nonlinearized equations of motion [2].…”