Correlation of Optical Observations of Objects in Earth Orbit

Association of optical tracklets from a geosynchronous belt survey via the direct Bayesian admissible region approach

“…The angle and angle-rate, nominally in right ascension α and declination δ, at the epoch of a tracklet may be estimated via a least-squares fit of the tracklet data to a polynomial model in time. These variables plus necessary parameters, such as the latitude ϕ and longitude Θ of the observation point, are referred to collectively as the attributable vector (Maruskin et al, 2009). Thus, each point on the AR combined with the attributable vector corresponds one-to-one with a state that the observed object may have taken.…”

“…Various methods applying the admissible region (AR) concept to the TSA problem for RSOs have been studied in recent years (Maruskin et al, 2009;Tommei et al, 2007;Farnocchia et al, 2010;DeMars and Jah, 2012). In this paper, we define the AR as a pdf constrained in the range ρ and rangerateρ directions via a few physical criteria such as that the orbit is elliptic, the object's range is within the sensing capabilities, and so on (Fujimoto and Scheeres, 2012a).…”

“…This approach becomes problematic especially in a survey-type observation strategy. Usually, only a limited number of observations are available per night per object, each over short observation arcs, or tracklets, that span a few minutes (Maruskin et al, 2009). Given such a small window of data, a large subset of the state space remains consistent with each tracklet, leading to poor convergence to the true solution if not divergence.…”

“…This approach ensures more control over the sample set than choosing objects directly from ARs. Each state is then displaced in the 6 coordinate directions of the inertial topocentric spherical coordinate frame one by one: ∆ρ = 6.059 km, ∆ρ = 13.71 km/hr, ∆α = ∆δ = 1.62 arcsec, and ∆α = ∆δ = 3.6 · 10 −3 arcsec/sec (Maruskin et al, 2009). These displacements correspond to the size of one admissible region sample subset when the sample size is ∼ 10 5 and when Gaussian observation errors of σ = 2 arcsec in both α and δ are considered up to 3-σ.…”

“…In space situational awareness (SSA), the vast majority of observations of objects beyond low-Earth orbit are made by optical sensors, which measure a time history of angles called "tracklets" for a given object (DeMars et al, 2009;Tommei et al, 2007;Maruskin et al, 2009). The range and rangerate, however, remains largely unconstrained, and thus multiple tracklets must be combined in order to obtain a full 6-dimensional state estimate.…”