Sam Wishnek, Ball Aerospace; Joshua Wysack, Ball Aerospace
Keywords: fisher information, IOD, orbit determination, cislunar
Abstract:
As the number of NGOs and countries interested in launching satellites beyond the near-Earth environment grows, so does the importance of the tools used to detect and track these satellites. Initial orbit determination (IOD) is the first step in the process of establishing an understanding of the state of a space object. It is important for building a first state estimate to inform every subsequent step in orbit determination. Initial orbit determination is an essential step for estimating the state of an unknown space object. It is a preliminary requirement for both batch and sequential filters that can provide precise estimates of the state and a valuable product on its own for building an actionable understanding of the objects orbit. However, the complex dynamics beyond the near-Earth environment make IOD a difficult task. IOD traditionally makes heavy use of the simplifications afforded by pure two-body dynamics, and the complexity of the problem opens-up beyond this environment. We have previously developed a method for IOD beyond the near-Earth, however this method suffers from high sensitivity to measurement error which limits its real-life utility [1]. By taking a new approach to the problem, we have developed a solution to this problem by allowing additional measurements to inform the estimate. Furthermore, we take an information theoretic approach that extends this solution to improving the understanding of space objects with less than the required number of observations to find a full state through IOD.
Several new approaches are taken to improve these results. First, IOD traditionally operates on the minimum number of observations required to estimate a state. For example, three angles-only observations have six constraints to fully determine the six-element dynamical state. These methods include algorithms such as Gooding and Double-R. In practice, this can mean neglecting other available data if more than the minimum number of observations were taken. Observations are often taken in short bursts, and traditionally only a single measurement is used per burst. By folding these additional measurements into the solution, we can improve the resulting estimates tolerance for measurement error. This places the developed algorithm between traditional IOD and batch least squares. The former accepts only the minimal amount of data while the latter can accept an arbitrary amount but expects a good initial estimate of the state. In addition, by understanding the observers capabilities we can also reverse the problem and determine the optimal time to take an additional observation that completes the state space and is most likely to yield a reliable IOD result. For example, if more observations in the near-term would have little impact on the quality of the estimate, it would be more efficient to task the sensor elsewhere and return when a measurement would have more impact. This kind of scoring for the expected impact of an observation is essential for understanding the collection schedule that best uses the available sensors.
Second, artificial space-objects are more likely to inhabit certain favorable orbits. These include special orbit geometries such as geosynchronous, sun-synchronous, Molniya, and the cislunar three-body periodic orbits. By informing the orbit determination algorithm of these orbits we can more quickly and reliably solve for these cases that can otherwise be hard to estimate due to the instability of the orbits. The existing algorithm searches the full-feasible space and begins its optimization by spreading sample points across the full admissible region. By incorporating an understanding of orbits preferred for artificial space objects, those regions can be sampled more densely and potentially converge to a solution quicker than the naïve approach.
Even without sufficient quality or number of measurements to perform IOD, it is still possible to glean useful information about the space object such as orbit class. The information theoretic approach can be leveraged in combination with admissible regions to determine feasible spaces in state space that a space object could exist within. This is applicable to scenarios without enough observations to fully determine the state. Similar to how a human observer can glance at a satellite streaking across the sky and immediately understand what kind of orbit it probably has; this kind of understanding can be useful for systems without a human in the loop. While a single solution may not be possible for these cases, by developing an understanding of the space in which the object could exist we can build actionable intelligence that could be useful for scheduling follow-up observations or classifying the target.
Wishnek, Samuel, Marcus J. Holzinger, and Patrick Handley. “Robust cislunar initial orbit determination.” AMOS Conf. Proc. 2021.
Date of Conference: September 19-22, 2023
Track: Astrodynamics