Mark A. Vincent, Raytheon
Keywords: maneuver trade space plot, propagations models, thresholds, operations
Abstract:
There have been steady refinements in the algorithms used in assessing the conjunctions of space objects and in the methods to mitigate the risk associated with them. However, several operational challenges remain in the implementation of these techniques. Even before the recent increase in objects due to mega-constellations and the ability of the Space Fence to track more objects, experience has shown that the bulk of the time spent by navigation teams is dealing with conjunctions.
Somewhat ironically, the situation where the estimated Probability of Collision (Pc) is high because of a combination of calculated miss distances and uncertainties being low, is easier to address since the corresponding Risk Mitigation Maneuver (RMM) that is needed is well defined. The exception is when a larger RMM would conflict with other requirements, for example maintaining orbital parameters for scientific reasons. In general, the more difficult case is when the Pc hovers near the maneuver threshold and the Pc changes as time to the Time of Closest Approach (TCA) is reduced. These changes are mainly due to new observations of the secondary object but can also occur to a lesser degree because of new data such as updated predictions of atmospheric parameters. Compounding the problem is the natural behavior of the Pc to be low earlier on as the state uncertainties are large, then reach a maximum Pc over time and then decrease as the uncertainties becomes much less than the miss distance, represented by the so-called Alfano Curves [1].
The Alfano Curve behavior implies that in almost all cases it is best to wait until as late as possible to make the decision on the RMM. Practical considerations such as uploading the command file to the spacecraft and on-board preparations that are necessary to do a burn have to also be taken into account. Nevertheless, reducing the time to design the maneuver allows for later observational data to be included, perhaps allowing the best scenario of all, not having to execute the RMM.
Arguably the most useful tool available for making decisions about the size and direction of an RMM, including the possibility of not having to do the maneuver at all, is the Maneuver Trade Space (MTS) plot. As depicted in Figure 1 the horizontal axis represents the magnitude of an RMM, in either the positive or negative Transverse direction, and the vertical axis is the time of maneuver with respect to TCA. The color scale represents the Pc resulting from doing the corresponding maneuver (including the new NASA standard post-maneuver threshold of 3.16 x10-6).
The technical core of this paper will analyze the trade-offs between the time it takes to generate MTS plots and their accuracy. The basic model implemented in the MONTE software at JPL uses the state and covariance information of the two objects at their TCA that is available in a Conjunction Date Message (CDM) posted to the Space Track website. The state of the primary object is propagated backwards in time from TCA to the earliest chosen maneuver time and then at each chosen time step, a velocity change corresponding to an instantaneous maneuver is applied to the nominal state and then the new state is propagated back to a new TCA, close to the original one. The new Pc value is calculated with the newly created primary object state, a simply adjusted (i.e. two-body propagation, for the DTCA) secondary state as well as the original covariances, that latter being in Radial Transverse Normal (RTN) coordinates. It is the propagations back and forth that consume the vast majority of the computer time, so the fidelity of the models used in this process was the focus of this investigation.
The study was limited, at least initially, to the size of the gravity field used in the propagations, with atmospheric drag being the candidate for an expanded investigation. It should be emphasized that some of the errors induced when propagating backwards are cancelled when propagating forwards. The remaining errors can be thought of as being caused by the non-linearities in the process, which is one reason that the State Transition Matrix (STM) approach was included in the analysis. An example of the preliminary results is shown in Table 1. It represents a propagation backwards (and forwards) of 12 hours, which is a common value used in MTS plots, although usually RMMs are chosen to occur 0.5 or 1.5 orbits prior to TCA (i.e. later on, while optimizing the radial separation desired at TCA). Likewise, this table represents an RMM of 5 cm/s which is at the high end of the magnitude usually needed to safely mitigate a conjunction. Note, only the FULL model, used here as the reference, contains atmospheric drag and solar radiation pressure.
Table 1. End-point Deviations for a 5 cm/s RMM and a 12-hour Propagation
A full discussion of all the results will be presented in the paper, but the smaller sized gravity fields look promising as a good compromise between accuracy and computer speed. Further speed enhancements to the J2-only method and Mean element propagations will be added to the investigation. Separate analyses were done, both numerically and analytically, to determine how the deviations of the end state typically affect the value of Pc. One particularly interesting, though not unexpected, conclusion is that the error in the Transverse component is least important and the error in the Radial component is most important, the latter albeit for oblique orbit crossings.
The paper will also discuss other operational challenges such as the use of a Planning Threshold and how that produces a yet-to-be-solved issue of picking a RMM magnitude even though the actual maneuver execution threshold has not yet been exceeded.
[1] Alfano, S, Relating Position Uncertainty to Maximum Conjunction Probability, J. Astronautical Sci, Vol. 53, No.2, 2005.
Figure 1. Maneuver Trade Space Example
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Date of Conference: September 14-17, 2021
Track: Conjunction/RPO