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Tues., Aug. 18, 9:00 a.m. - 12:15 p.m. (lunch provided)
In light of the recent Iridium-Cosmos collision, the topic of Conjunction Analysis has become increasingly more important to satellite owners and operators. This half-day workshop will discuss AGI's latest research in this field and present real-world results. Please signify interest in attending during registration. Seating is limited.
A Description of Filters for Minimizing the Time Required for Orbital Conjunction Computations
Identifying potentially dangerous conjunctions is most commonly done by determining periods of time when two objects have an unacceptable risk of collision. Solving this problem for the entire catalog of objects vs. all other catalogued objects quickly illustrates the need for computational acceleration techniques.
Hoots et al.1 designed a series of three filters through which candidate objects have to pass before a final determination of the close approach distance is made. Two of the filters are purely geometrical and one uses the known properties of the orbital motion of the two objects. These filters serve to "weed out" the majority of the objects in the catalogue and greatly reduce the number of computations needed. After the application of the filters, the trajectories of the remaining candidate objects are sampled to determine the actual close approach periods. The three filters will be referred to as the apogee/perigee filter, the orbit path filter and the time filter. These filters are easy to understand, but in practice they have been shown to be inadequate when implemented as originally described. Additionally, the filters were originally designed for use with a space catalog comprised solely of two line element (TLE) sets. Now that a special perturbations version of the space catalog is being generated, any dependence on TLEs must be eliminated.
For each of the filters put forth in Hoots et al., we will examine the premise of the filter, demonstrate failure cases and provide details of an improved implementation. The assumptions and potential failure cases for the improved implementations will be identified. Requirements for the use of computational pads will be examined along with the associated impact on computation time. The computational efficiency provided by each filter will be tabulated both independently and in conjunction with other filters. Finally, the reliability of the filtering process will be evaluated using an "all on all" example where results will be generated with and without the use of conjunction filters.
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A New Measure of Nonlinearity for Relative Motion during Close Approach
A new measure of nonlinearity for relative motion during close approach is introduced. It is based on the second order expansion of the two-body differential equation. The measure compares contributions from the first and second order terms and quantifies nonlinearity of the relative motion by the relative significance of the second order term. Given this measure and some nonlinearity threshold, a volume of space around a primary satellite can be defined within which the relative motion of any secondary satellite or a piece of debris can be considered linear.
Assessing Satellite Conjunctions for the Entire Space Catalog using COTS Multi-core Processor Hardware
This presentation discusses results for the all-on-all conjunction assessment of ~12,000 objects over both a one-day and five-day analysis period. Two methods for obtaining the state information for the space objects are considered. The first method utilizes analytical propagation of the orbit state from known elements at a given epoch (i.e., using SGP4 with TLEs). Analytical propagation reduces the computer memory footprint of each object at the expense of reduced accuracy of the ephemerides themselves. The second method models the ephemeris of each space object using a table of ephemeris coupled with an interpolation method. The accuracy of the ephemeris can be made quite high using this scheme; however, the memory footprint per object is greatly increased.
Two different software implementations will be used. The first software implementation is a general purpose COTS 32-bit application which has, as part of its feature set, the ability to perform conjunction analysis between space objects. The second software implementation is a custom application designed specifically to perform conjunction analysis between space objects, but built using a set of COTS software components.
Performance and accuracy of the determination will be presented using three hardware configurations: a single 32-bit 4Gb RAM dual-core COTS personal computer (~$2.5K); five 32-bit 2Gb RAM dual-core COTS personal computers (each ~$2.5K); and a single 64-bit 32Gb RAM 4-core dual processor COTS personal computer (~$5K). Each will be running on a commonly available Windows operating system.
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BREAK
10:30 a.m. - 10:45 a.m.
Anti-Satellite Engagement Vulnerability
This presentation discusses several simplifying assumptions that can be made to initially assess the threat from an ASAT interceptor to produce a conservative engagement volume. An initial determination of vulnerability can be made by assuming the interceptor is given all its energy at launch and follows a ballistic trajectory to the target. The resulting trajectory begins at the launcher altitude and follows a simple two-body dynamical path until reaching the target satellite. The mathematical equations for such free-flight representation are explained by Bate in describing ballistic missile trajectories for a spherical, rotating earth. This work modifies their approach because the target is in orbit and the launcher can be located above the earth's surface. The effect of earth rotation is addressed by transforming from the ECEF frame to an Earth-Centered Inertial (ECI) frame.
An engagement volume relative to the interceptor's launch platform is determined by creating a sufficient family of forward trajectories based on different initial launch azimuths and elevations; this volume is sometimes referred to as a "kill basket." Entry and exit times through this volume define the bounds of satellite vulnerability for a specific launcher and specific type of ASAT missile on an ascending or descending intercept profile. Alternately, a vulnerability region can be represented as a geographical footprint relative to satellite position that encompasses all possible launcher locations for a specific interceptor. This is accomplished by creating a sufficient family of backward trajectories from the target satellite using maximum range equations for ascending or descending intercepts based on the ASAT missile's burnout energy.
These volumes and footprints are created by simply knowing the interceptor's final ECEF energy and are only approximations due to the aforementioned assumptions. The intercept trajectory time of flight from launch to burnout will be underestimated because the actual powered flight segment takes longer than its ballistic representation. The intercept range from launch to burnout will be overestimated because the actual powered flight covers less ground than its ballistic representation. This causes the preliminary analysis to be conservative, creating an oversized volume or footprint. Because of this, the results are adequate for understanding and visualizing the threat, as well as determining if more detailed analysis is required. The actual missile fly-out profile for a specific engagement would be required to more accurately assess the threat.
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Analysis of the Iridium 33-Cosmos 2251 Collision
On 2009 February 10, Iridium 33 - an operational US communications satellite in low-Earth orbit - was struck and destroyed by Cosmos 2251 - a long-defunct Russian communications satellite. To better understand the circumstances of this event and the ramifications for avoiding similar events in the future, this presentation provides a detailed analysis of the predictions leading up to the collision, using various data sources, and looks in detail at the collision, the evolution of the debris clouds, and the long-term implications for satellite operations. The only publicly available system available to satellite operators for screening for close approaches, SOCRATES, did predict this close approach, but it certainly wasn't the closest approach predicted for the week of February 10. In fact, at the time of the collision, SOCRATES ranked this close approach 152 of the 11,428 within 5 km of any payload.
A detailed breakdown is provided to help understand the limitations of screening for close approaches using the two-line orbital element sets. Information is also provided specifically for the Iridium constellation to provide an understanding of how these limitations affect decision making for satellite operators. Post-event analysis using high-accuracy orbital data sources will be presented to show how that information might have been used to prevent this collision, had it been available and used. Analysis of the collision event, along with the distribution of the debris relative to the original orbits, will be presented to help develop an understanding of the geometry of the collision and the near-term evolution of the resulting debris clouds. Additional analysis will be presented to show the long-term evolution of the debris clouds, including orbital lifetimes, and estimate the increased risk for operations conducted by Iridium and other satellite operators in the low-Earth orbit environment. The final portion of the presentation will look at how collaborative efforts, such as the current Data Center operations supporting SOCRATES-GEO, might be used to reduce the overall risk of similar events in the future.
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Discriminating Threatening Conjunctions with Data Fusion Principles
The objective of the presentation is to apply information theory and data fusion principles to discriminating the most important satellite conjunctions from thousands of close approaches that occur every day. The significance of predicted conjunctions is now determined from single conjunction assessments based on the most current orbit data. Generally, attention focuses on the few most probable conjunctions at each reporting interval. The hierarchy of probability changes with each assessment. Highest probabilities on previous assessment may be supplanted by currently more likely events. However, the probabilities that caused concern previously generally have not changed, and conjunctions that demanded attention previously and which are yet to come still deserve attention. We will demonstrate conjunction significance assessment techniques that fuse past conjunction reports, information about the conjunction partners, and estimates of the consequences should collision occur. We will show that these techniques would have discerned the Iridium 33 - Cosmos 2251 collision days before it happened. We will also show how these techniques illuminated several important events since the Iridium/Cosmos collision.
Once a conjunction rises to immediate high probability, we determine how many other conjunctions the most significant collision partner might be exposed to within the assessment period. We then compound the probabilities of all of these estimated events in chronological order. The important measure is how likely the most valuable asset is to collide with anything during the assessment period, not just how likely the single highest probability is. We demonstrate this with a very recent cluster of conjunctions experienced by Cosmos 1818. We assess consequences with trusted fragmentation models and note the distribution of fragment masses and trajectories. We also consider the characteristics of the satellite missions and payloads.
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