Continuing Kepler's Quest Assessing Air Force Space Command's Astrodynamics Standards (2012) / Chapter Skim
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2 Astrodynamics Algorithms
2 Astrodynamics Algorithms
Pages 19-43
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From page 19... ...
The current algorithms are not positioned to be effectively responsive to future challenges in space situational awareness. Monitoring the growing population of objects in Earth orbit will require improved algorithms including fundamentals such as force model evaluation and statistical orbit determination, and critical tasks such as conjunc tion analysis and sensor resource management.
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In particular, a number of specific technical areas are discussed in which the space situational awareness enterprise is likely to expand, many of them requiring the development of standardized astrodynamics algorithms beyond the current set. These representative technical areas are perceived by the committee as critical to meeting future needs of AFSPC, the JSpOC, the warfighter, and the broader space situational awareness community.
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:70-71, 2008. ATMOSPHERE MODELS Atmospheric drag is the largest source of uncertainty in orbit determination and prediction for low-perigee objects.
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Atmosphere models may be broadly divided into two classes: empirical models, which represent the average behavior of past data under specified conditions, and physical models, which solve the time-dependent fluid and photochemical equations that govern the atmosphere. In practice, however, empirical models usually include some physics (especially the hydrostatic constraint)
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Mayr, and W.E. Potter, A global thermospheric model based on mass spectrometer and incoherent scatter data MSIS, 2, Composition, Journal of Geophysical Research 82:2148-2156, 1977.
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Unexplained density variability occurs on interannual, decadal, and longer time scales, and so a model that is optimized for the most recent solar cycle is likely to outperform models that rely on decades-old data.20 One disadvantage of JB2008 is that it overrides J70's physical constraint of hydrostatic equilibrium, rendering the model less suitable as a basis for assimilating data types other than mass density data or for extrapolating assimilated mass density data. Several physical models of the thermosphere have been developed over the past three decades and are currently used primarily for research purposes.
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Veronig, Global thermospheric density variations caused by high-speed solar wind streams during the declining phase of solar cycle 23, Journal of Geophysical Research 113:A11303, doi:10.1029/2008JA013433, 2008.
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From page 26... ...
Among the most important perturbations are nonspherical gravity, luni-solar gravitational perturbations, atmospheric drag, solar radiation pressure, and propul sion. AFSPC astrodynamics algorithms deal effectively with most of these forces in the context of current space catalog operations, but the future environment will require improved force models.
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From page 27... ...
These include, for example, incorporation of dynamic fit spans and time series methods that have been developed within AFSPC, use of extended Kalman filters with imposed stochastic accelerations,38,39 development of multi-dimensional nongravitational models that more accu rately capture the interaction of an object with the environment (including the effects of atmospheric composi tion and winds) , and the inclusion of coupling between estimates of an object's attitude and its orbit estimation process.40,41,42 To a significant degree, improvement of nongravitational drag force models in the catalog is a limiting factor for ephemeris improvement.
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From page 28... ...
. While the latter limitation can be remedied in part with improved nongravitational force models, the former can be remedied with modern computational strate gies such as parallel computing and flexible hardware and software implementations.
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Recent innovations in high-fidelity gravity modeling have demonstrated computational speeds up to two orders of magnitude faster than conventional methods, through the use of sophisticated interpolation methods and new formulations amenable to parallel evaluation.52,53,54,55,56,57,58 It is noted and applauded that some of these efforts have been and are currently being funded by the Air Force Office of Scientific Research for space situational awareness and future catalog maintenance purposes. Finding: The development and use of higher-fidelity force models, both nongravitational and gravita tional, will yield significant improvements to the current catalog accuracy.
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From page 30... ...
In addition to advanced computer architectures, the achievement of a robust system will require possible advances in data association methods, orbit propagation, orbit determination, bias estimation and mitigation, batch and nonlinear filtering methods, and report-to-orbit updates. Data Association The data association method currently used in AFSPC algorithms is a nonstatistical fixed gated association method called ROTAS (Report Observation Association)
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From page 31... ...
Finding: Advanced data association methods such as multiple hypothesis tracking will produce a signifi cant improvement in the automation of the space surveillance system, including the sensor processing. The algorithms should be adapted to high-performance computing and advanced computer architectures and should make use of kinematic, feature, and nontraditional data.
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From page 32... ...
Finding: Future computational demands such as the characterization of uncertainty and use of high fidelity models may require the development and use of fast and accurate ordinary differential equation propagators that take advantage of advanced computer architectures and parallel formulations. Statistical Initial Orbit Determination Currently, initial orbits (sensor tracks)
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Furthermore, the use of modern algebraic manipulation tools can provide high-order analytic theories that were impossible to produce in decades past. Such high-order methods and other analytic innovations can provide insight and benefit to a variety of future astrodynamics space situational awareness tasks.89,90,91,92,93,94 It is therefore imperative that the astrodynamics community and AFSPC maintain their expertise, familiarity with, and continued support for analytic theories (in the context of both opera tions and theoretical development)
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Until and unless a program is developed to solve this issue, such as AFSPC creating such courses, or placing pressure on university systems to do so, it is unrealistic to expect current AFSPC personnel to adopt these mathematical approaches.
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Correct characterization of non-Gaussian probability density functions arising from nonlinear transforma tions such as nonlinear dynamics and coordinate transformations; 5. Correct characterization of errors in the model dynamics (e.g., atmospheric drag and solar radiation)
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In this case, the covariance remains valid over 50 orbits or so; however, it also degrades in due course. This example illustrates the problem of using covariances to represent the uncertainty and suggests that a better represen tation of the probability density function is needed if one is to achieve statistically robust characterization of uncertainty, which again is fundamental to achieving a robust capability across the Space Surveillance Network.
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37 ASTRODYNAMICS ALGORITHMS Figure 2.1.1 Figure 2.1.1 right
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The connection between these two approaches, namely, differential corrections (or the Gauss Newton method) and filtering and smoothing, is provided in the paper by Bell.105 For the propagation of uncertainty, the extended Kalman filter is often used; however, the unscented Kalman filter should also be considered.106,107 As illustrated in Figure 2.1.1, more general nonlinear filtering methods are needed that can more closely approximate the evolution of the true probability density function.
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112 K.J. DeMars, "Nonlinear Orbit Uncertainty Prediction and Rectification for Space Situational Awareness," Ph.D.
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Instead, in this section the committee provides a brief overview of recent space situational awareness research, and then focuses on a key framework perceived by the committee to be particularly impactful in terms of meeting future JSpOC space situational awareness needs. Broad Research in Space Situational Awareness Recent research in the realm of space situational awareness has cast a wide net: a survey of recent conference presentations at the yearly Advanced Maui Optical and Space Surveillance Technologies (AMOS)
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From page 41... ...
Horwood, and A.B. Poore, "Space object maneuver detection via a joint optimal control and multiple hypothesis tracking approach," Paper AAS-12-159, 22nd AAS/AIAA Space Flight Mechanics Meeting, Charleston, S.C., January 2012.
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From page 42... ...
Such relational databases have been developed to support the storage and retrieval of dynamical and contextual information for scientific missions, and have become a worldwide standard.127,128 In those applications, each object is provided with an identification number, which then can be used to uniquely associate many different aspects of that body, including ephemeris, attitude, and estimated constants. For complex bodies, these ID numbers can be further nested, allowing for a detailed and high-dimensional model to be tracked, thereby providing a framework for tracking satellite clusters and formations in the space situational awareness population.
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From page 43... ...
. Recommendation: Air Force Space Command should work with Air Force Materiel Command, the National Aeronautics and Space Administration, the National Oceanic and Atmospheric Admin istration, and other community members to create and expand research programs in the astro dynamics research and development community through the Air Force Research Laboratory to: • Measure, model, and forecast conditions in the upper atmosphere; • Develop and implement improved nongravitational models for solar radiation pressure and atmospheric drag; • Develop and implement continued improvements to gravitational modeling; • Investigate new data association methods, especially for breakups in low Earth orbit and geostationary Earth orbit clusters; • Develop a program to better characterize sensor-level errors including biases to improve the input to orbit determination; • Improve nonlinear estimation and the representation of uncertainty to ensure realism in estimations of uncertainty (covariance)
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