Analytical Nonlinear Propagation of Uncertainty in the Two-Body Problem

Fujimoto, Kohei; Scheeres, Daniel J.; Alfriend, Kyle T.

doi:10.2514/1.54385

Cited by 66 publications

(29 citation statements)

References 9 publications

(26 reference statements)

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“…Here the linearized dynamics errors have non-zero components in both the tangential and normal directions. It is interesting to note that Fujimoto et al 11 In the examples depicted in Fig. 6 and Fig.…”

Section: Isolation Of Linearized Dynamics Errorsmentioning

confidence: 99%

“…One approach is to change the coordinates used for propagating the covariance, such as classical orbit elements, 8 equinoctial orbit elements, 4,7,9,10 Poincaré orbit elements, 11,12 polar coordinates, 7 and curvilinear coordinates. 4,13,14 Another approach is to simply transform the Cartesian covariance into a more suitable representation using Eq.…”

Section: B Techniques To Recover the Non-gaussian Error Volumementioning

confidence: 99%

“…error transition tensor. 11,15,16 Another approach employing Gaussian mixture models 17 addresses the limitations of representing the error volume as a single Gaussian probability density function (pdf). Gaussian sum filters estimate any arbitrary pdf as a weighted sum of Gaussian components and have been successfully applied to determining satellite error volumes.…”

Section: B Techniques To Recover the Non-gaussian Error Volumementioning

confidence: 99%

See 2 more Smart Citations

Impact Of Non-Gaussian Error Volumes On Conjunction Assessment Risk Analysis

Ghrist

Plakalovic

2012

AIAA/AAS Astrodynamics Specialist Conference

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An understanding of how an initially Gaussian error volume becomes non-Gaussian over time is an important consideration for space-vehicle conjunction assessment. Traditional assumptions applied to the error volume artificially suppress the true non-Gaussian nature of the space-vehicle position uncertainties. For typical conjunction assessment objects, representation of the error volume by a state error covariance matrix in a Cartesian reference frame is a more significant limitation than is the assumption of linearized dynamics for propagating the error volume. In this study, the impact of each assumption is examined and isolated for each point in the volume. Limitations arising from representing the error volume in a Cartesian reference frame is corrected by employing a Monte Carlo approach to probability of collision (P c ), using equinoctial samples from the Cartesian position covariance at the time of closest approach (TCA) between the pair of space objects. A set of actual, higher risk (P c ≥ 10 -4 ) conjunction events in various low-Earth orbits using Monte Carlo methods are analyzed. The impact of non-Gaussian error volumes on P c Nomenclature for these cases is minimal, even when the deviation from a Gaussian distribution is significant.

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Section: Isolation Of Linearized Dynamics Errorsmentioning

confidence: 99%

Section: B Techniques To Recover the Non-gaussian Error Volumementioning

confidence: 99%

Section: B Techniques To Recover the Non-gaussian Error Volumementioning

confidence: 99%

See 1 more Smart Citation

Impact Of Non-Gaussian Error Volumes On Conjunction Assessment Risk Analysis

Ghrist

Plakalovic

2012

AIAA/AAS Astrodynamics Specialist Conference

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“…Techniques for such approaches have usually involved either higher order expansions about the nominal trajectory [10,5], multiple nonlinear propagations of a distribution of state-space points [2], or some hybrid of the two approaches [4]. There has been some recent progress in this area; Coffee et al [2], for instance, introduced a computational method for extracting and using dynamical "channels" through the state space of the circular restricted three-body problem (CR3BP).…”

Section: Introductionmentioning

confidence: 99%

Efficiently evaluating reachable sets in the circular restricted 3-body problem

Komendera

Garland

Bradley

et al. 2015

IEEE Trans. Aerosp. Electron. Syst.

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In space mission trajectory planning in dynamic environments, such as at asteroids, scenarios leading to failure must be discovered. Given an initial state of a spacecraft about an asteroid, failure can be simply quantified as impact of the vehicle with the asteroid or escape of the vehicle from the asteroid. For mission planning and execution purposes it is necessary to perform maneuvers to avoid such outcomes, however the overall set of possible maneuvers that either avoid impact or escape can be a complex set that cannot be analytically characterized. This paper introduces a reachable set explorer (RSE) for exploring the reachable set of a spacecraft-the set of trajectories under a range of V expenditures. This approach is applied to the circular restricted 3-body problem (CR3BP) where a brute-force approach is intractable. RSE focuses on the boundaries between impact, escape, and in-system regions, known as the end-result regions. Manuscript

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“…On the other hand, Monte Carlo simulations provide a high precision, but call for numerous computations. Based on the Taylor series expansion theory, Sengupta et al [11][12][13] proposed a second-order state transition tensor (STT) method for relative motion, which provided an analytical characterization of the secondorder nonlinearity. In the current paper, this second-order STT method is employed for error propagation of target…”

Section: Introductionmentioning

confidence: 99%

Uncertainty Engagement Analysis of Exoatmospheric Interceptor Based on Reachable Set Model

Chai

Chen

Zhang

et al. 2015

AIAA Atmospheric Flight Mechanics Conference

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This paper studies the engagement analysis problem of exoatmospheric interceptors. Firstly, an interceptor reachable set (RS) model with consideration of Earth rotation is developed. Secondly, the algorithms of intercept window analysis and launch parameter determination are proposed based on the RS model for performing ideal engagement analysis, which neglects the uncertainty. Thirdly, statistic errors are taken into account and propagated by employing the second-order state transition tensor (STT) method. Lastly, uncertainty engagement analysis is explored to evaluate the interception result under the influence of errors. Simulation example shows that the proposed approach is effective and beneficial for searching better launch solutions of interceptor. The established RS model is also applicable to other relative fields.

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Analytical Nonlinear Propagation of Uncertainty in the Two-Body Problem

Cited by 66 publications

References 9 publications

Impact Of Non-Gaussian Error Volumes On Conjunction Assessment Risk Analysis

Impact Of Non-Gaussian Error Volumes On Conjunction Assessment Risk Analysis

Efficiently evaluating reachable sets in the circular restricted 3-body problem

Uncertainty Engagement Analysis of Exoatmospheric Interceptor Based on Reachable Set Model

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