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

Ghrist, Richard W.; Plakalovic, Dragan

doi:10.2514/6.2012-4965

Cited by 15 publications

(6 citation statements)

References 12 publications

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“…Moreover, a method that couples Monte Carlo with orbital dynamics approximation, obtained by means of polynomial chaos expansion, was introduced to compute satellite collision probability with reduced computational effort (Jones and Doostan, 2013). Monte Carlo methods were also used to study the impact of non-Gaussian probability density functions on collision probability computation (Ghrist and Plakalovic, 2012).…”

Section: Introductionmentioning

confidence: 99%

A high order method for orbital conjunctions analysis: Monte Carlo collision probability computation

Morselli

Armellín

Lizia

et al. 2015

Advances in Space Research

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Three methods for the computation of the probability of collision between two space objects are presented. These methods are based on the high order Taylor expansion of the time of closest approach (TCA) and distance of closest approach (DCA) of the two orbiting objects with respect to their initial conditions. The identification of close approaches is first addressed using the nominal objects states. When a close approach is identified, the dependence of the TCA and DCA on the uncertainties in the initial states is efficiently computed with differential algebra (DA) techniques. In the first method the collision probability is estimated via fast DA-based Monte Carlo simulation, in which, for each pair of virtual objects, the DCA is obtained via the fast evaluation of its Taylor expansion. The second and the third methods are the DA version of Line Sampling and Subset Simulation algorithms, respectively. These are introduced to further improve the efficiency and accuracy of Monte Carlo collision probability computation, in particular for cases of very low collision probabilities. The performances of the methods are assessed on orbital conjunctions occurring in different orbital regimes and dynamical models. The probabilities obtained and the associated computational times are compared against standard (i.e. not DA-based) version of the algorithms and analytical methods. The dependence of the collision probability on the initial orbital state covariance is investigated as well.

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Section: Introductionmentioning

confidence: 99%

A high order method for orbital conjunctions analysis: Monte Carlo collision probability computation

Morselli

Armellín

Lizia

et al. 2015

Advances in Space Research

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“…where n(0, C Θ ) is a multivariate normal distribution with zero mean and covariance matrix C Θ . This assumption may break down if a conjunction analysis is done too far in advance [38] or if too few data are used to estimate the satellite state or if there is an unaccounted for bias error in the filter algorithm or data. For simplicity, we persist in the normality and unbiasedness assumptions.…”

Section: (A) Confidence Regionsmentioning

confidence: 99%

“…Trajectory uncertainties in conjunction analysis are usually measured in hundreds of meters [38]. For conjunction analysis done more than a week in advance, those uncertainties can grow to kilometers [39]. As a consequence, S /R ratios greater than ten are the rule, not the exception.…”

Section: False Confidencementioning

confidence: 99%

Satellite conjunction analysis and the false confidence theorem

Balch¹,

Martin

Ferson

2019

Proc. R. Soc. A.

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Satellite conjunction analysis is the assessment of collision risk during a close encounter between a satellite and another object in orbit. A counterintuitive phenomenon has emerged in the conjunction analysis literature: probability dilution, in which lower quality data paradoxically appear to reduce the risk of collision. We show that probability dilution is a symptom of a fundamental deficiency in epistemic probability distributions. In probabilistic representations of statistical inference, there are always false propositions that have a high probability of being assigned a high degree of belief. We call this deficiency false confidence. In satellite conjunction analysis, it results in a severe and persistent underestimation of collision risk exposure.We introduce the Martin-Liu validity criterion as a benchmark by which to identify statistical methods that are free from false confidence. If expressed using belief functions, such inferences will necessarily be non-additive. In satellite conjunction analysis, we show that Kσ uncertainty ellipsoids satisfy the validity criterion. Performing collision avoidance maneuvers based on ellipsoid overlap will ensure that collision risk is capped at the user-specified level. Further, this investigation into satellite conjunction analysis provides a template for recognizing and resolving false confidence issues as they occur in other problems of statistical inference.

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“…Uncertainty propagation plays a key role in many application fields of astrodynamics, such as vehicle navigation, orbit determination, target tracking, space situational awareness, as well as collision assessment [1][2][3][4][5][6]. Moreover, when a complete and accurate statistical description of the propagated statistics is of interest, uncertainty propagation poses the significant challenge of solving partial differential equations to map the probability density functions (PDF) [7][8][9], or carrying out particle-type, computationally demanding studies such as Monte Carlo simulations [3,[10][11][12]. Therefore, some approximations are usually introduced in practical applica-tions.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear orbital uncertainty propagation with differential algebra and Gaussian mixture model

Sun

Luo

Lizia

et al. 2018

Sci. China Phys. Mech. Astron.

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Nonlinear uncertainty propagation is of critical importance in many application fields of astrodynamics. In this paper, a framework combining the differential algebra technique and the Gaussian mixture model method is presented to accurately propagate the state uncertainty of a nonlinear system. A high-order Taylor expansion of the final state with respect to the initial deviations is firstly computed with the differential algebra technique. Then the initial uncertainty is split to a Gaussian mixture model. With the high-order state transition polynomial, each Gaussian mixture element is propagated to the final time, forming the final Gaussian mixture model. Through this framework, the final Gaussian mixture model can include the effects of high-order terms during propagation and capture the non-Gaussianity of the uncertainty, which enables a precise propagation of probability density. Moreover, the manual derivation and integration of the high-order variational equations is avoided, which makes the method versatile. The method can handle both the application of nonlinear analytical maps on any domain of interest and the propagation of initial uncertainties through the numerical integration of ordinary differential equation. The performance of the resulting tool is assessed on some typical orbital dynamic models, including the analytical Keplerian motion, the numerical J 2 perturbed motion, and a nonlinear relative motion.

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

Cited by 15 publications

References 12 publications

A high order method for orbital conjunctions analysis: Monte Carlo collision probability computation

A high order method for orbital conjunctions analysis: Monte Carlo collision probability computation

Satellite conjunction analysis and the false confidence theorem

Nonlinear orbital uncertainty propagation with differential algebra and Gaussian mixture model

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