Rigorous computation of orbital conjunctions

Armellín, Roberto; Morselli, Alessandro; Lizia, P. Di; Lavagna, Michèle

doi:10.1016/j.asr.2012.05.011

Cited by 11 publications

(3 citation statements)

References 13 publications

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“…A DA algorithm has been developed by the authors to compute the arbitrary order Taylor expansions of TCA and DCA with respect to uncertain initial conditions in a general dynamical model (Armellin et al, 2012). As presented in detail in Morselli et al (2014), the Taylor expansions of the state vectors x polynomial map of the relative distance between the two objects is then computed through simple algebraic manipulations.…”

Section: High Order Expansion Of Dca and Tcamentioning

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: High Order Expansion Of Dca and Tcamentioning

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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“…This unique mathematical property makes VIOP interesting for many space-situational-awareness (SSA) activities, potentially in combination with statistical methods. Verified integration has previously been applied to computing Solar-System dynamics [7], intersections between near-Earth objects and Earth [8,9], and satellite conjunctions [6,10]. Verified predictions of the Iridium-Cosmos collision were studied in Ref.…”

Section: Introductionmentioning

confidence: 99%

Verified Regularized Interval Orbit Propagation

Geul

Mooij

Noomen

2021

Journal of Guidance, Control, and Dynamics

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Verified interval orbit propagation provides mathematically guaranteed solutions of satellite position and velocity over time. These verified solutions are useful for conjunction analysis and other space-situational-awareness activities. Unfortunately, verified methods suffer from overestimation and explosive interval growth, limiting the possible propagation time and thus their applicability. Different orbital-element state models have been shown to increase the maximum propagation time to a degree, but at the expense of significant overestimation introduced by the state transformations. This paper proposes the Dromo state model for verified integration. Dromo is a regularized variation-of-parameter formulation of the perturbed two-body equations of motion.Taylor models are implemented for both integration and transformation. Moreover, a technique is developed for dealing with time uncertainty resulting from verified regularized propagation. Dromo significantly prolongs the maximum forecasting window, producing verified trajectories of days up to weeks in duration for the low-Earth orbit regime. A sensitivity analysis of the integrator settings identifies combinations that produce stable and computationally efficient solutions. A sensitivity study of the orbital parameters shows that the method is applicable to a large orbital regime, especially for low-Earth orbit regions that contain high densities of space debris.

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“…A method to compute first guess values of TCA and DCA was developed in (Armellin et al, 2012). This method is based on the propagation of TLE with SGP4/SDP4 and the identification of the conjunction by the rigorous solution of a global optimization problem with the algorithm COSY-GO (Makino and Berz, 2005).…”

Section: First Guess Of Tcamentioning

confidence: 99%

A high order method for orbital conjunctions analysis: Sensitivity to initial uncertainties

Morselli

Armellín

Lizia

et al. 2014

Advances in Space Research

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A high order method to quickly assess the effect that uncertainties produce on orbital conjunctions through a numerical high-fidelity propagator is presented. In particular, the dependency of time and distance of closest approach to initial uncertainties on position and velocity of both objects involved in a conjunction is studied. The approach relies on a numerical integration based on differential algebraic techniques and a high-order algorithm that expands the time and distance of closest approach in Taylor series with respect to relevant uncertainties. The modeled perturbations are atmospheric drag, using NRLMSISE-00 air density model, solar radiation pressure with shadow, third body perturbation using JPL's DE405 ephemeris, and EGM2008 gravity model. The polynomial approximation of the final position is used as an input to compute analytically the expansion of time and distance of closest approach. As a result, the analysis of a close encounter can be performed through fast, multiple evaluations of Taylor polynomials. Test cases with objects ranging from LEO to GEO regimes are considered to assess the performances and the accuracy of the proposed method.

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Rigorous computation of orbital conjunctions

Cited by 11 publications

References 13 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

Verified Regularized Interval Orbit Propagation

A high order method for orbital conjunctions analysis: Sensitivity to initial uncertainties

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