Hybrid Method for Uncertainty Propagation of Orbital Motion

Park, Inkwan; Scheeres, Daniel J.

doi:10.2514/1.g001834

Cited by 13 publications

(14 citation statements)

References 23 publications

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“…Equations (27), (35) and 41 properties. To address this problem, a method to propagate the non-Gaussian PDF is developed by combing the nonlinear covariance propagation with a GMM approach.…”

Section: Nonlinear Propagation Of Probability Density Functionmentioning

confidence: 99%

“…It is noted that the transitive STTs in Eqs. (27), (35) or (41) only need to compute once for propagating all the Gaussian mixtures, because all the nonzero mean Gaussian mixtures can be nonlinearly propagated using the same STTs.…”

Section: ( )mentioning

confidence: 99%

“…To avoid these shortcomings, some nonlinear analytical or semi-analytical techniques had been developed in recent years, such as the unscented transformation (UT) method [23], the polynomial chaos (PC) method [24,25], the state transition tensors (STTs) method [26,27], the differential algebraic (DA) technique [28,29], the Gaussian mixture model (GMM) [30][31][32], and the method of solving Fokker-Planck equation (FPE) [33,34]. The UT method [23] delivers an efficient, second-order approximation only for the first two moments of the mapped statistical distributions by using less than 2n+1 sigma-points.…”

Section: Introductionmentioning

confidence: 99%

“…In comparison to UT, the PC method [24,25] can provide more accurate information on higher-order moments and the entire PDF, however, it suffers from the problem of dimensionality. The STTs-based methods [26,27] can analytically propagate uncertainty and requires no random samples once the STTs are integrated along the nominal trajectory. However, high-order derivatives of the governing dynamics need to be computed for these methods, which will be very complex for high-fidelity dynamic systems.…”

Section: Introductionmentioning

confidence: 99%

“…The nonlinear uncertainty propagators mentioned above [23][24][25][26][27][28][29][30][31][32][33][34] mainly focus on the propagation of absolute states uncertainties of satellites, which is usually performed by ground control centers. However, the uncertainty propagation for formation-flying satellites needs to be carried out onboard [16].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Nonlinear Analytical Uncertainty Propagation for Relative Motion near J2-Perturbed Elliptic Orbits

Yang

Luo

Lappas

et al. 2018

Journal of Guidance, Control, and Dynamics

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An analytical uncertainty propagation method based on state transition tensors (STTs) has been developed for satellite relative motion near J2-perturbed, elliptic orbits. The STTs used to propagate the relative state uncertainty are derived by adding a correction into the original STTs for propagating relative state. A new set of transitive STTs is further derived in order to propagate uncertainties for relative motion with abrupt state jumps, e.g. impulsive maneuvers executing on any of the two satellites. The nonlinear analytical solution for propagating the first two moments and the probability density function are formulated by combining the STTs with a Gaussian mixture model. Numerical results show that the proposed method outperforms the linear covariance method and provides good agreement with Monte Carlo simulations on nonlinear, non-Gaussian uncertainty propagation. Moreover, as the STTs can be analytically computed and account for the J2-perturbation, the proposed uncertainty propagator is computationally efficient, which will be potentially useful for onboard conjunction analysis in satellites formulation flying mission.

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Section: Nonlinear Propagation Of Probability Density Functionmentioning

confidence: 99%

Section: ( )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Nonlinear Analytical Uncertainty Propagation for Relative Motion near J2-Perturbed Elliptic Orbits

Yang

Luo

Lappas

et al. 2018

Journal of Guidance, Control, and Dynamics

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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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Nonlinear semi-analytical uncertainty propagation of trajectory under impulsive maneuvers

2018

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Hybrid Method for Uncertainty Propagation of Orbital Motion

Cited by 13 publications

References 23 publications

Nonlinear Analytical Uncertainty Propagation for Relative Motion near J2-Perturbed Elliptic Orbits

Nonlinear Analytical Uncertainty Propagation for Relative Motion near J2-Perturbed Elliptic Orbits

Nonlinear orbital uncertainty propagation with differential algebra and Gaussian mixture model

Nonlinear semi-analytical uncertainty propagation of trajectory under impulsive maneuvers

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