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

Abstract

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.

The J 2 Relative Perturbation Analysis of Satellite Formation under the Requirement of Relative Position Maintenance with Millimeter-Level Accuracy

“…Based on the Gim-Alfriend's studies, Sengupta et al [16] developed a second-order state transition tensor (STT) and a nonlinear solution including the effects of J 2 perturbation by combining the Keplerian STT with Gim-Alfriend's [7] linear model. Then, Yang et al [17] derived a more complete second-order STT for relative motion under the J 2 -perturbed elliptic orbits based on the Sengupta et al's [16] work. The two studies above [16,17] did not consider the effect of J 2 perturbation of the second-order transformation from the rectilinear relative state to the osculating ROEs and the second-order propagation of the mean ROEs.…”

“…Then, Yang et al [17] derived a more complete second-order STT for relative motion under the J 2 -perturbed elliptic orbits based on the Sengupta et al's [16] work. The two studies above [16,17] did not consider the effect of J 2 perturbation of the second-order transformation from the rectilinear relative state to the osculating ROEs and the second-order propagation of the mean ROEs. Similar to the methods in [16,17], Zhen et al [18] developed a second-order analytical STT for relative motion under the J 2 -perturbed elliptic orbits by using the geometric method, and the result is more accurate than that of previous linear or nonlinear analytic methods.…”

Reachable domain for satellite relative motion along elliptic orbit with uncertainty and process noise

“…10 Yang et al. 11 developed a nonlinear analytical uncertainty propagation method using the state transition tensors, where the J 2 perturbation was included.

Figure 1.Relationship between the RRD and the uncertainty propagation problem.

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“…1 For satellite's relative motion along elliptic orbits, Lee et al 9 proposed a linear analytical uncertainty propagation method based on the analytical solution of the Tschauner-Hempel equations. 10 Yang et al 11 developed a nonlinear analytical uncertainty propagation method using the state transition tensors, where the J 2 perturbation was included.…”

An Analytical Method for Calculating Short-Term Space Interception Probability

“…As for the uncertainty propagation problem in orbital mechanics, there is much relevant research literature [4][5][6]. For the linear propagation process of error, the literature [7] used linear covariance analysis to study the orbit error propagation.…”