Real-Time Relative Positioning of Spacecraft over Long Baselines

Abstract

This paper deals with the problem of real-time onboard relative positioning of low-Earth-orbit spacecraft over long\ud baselines using the Global Positioning System. Large intersatellite separations, up to hundreds of kilometers, are of\ud interest to multistatic and bistatic synthetic-aperture radar applications, in which highly accurate relative positioning\ud may be required in spite of the long baseline. To compute the baseline with high accuracy, the integer nature of dualfrequency,\ud double-difference carrier-phase ambiguities can be exploited. However, the large intersatellite separation\ud complicates the integer-ambiguities determination task due to the presence of significant differential ionospheric\ud delays and broadcast ephemeris errors. To overcome this problem, an original approach is proposed, combining an\ud extended Kalman filter with an integer least-square estimator in a closed-loop scheme, capable of fast on-the-fly\ud integer-ambiguities resolution. These integer solutions are then used to compute the relative positions with a singleepoch\ud kinematic least-square algorithm that processes ionospheric-free combinations of debiased carrier-phase\ud measurements. Approach performance and robustness are assessed by using the flight data of the Gravity Recovery\ud and Climate Experiment mission. Results show that the baseline can be computed in real time with decimeter-level\ud accuracy in different operating conditions

Geometric total electron content models for topside ionospheric sounding

“…The empirically-derived mapping function proposed by Lear in [11] has reportedly shown good prediction capabilities (see, e.g. [2], [11]- [14]) and is thus taken as a reference.…”

“…Comparing the two mapping functions, they coincide if the following matching conditions hold, which are exemplified for a few realistic scenarios in Hence, Lear's mapping function yields the same results of the thick shell model for receivers in space, Eq. 12, provided that the matching conditions (14) are satisfied. As such, Lear's mapping function can be reasonably assumed to arise from a thick shell model, particularized for a certain (h m ,h M ), which obey the matching conditions.…”

Ionospheric delays compensation for on-the-fly integer ambiguity resolution in long baseline LEO formations

“…A closed-loop scheme for integrating an EKF and an integer resolution approach has been proposed in [11] and it is considered herein as a reference solution for real-time onboard CDGPS in long baseline applications. The main features of this reference scheme are briefly recalled in the following, and the interested reader is referred to [11] for further details. The proposed approach, conceptually sketched in Figure 1, consists in a two-step solution: first DD integer ambiguities are estimated On-The-Fly (OTF) using as little computational effort as possible.…”

“…The magnitude of the DD ionospheric delays mainly depends on the baseline's magnitude, on the receivers' orbits, and on the ionospheric activity. For receivers in polar LEO separated by few hundreds of kilometers the DD delays can be about 0.5 meters in mild ionospheric conditions [10], and can increase by more than one order of magnitude depending on the ionosphere's status [11], Thus, the ionospheric delays must not only be compensated in the applications of interest, but the effectiveness of their compensation can greatly depend on the ionospheric activity. Several approaches exist for compensating the ionospheric delays in spaceborne applications.…”

“…The effectiveness of these two approaches in compensating ionospheric delays is then evaluated by comparing their relative positioning accuracy that can be obtained on actual flight data. This is done using a recently developed common relative positioning approach [11], which is described next.…”