A Long‐Term Broadcast Ephemeris Model for Extended Operation Of
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Received: 7 August 2020 Revised: 12 October 2020 Accepted: 13 October 2020 DOI: 10.1002/navi.404 ORIGINAL ARTICLE A long-term broadcast ephemeris model for extended operation of GNSS satellites Oliver Montenbruck Peter Steigenberger Moritz Aicher Deutsches Zentrum für Luft- und Raumfahrt (DLR), German Space Abstract Operations Center (GSOC), 82234 GNSS positioning relies on orbit and clock information, which is predicted on Weßling, Germany the ground and transmitted by the individual satellites as part of their broadcast Correspondence navigation message. For an increased autonomy of either the space or user seg- Oliver Montenbruck, DLR/GSOC, ment, the capability to predict a GNSS satellite orbit over extended periods of up Münchener Str. 20, 82234 Weßling, Germany. to two weeks is studied. A tailored force model for numerical orbit propagation Email: [email protected] is proposed that offers high accuracy but can still be used in real-time environ- ments. Using the Galileo constellation with its high-grade hydrogen maser clocks as an example, global average signal-in-space range errors of less than 25 m RMS and 3D position errors of less than about 50 m are demonstrated after two-week predictions in 95% of all test cases over a half-year period. The autonomous orbit prediction model thus enables adequate quality for a rapid first fix or contingency navigation in case of lacking ground segment updates. KEYWORDS autonomy, broadcast ephemeris, Earth orientation parameters, force model, GNSS, orbit pre- diction, SISRE 1 INTRODUCTION Current GNSSs thus largely depend on the availability of ground-based orbit determination and time synchroniza- Positioning in global navigation satellite systems (GNSSs) tion (OTDS) as well as regular upload capability to supply is enabled through pseudo-distance measurements to at orbit and clock information to the users. A greater inde- least four tracked satellites along with knowledge of the pendence can be achieved through autonomous onboard satellites’ positions and clock offsets (Langley et al., 2017). orbit determination based on measurements with inter- The latter information is made available in the form satellite links (ISLs; Ananda et al., 1990)butisnotgener- of broadcast ephemerides transmitted by each individ- ally available in today’s GNSSs. GPS has implemented ISLs ual satellite as part of its navigation message. Broadcast in Block IIR (Rajan, 2002), Block IIF (Fisher & Ghasemi, ephemerides describe the orbital motion and clock offset 1999),andGPSIII(Maineetal.,2003) satellites, but it is variation through a small set of parameters over a limited not publicly disclosed whether and to what extent they validity range of less than a few hours. Batches of multi- can also be used for an autonomous onboard generation ple ephemeris data sets covering a larger period of time are of ephemeris data. BeiDou has implemented ISLs with pre- obtained from orbit and clock determination and predic- cise ranging capability on all satellites of the BDS-3 constel- tion in the ground segment and routinely uploaded to the lation (Wang et al., 2019;Yangetal.,2019;Zhouetal.,2018) GNSS satellites. Depending on the constellation architec- and makes use of such measurements in the ground-based ture, this information is refreshed on representative time ODTS process. Even though autonomous navigation con- scales of one hour to a day. cepts based on these ISLs are addressed in various studies NAVIGATION. 2020;1–17. wileyonlinelibrary.com/journal/navi © 2020 Institute of Navigation 1 2 MONTENBRUCK et al. (see, e.g., Tang et al., 2018; Guo et al., 2020), their onboard Numerical orbit propagation of GPS and GLONASS was implementation status is unclear. Galileo considers ISLs to studied earlier in Seppänen et al. (2012)asameansto enhance the ODTS process for next generation satellites reduce the time-to-first-fix of consumer grade receivers in (Fernandez et al., 2010; Amarillo Fernandez, 2011), but it the absence of network assistance. Here, prediction peri- is likewise open whether ISL measurements will also be ods of up to four days were considered and clock stability used for autonomous on-board orbit determination. was identified as a key limitation for the achievable SISRE In the absence of full-featured autonomous orbit deter- and the resulting positioning accuracy. mination and prediction capability (“autonav”), a routine In the present study, we assess necessary force model upload of broadcast ephemeris fitted to a long-term orbit improvements to bridge periods without broadcast prediction can be used as a backup in case of the extended ephemerides of up to 14 days through numerical orbit loss of contact between the control segment and a GNSS prediction. The related error budgets in terms of orbit satellite. A corresponding “extended mode” is defined errors, SISRE, and single point positioning (SPP) per- in GPS (IS-GPS-200K, 2019), during which the satellites formance are discussed. As a reference case, we select provide a ranging capability with reduced performance the Galileo constellation, which does not presently offer for at least 14 days after the last successful upload. The ISLs or autonav capabilities, but is particularly promising globally averaged signal-in-space range error (SISRE) in terms of long-term orbit and clock modeling. Among degrades gracefully over time and is specified to remain others, Galileo employs a highly homogeneous constel- below a 95th-percentile value of 388 m throughout this lation in terms of satellite platforms, which facilitates two-week period (DOD, 2020). This value includes orbit the use of a common dynamical model in a long-term and clock contributions and represents an upper limit orbit propagator. In addition, Galileo offers highly stable for the overall constellation performance. In practice, a atomic frequency standards, which helps to confine notably better performance has been demonstrated in a the respective SISRE contribution. On the other hand, 70-day long-term propagation test conducted with the Galileo involves a pair of satellites in moderately eccentric GPS III-1 satellite in mid-2019. Here, worst-user-location orbits, which provide additional insight into the capa- SISRE values remained below 45 m after 20 days and bilities of numerical as opposed to analytical long-term below 600 m after 70 days (Steigenberger et al., 2020). orbit models. While the daily upload of broadcast ephemeris batches We start this study with an assessment of the Galileo covering a long period of time can address the needs orbit prediction accuracy that can be achieved with state- of extended operations, it implies a high uplink capac- of-the-art models considering a ground-based GNSS orbit ity and adequate onboard storage. Even though improved determination and subsequent prediction. The respective ephemeris compression techniques may contribute to a results are used to identify actual limits in the long-term reduction of the required data volume, they are not predictability of a GNSS orbit and provide a reference for expected to change this situation in a fundamental man- the performance assessment of a simplified (analytical or ner and would also require a change of the established numerical) orbit propagator. ephemeris models and representation. In a second step, a tailored force model is identified Within this study, we consider the feasibility of long- that can be used to propagate a GNSS satellite orbit term ephemeris prediction through numerical integration. based on an initial state-vector and auxiliary parameters Other than analytical models, numerical orbit models can from a ground-based orbit determination process. Aside provide a close-to-reality representation of forces acting on from a trade-off of gravitational force models, a combined a GNSS satellite and are therefore well suited to describe analytical-plus-empirical solar radiation pressure (SRP) orbital perturbations over extended periods. In accord with model is presented to offer an adequate representation of practical needs, propagation errors in numerical orbit pre- non-gravitational contributions. Finally, a numerical inte- diction are close to zero near the reference epoch and gration scheme is identified that combines low complexity grow gradually over time. This is different from analytical with proper efficiency and is thus well suited to be used orbit models based on “general perturbation” theories that on receiver or on-board processors with limited computa- exhibit a model-dependent best-fit error at all times due tional capabilities. to a simplified representation of short-periodic perturba- Conceptually, the numerical orbit propagator can be tions. In principle, a single state vector and a limited set executed inside a GNSS satellite to provide real-time infor- of auxiliary parameters, such as force model coefficients mation on its own instantaneous position and velocity or, and Earth orientation parameters, can be used to predict a alternatively, inside a user receiver to compute the orbits GNSS orbit over “arbitrary” times with the graceful degra- of the entire constellation at a time. Given the computa- dation of accuracy. tional effort associated with long-term orbit integration, MONTENBRUCK et al. 3 TABLE 1 Processing standards for Galileo orbit determination and prediction Data, models, algorithms Precise Tailored Observations Dual-frequency code and phase observations from Cartesian satellite positions 80 globally distributed monitoring stations of the International GNSS Service