Signal-in-Space Range Error Analysis of the Simulated Broadcast Ephemerides for the Kepler System.

Kurzfassung

Kepler navigation system is a DLR’s proposal for the next generation of GNSS. It comprises a constellation of Galileo-like satellites augmented by Low Earth Orbit (LEO) satellites and exploits optical inter-satellite links (OISLs) for constellation-wide clock synchronization, communication and precise ranging. In our previous works we analyzed extensively precise orbit determination (POD) performance of this system. We simulated various Kepler scenarios, and the POD results were compared to the baseline Galileo scenario. We demonstrated, that Kepler precise orbits can achieve sub-cm Signal in Space Range Errors (SiSREs) compared to few cm for Galileo. However, precise orbits – based on measurement data, are only available with substantial delay and cannot be used for real-time navigation directly. Operational GNSS provides predicted orbits and clock offsets which are distributed in the navigation message for user positioning. Thus, we extended our POD system with prediction and generation of navigation messages. In this contribution, we focus on the analysis of orbit, clock and Earth rotation parameter (ERP) prediction errors for Galileo and selected Kepler scenarios. The Galileo clocks were simulated using a model for Passive Hydrogen Masers with a stability and drift consistent with the precise clocks estimated by the Center for Orbit Determination in Europe (CODE). For the Kepler system, the clocks are assumed to be synchronized and were simulated as null value with a Gaussian noise of 3-10 ps (1-3 mm). The Galileo F/NAV broadcast ephemeris model, which consists of 15 orbital parameters, is used for our analysis. The parameters were fitted to the predicted orbits with a least-squares adjustment and truncated in the navigation message according to the number of bits allocated to each parameter. The clock prediction model consists of a constant and a drift term obtained from linear fit to the clocks estimated in POD. The accuracy of the predicted orbits and clocks found depends on the constellation, POD modelling errors and the propagation interval. In our analysis, we considered scenarios with perfect models and, for more realistic results, with a number of modeling errors introduced in the POD. For all analyzed cases we report global average Signal in Space Range Error (SiSRE) which accounts for orbit and clock errors and is a key performance indicator of a navigation system. Our simulations show, that the Galileo system is capable of providing broadcast data with SiSRE at a dm level, consistent with 1-2 dm SiSRE for the actual broadcast data. For the Kepler system the clocks are synchronized with 1-3 mm precision and there are no additional clock prediction errors. The orbit prediction errors can be well below 1 cm due the exploitation of precise intersatellite ranges. However, the accuracy of predicted Earth rotation parameters (ERPs), which are used in transformation of the orbits from the Earth-Center-Inertial (ECI) to Earth-Centered Earth-Fixed frame (ECEF), have a significant impact on the accuracy of the predicted orbits in ECEF. Currently, we have implemented in our prediction system a simple linear extrapolation of ERPs based on values estimated in POD. We found, that this introduces significant errors in the orbit cross- and along-track direction, increasing the SiSRE by up to a decimeter after 24 h. Therefore, precise modelling and prediction of ERPs is an important factor for achieving sub-cm SiSRE for the Kepler system. We identified two other parameters, GNSS ionosphere-free pseudo-range hardware delays (HDs) and antenna radial phase center offsets (PCOs), that are relevant for SiSRE. For Galileo, they are not critical since HDs and most of the PCO error are absorbed by the estimated satellite clocks and, if assumed stable, do not degrade the accuracy of the clock prediction. For Kepler, where clocks are synchronized in the optical domain and are not estimated in POD, errors of these parameters directly affect SiSRE and must be precisely calibrated. We analyzed also in details the impact of broadcast parameter fit interval length, varying from 10 minutes to 4 h, and parameter truncation on the accuracy of reconstructed orbits and SiSRE. We found, that the maximum orbit fit error for intervals up to 2 h contributes to SiSRE at few mm level, while the fit interval of 4 h can increase SiSRE by a decimeter. The parameter truncation errors are not dependent on the fitting interval and increase SiSRE by an average of 1 cm and maximum of 3 cm. Such errors can be seen as a SiSRE limiting factor for highly accurate Kepler orbits (below 1 cm) and need to be mitigated, e.g. by allocation of more bits to most relevant parameters. Finally, we concluded that SiSRE below 1 cm can be continuously achieved for the Kepler system, which is at least an order of magnitude smaller than for Galileo. However, this requires precisely calibrated GNSS hardware delays and antenna phase center offsets.