GNSS-Based Enhanced Precise Orbit Determination for Moon Transfer Orbit
Joseph Locantore and Franco Gottifredi, WAY4WARD s.r.l., Italy
Location: Beacon B
Although the use GNSS (Global Navigation Satellite System) is widely spread in LEO and terrestrial applications, the recent interest in the Moon exploration, expressed by the scientific community, led companies and institutions to study the exploitation of GNSS for Lunar applications with the aim of reducing the operational costs. These applications bring new challenges not only for the faced scenario but also for the tests of the new implemented algorithms. When the spacecraft is well above the GNSS constellations the visibility tends to decrease and the received signals will come either from the main lobe of the transmitter antenna, partially shadowed by the Earth, or from the secondary lobe. The signal’s power at the space receiver will be definitely lower with respect a terrestrial or LEO user due to the higher propagation distance between GNSS satellites and receiver, which consequently experiences a higher free space loss with respect a user close to the Earth. A filtered GNSS navigation solution represents the best approach thanks to the combination of dynamical forces estimation and the GNSS measurements, and solves the accuracy problems affecting not filtered least square solutions, which decreases proportionally to the distance from GNSS constellation and become practically unsuitable at lunar distance. Another challenge is represented by the difficult generation of simulating environment for testing this kind of algorithms; in fact, few tools are available on the market capable to simulate the receiver visibility and the related measurements. These tools, such as newest versions of Spirent simulators, are expensive to buy or rent for small companies, low-cost missions or research applications.
On these grounds, this work proposes the application of an alternative tool, called GNSS Outer Orbits Data Simulator (GOOD Sim) and internally developed by WAY4WARD s.r.l., which has been exploited for the implementation and test of an Extended Kalman Filter optimized for MTO called Moon EPOD (Enhanced Precise Orbit Determination)
The GOOD Sim consists of three main modules: 1) Trajectory Definition, 2) Visibility analysis, 3) Raw Data Generation; each of them provides a User Interface (UI) in order to make its functionalities easier and more understandable for the user.
The first module includes an orbit propagator for the estimation of the receiver satellite trajectory in ECI J2000 reference frame through the numerical integration of the geocentric orbital equations of motion for an MTO trajectory. This scientific simulation begins at a user-defined epoch and geocentric state vector (position and velocity vectors) representing the point of trans-lunar injection (TLI) and ends a user-defined final epoch coincident to defined Moon-centred (selenocentric) distance. The TLI condition can be directly computed by the software through the resolution of the Lambert’s Problem or can be recovered from an external mission cost optimization process output, performed for example by the NASA General Mission Analysis Tool (GMAT). Currently, the geocentric equations of motion include the non-spherical gravity effects of the Earth, the point-mass gravity of the Sun and Moon and the solar radiation pressure; new forces have been planned to be introduced in the future versions of the tool such as non-spherical gravity effects of the Moon.
The Visibility Analysis module exploits the “Advance Constellation Visibility Generator” (ACVG), a WAY4WARD property tool, in order to provide the GNSS Space Vehicles’ orbits, geometric and electromagnetic satellite visibility divided for receiver antennas, transmitter lobes and ionosphere affected signals. It receives in input the defined trajectory, the epoch, the GNSS almanacs, the receiver antenna configuration and signal frequency.
The Raw Data Generator recovers the measurement’s errors at the selected frequency and combines them with the true range according to the visibility analysis estimating the raw GNSS measurements code phase (pseudorange) and carrier phase for the chosen mission scenario.
The Moon EPOD filter exploits an Ionosphere-free multi constellation (GPS and Galileo) measurements model at single frequency called GRAPHIC (Group And Phase Ionospheric Correction), which compensates the ionosphere delay by the average of pseudorange and carrier phase measurements. This approach results to be the best solution for computational effort and accuracy with respect to the double frequency methods because the GRAPHIC technique will work nominally even if there isn’t the ionosphere error, in fact the resultant measure will be an average between carrier phase and code pseudorange in terms of accuracy and noise. In contrast, dual frequency combinations will not perform in the same way in that condition, because the code/carrier phase combinations will be affected by a higher error without the benefit of removing the ionospheric contribution. Besides, the adoption of dual frequency solutions in MTO mission will not grant the same number of available measurements for the POD algorithm to work properly. In fact, in order to build the measure, both observables for example at L1/E1 and L5/E5a should be available at the same time. This condition can’t be satisfied for all the mission duration and prevents the exploitation of the Measurement Update step of the EKF for a longer time interval with respect to the single frequency solution. As result, the state vector estimation will rely just on the dynamic model propagation with a corresponding lower accuracy.
In order to test the functioning and performance of the filter, two different analyses have been done generating scenarios respectively at L1/E1 and L5/E5a frequencies. The test assumes the same MTO trajectory with a time of flight of six days with the Moon EPOD continuously working. During this time interval the receiver has experienced a mean visibility of 5 Space Vehicles (SVs) at L1/E1 and L5/E5a. The tests have demonstrated the possibility to achieve lunar distances through the GNSS support with different accuracy depending on the adopted frequency. In fact, the visibility combined with the measurements error affect differently the filter performance showing a greater robustness and accuracy at L5/E5 band with a 3D position error of 46m (2 sigma) with respect to ones achieved by L1/E1 frequency equal to 430m (2 sigma).
This work proposes an innovative approach for the precise orbit determination based on GNSS for lunar missions as well as an alternative and affordable tool for generating testing scenarios and raw data for companies and institutions that are not able to access the available market solutions. The GOOD Sim tool will be exploited in the ASI (Italian Space Agency) co-funded project CELESTE for the test of Moon EPOD algorithm, developed by WAY4WARD s.r.l., for Moon Transfer Orbit scenarios. This project is currently on going and the consortium is led by QASCOM s.r.l. with WAY4WARD s.r.l. and D-ORBIT S.p.A. as core partners.
Finally, the GOOD Sim tool and the Moon EPOD filter show a great potential for further improvements through the introduction of new features. The GOOD Sim, thanks to its modular design, can be updated by adding new measurement error models for the Raw Data Generator, in order to take into account more noises characterizing the lunar environment. On the other hand, the combination of L1/E1 and L5/E5a measurements could increase the visibility and the achievable performance of the Moon EPOD.