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Session B3: Lunar Navigation and Time

Stellar Navigation on the Moon - A Compliment, Support and Back-up to Lunar Navigation
Joshua Critchley-Marrows, Xiaofeng Wu, Iver Cairns, The University of Sydney, Australia
Location: Beacon B

Stellar navigation was first conceived by the Ancient Greeks and has been used throughout the millennia to navigate humanity across the globe, from the neighbouring village to the new world. This strong scientific foundation inspired the first Apollo astronauts to utilise the stars for navigation through Earth orbit into selenocentric proximity. However, since the popularisation of Global Navigation Satellite System (GNSS) navigation, visual-based navigation have become a fringe topic of study. With vulnerability and availability issues apparent with GNSS [1], seeking alternative forms of navigation have brought this topic back to the fold.
Much research and development was made into stellar and celestial navigation when the Soviet-era space race was in full force. A series of National Aeronautical and Space Administration (NASA) supported research and development projects were conducted during the Apollo missions [2][3][4][5].
In 1968, a year before the Apollo moon-landing, a hand-held sextant was qualified in space flight [3]. Designed for attitude, the device is capable of meeting accuracies to 10 arcsec, measuring both stars and the lunar horizon. Later steps towards autonomous star measurements paved the way to the star tracker, to this day the most accurate determination instrument for spacecraft.
Concepts of using the stars for determining a position and orbital estimate arose during and beyond Apollo. Theoretical accuracies at the km were estimated, given the capability of instrumentation during the original space race era [6]. Research continued up until the end of the century, when the incoming GNSS system was envisioned to also support spacecraft navigation in the increasingly popular Low Earth Orbit (LEO) [7]. Since the Moon had lost much of its initial popularity, research and development attention focused to in-orbit GNSS.
As a return to the Moon appears on the horizon, away from terrestrial GNSS, as well as issues of heavy reliance on radionavigation infrastructure, alternatives for in-orbit autonomous navigation have been increasingly discussed[8][9][10][11][12]. Largely these have focused on close proximity navigation, a relative positioning capability, as well as fast moving pulsars that would rely on a high-fidelity optical system. Given limitations to using these sources, a return to stellar and celestial navigation appears required and necessary.
Kuehl studied the combination of a horizon and star sensor for geosynchronous satellites, where point solution accuracies of 60 km and converged navigation solutions of 5 km were measured [8]. This was realised with a star sensor of 10 arc-sec pointing accuracy and a single frame Earth-reference of 0.1°. Even though not a high accuracy, the results are promising, especially given the restrictive boundaries of the scenario, and limited considered measurement instruments.
Dilectis studied navigation using Earth and Moon images alone, measuring the distance error to a celestial body at the 1-2 km level [11]. This is a substantial improvement to those considered by Kuehl. Other studies have come to similar conclusions for horizon or Earth/Moon measuring instruments [13][14]. However, the combination of the star sensor with an orbiting lunar satellite or lunar ground vehicle has not been considered. The compliment of such a system to future lunar navigation infrastructure would be of interest, given the increasing number of potential missions [15].
It is apparent from literature that a sextant system would rely on two core components, a star sensor and a ‘Moon sensor’. The sensor has been considered to take the form of a horizon or celestial sensor, but it could also take the form of a sun sensor, or accelerometer, capable of measuring features with respect to the Moon. A high accuracy and availability in different operational environments is crucial though to performance. A simple LLS model may be applied to the system.
Taking the star sensor accuracy to be 0.01°, which is common to most star systems, and a field of view size of 30°, the performance of the system may be estimated based on the Earth-sensor accuracy. If the pointing vector accuracy is below 0.01°, then a decametre accuracy may be derived.
This model does not account for any improvements that may be made by dynamic filtering or sensor fusion. The demonstrated potential is clear, where the requirements for the market applications discussed in the previous section could be satisfied in most scenarios.
Lunar navigation requirements have been summarised in recent international space agency documentation. It is seen that navigation infrastructure is required to support future missions to the Moon, as an increasing number of private organisations seek travel. Needs are captured in initiatives such as Moonlight by the European Space Agency (ESA) [15], and LunarNet by NASA [16]. These efforts have captured requirements for different mission phases. It is identified that current systems are insufficient.
The requirements proposed by ESA for each mission phase are at the kilometer scale, with some scenarios at 100 m [15]. The theoretical accuracies of the system would appear to be met, especially if the great pointing accuracy of 0.01° to the Moon could be achieved.
The paper will evaluate further the potential of a stellar based navigation system to be applied on the Moon. Sensor assemblies including horizon or celestial images, accelerometers and sun sensors will be considered. The system potential to be applied as a core navigation module or as a supporting element to future lunar navigation infrastructure will also be considered, considering alternative parameters such as availability and integrity. Beyond mere alternative navigation systems, the sensor may form part of a future lunar navigation satellite system, or as a navigation aid to more precise positioning instruments for close proximity operations.
[1] S. Thombre et al., “GNSS Threat Monitoring and Reporting: Past, Present, and a Proposed Future,” J. Navig., vol. 71, no. 3, pp. 513–529, May 2018, doi: 10.1017/S0373463317000911.
[2] J. Mietelski, “A Simple Method of Lunar Surface Navigation,” Icarus, vol. 9, pp. 315–325, Feb. 1968.
[3] B. A. Lampkin and D. W. Smith, “A Hand-held Sextant Qualified for Space Flight,” NASA, Washington, DC, 1968.
[4] H. A. Garcia and W. J. Owen, “Design and Analysis of a Space Sextant for High Altitude Navigation,” https://doi.org/10.2514/3.57131, vol. 13, no. 12, pp. 705–709, May 2012, doi: 10.2514/3.57131.
[5] B. A. Lampkin, “Sextant Sighting Performance for Space Navigation Using Simulated and Real Celestial Targets,” Navigation, vol. 12, no. 4, pp. 312–320, Dec. 1965, doi: 10.1002/J.2161-4296.1965.TB02149.X.
[6] K. D. Hicks and W. E. Wiesel, “Autonomous orbit determination system for earth satellites,” J. Guid. Control. Dyn., vol. 15, no. 3, pp. 562–566, 1992, doi: 10.2514/3.20876.
[7] M. Ripley, Cooper, Daly, and P. Silvestrin, “A dual-frequency GNSS sensor for space applications,” Int. J. Satell. Commun., vol. 16, pp. 273–282, 1998, doi: 10.1002/(SICI)1099-1247(199811/12)16:6.
[8] C. T. F. Kühl, “Combined Earth/Star Sensor for Attitude and Orbit Determination of Geostationary Satellites,” University of Stuttgart, Stuttgart, 2005.
[9] L. M. B. Winternitz et al., “SEXTANT X-ray Pulsar Navigation Demonstration: Additional On-Orbit Results,” in SpaceOps Conference, 2018, pp. 2538–2547, doi: 10.2514/6.2018-2538.
[10] J. A. Christian, “StarNAV: Autonomous Optical Navigation of a Spacecraft by the Relativistic Perturbation of Starlight,” Sensors 2019, Vol. 19, Page 4064, vol. 19, no. 19, p. 4064, Sep. 2019, doi: 10.3390/S19194064.
[11] Francesco de Dilectis, “Vision-Based Autonomous Navigation using Moon and Earth Images,” Texas A&M University, College Station, 2014.
[12] B. Maass, S. Woicke, W. M. Oliveira, B. Razgus, and H. Krüger, “Crater Navigation System for Autonomous Precision Landing on the Moon,” https://doi.org/10.2514/1.G004850, vol. 43, no. 8, pp. 1414–1431, Apr. 2020, doi: 10.2514/1.G004850.
[13] H. Marais Van Rensburg, M. M. Blanckenberg, and W. H. Steyn, “An Infrared Earth Horizon Sensor for a LEO Satellite,” University of Stellenbosch, Stellenbosch, 2008.
[14] V. H. Adams and M. A. Peck, “Interplanetary Optical Navigation,” Jan. 2016, doi: 10.2514/6.2016-2093.
[15] “ESA Moonlight Initiative - LCNS User Scenario Document,” Noordwijk, Nov. 2020.
[16] “LunaNet Concept of Operations and Architecture,” Sep. 2020.



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