Towards a Daytime and Low-altitude Stellar Positioning System: Challenges and First Results

Loïc Barbot, Marc Ferrari, Johan Montel, Yannick Roehlli, Jean-Luc Gach, William Thuillot, Kjetil Dohlen

Peer Reviewed

Abstract:	Since the emergence of electronic image sensors, stellar pictures can be easily processed by computers to identify stars and measure angles: distance between light spots on the same scene or angle above the visible horizon, like the sextant does for celestial navigation. Adding an inclinometer on the camera axis, the computer is now able to calculate the attitude angles (course, trim and list) in a local coordinate system and the position (latitude, longitude and even altitude). The last coordinate, time, may be measured by observing angular distances on the celestial sphere between stars located near the orbit of a satellite (Moon or LEO). If the sensor is on a vehicle, gyroscopes are necessary to smooth the rotations or vibrations. Going from this appealing theory to the reality of a daytime stellar positioning system hides many challenges such as detecting stars by day, at low altitude or in bad weather. If the level of accuracy increases, many sources of error emerge, e.g., sky background, diffraction limit, vertical deflection. Many prototypes or manufactured products have shown the potential of a stellar positioning system thanks to the maturity of technologies like inertial sensors and silicon CMOS detectors. Most of these applications are designed for altitude operations such as: • yield the attitude angles of satellites, stratospheric balloons, high altitude aircraft or missiles; • adjust the inertial system of civil aircraft; • measure satellite parameters from immobile ground telescopes in altitude; • but rarely for positioning. The last challenge lies in tracking stars from a moving vehicle during daytime at low altitude: sea or land. The lower layers of atmosphere add numerous perturbations, forcing to work by day in infrared band, where silicon sensitivity ends and InGaAs sensitivity starts (or other technologies). This paper aims at looking for a compromise between detector technologies, stars detectability, duration of availability and accuracy of results for a stellar positioning system on a moving vehicle on the ground or at sea. A first parameter is the transmission of the atmosphere: when wavelength increases, scattering decreases but thermal emissions in infrared submerge starlight. Some bands obscure it but transmit photons from molecular resonance fluorescence of sunlight. A rigorous simulation of radiative transfer with local weather parameters is necessary to figure out the best band of transmission. Secondly, the number of observable stars in each band, with a given magnitude or flux, increases with the wavelength… except in R (0.6-0.7?m) and I (0.7-1.0?m) bands where we have few data in star catalogs: the magnitudes of many stars have been calculated by comparing their known data and their spectral type, confirming the tendency. Lastly, silicon technology for light detection is well developed thanks to public cameras and smartphones: the size and number of pixels on a sensor allow a high accuracy on angular distance measurements. In the opposite, Short Wave InfraRed detectors (SWIR: 1.0–2.5 ?m) suffer bigger pitch and poor definition. But the potential of SWIR detectors remains high, and their performances are improving quickly. Betting on this ascending technology readiness, daytime star tracking tests have been realized: simulations are confirmed, and new challenges occur. Table of contents. 1 – Observation tool 2 2 – Observation through the atmosphere 2 3 – Detectable stars from ground 4 4 – Single star or multi stars observation 5 5 – Tests with InGaAs camera 8 6 – Accurate visible horizon? 8
Published in:	Proceedings of the 2022 International Technical Meeting of The Institute of Navigation January 25 - 27, 2022 Hyatt Regency Long Beach Long Beach, California
Pages:	1371 - 1379
Cite this article:	Barbot, Loïc, Ferrari, Marc, Montel, Johan, Roehlli, Yannick, Gach, Jean-Luc, Thuillot, William, Dohlen, Kjetil, "Towards a Daytime and Low-altitude Stellar Positioning System: Challenges and First Results," Proceedings of the 2022 International Technical Meeting of The Institute of Navigation, Long Beach, California, January 2022, pp. 1371-1379. https://doi.org/10.33012/2022.18263
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