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An architecture for a visualbased PNT alternative
This work illustrates implementation using the simple architecture of a star tracker camera. Known as CROSS, the technology is a new navigation tool in development by the University of Sydney |
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Abstract
This paper treats the problem of positioning and navigation in the absence of GNSS. Given recently raised vulnerabilities for GNSS both on Earth and in space, the work revisits the old problem of the sextant in new light. The combination of stars and planetary horizons was the popular tool for autonomous navigation on-board spacecraft, but given the rise of GNSS receivers, this solution has been largely disregarded. New spacecraft missions beyond Earth have made new progress in visual-based navigation. The work utilises these new methodologies in the scenario that RF-derived positioning is unavailable, achieving a performance below 100 m.
An additional important consideration is the development of new navigation infrastructure in LEO and the Moon. Current methods seek to use GNSS and RF-derived sources for orbit determination, however, to be seen as ‘redundancy infrastructure’ for critical Earth and beyond applications, these signals cannot be the primary and only source of navigation reference. This paper utilises derived performances for visual-based methods and applies them to the ranging service problem. Most user scenarios in maritime, aviation and lunar domains are satisfied.
This work illustrates implementation using the simple architecture of a star tracker camera. Known as CROSS, the technology is a new navigation tool in development by the University of Sydney. As a star tracker is common device to many spacecraft platform, it simplifies implementation, given that redundant systems are always not a priority to the manufacturer.
1. Introduction
The security and authenticity of Position, Navigation and Timing (PNT) for management of Low Earth Orbit (LEO) satellites has never been more crucial. With the growth of enormous mega constellations, and the increased activity of malicious actors in the space arena, PNT systems need to be strengthened.
Radio Frequency (RF)-derived is the dominant PNT source being used in space today, leveraging off Global Navigation Satellite Systems (GNSS) and ground tracking infrastructure. Even though these mechanisms are highly accurate, they are also easily jammed and spoofed from malicious sources, as well as being limited in coverage and availability. Utilising visual-based methods can be more reliable and not as restrictive.
Stars and celestial bodies have long been considered separately in attitude determination applications [1–6]. However, a combination of these sources are now being considered for positioning, where operating in tandem provides an ability for relative positioning to the celestial body centre [7–13].
Recent missions have successfully used celestial navigation for the purposes of orbit determination, target tracking and rendezvous. Such missions include Hayabusa 2, which employed single target tracking at long distances and artificial landmark navigation on approach [14]. Similar approaches have been developed and successfully operated on DART [15] and OSIRIS REX [16] missions.
Even though missions have been successful in the use of visual-based navigation for relative positioning to small celestial objects such as asteroids, delivering an visual-based navigation system for absolute positioning is not as well developed. However, as mentioned, the need for alternatives to RF-derived positioning is necessary.
Some recent early stage studies have evaluated the use of the plan- etary body limb for the Earth orbit determination problem [10,17]. However, more successful results have been achieved for the case of the Moon [12,18,19]. The approaches developed for the Lunar scenario are treated for the Earth, as was initially adopted in Ref. [20].
This issue is especially challenging for the case of Earth due to the atmosphere, which develops a non-constant offset to the measured horizon. This issue is not developed in the literature, as noted in Ref. [21]. It is also present in other planetary systems of interest for exploration, such as Mars. This paper presents a potential to this problem.
An additional challenge presented to the navigator is miscalibration in the optical lens system. Star trackers are often employed to solve this problem [22]. The paper proposes solutions to this issue also modelling the effect of the Earth albedo effect.
The paper presents the potential performance of a visual-based PNT infrastructure for mega-constellations. Not only may this provide an alternative source of orbit determination reference for the spacecraft in orbit, but it might be also leveraged by future navigation constellations to support ranging services for terrestrial and lunar users. This future infrastructure is commonly coined LEO GNSS [23,24] and Lunar Communication and Navigation Satellites (LCNS) [25–27]. It is a requirement in various industries that any alternative service cannot rely on GNSS, and so it is a requirement that an orbit determination capability must be independent [28,29].
The novel nature of the work is presented by the following points:
• A complete and practical assessment to the use of visual-based navigation to support future ranging navigation infrastructure.
• A review of PNT requirements from terrestrial critical transport users and operators, as well as Earth-orbiting satellites and lunar spacecraft.
• A solution to the atmospheric offset problem for visual-based navi-gation in LEO. This may also be applied to other planetary bodies that may contain an atmosphere.
• An approach to multiple attitude and navigation camera systems, as well as an assessment to the effect of Earth albedo on star detection and misalignment correction.
• A performance evaluation for the introduction to LEO ranging infrastructure around the Earth, including a novel approach to its predicted performance. The paper starts by introducing the PNT landscape, illustrating the various required performances for both in-orbit satellites and terrestrial users of a space-based ranging service. An architecture is then introduced for position determination utilising visual-based references. After presenting and discussing the potential performance, this method for orbit determination is considered as part of a new type of GNSS-like ranging service.
2. The PNT landscape
PNT information is essential for most modern technology, from navigating ships and aircraft to providing time of transaction recordings for the financial market. The adoption of PNT across market sectors has been well considered within the literature [30–32]. Many articles especially emphasise the need for robust PNT across each domain, assuring its availability and integrity.
Given the importance of this information for system integrity, separate industrial bodies and organisations have captured minimum performance requirements for their respective technologies. Four different domains are reviewed in this paper, across aviation, maritime, terrestrial and lunar space, to understand target performance requirements that are required by a visual-based navigation alternative.
These requirements are driven with respect to both primary and back-up related PNT infrastructure, that should be assured for the sys-tem to act responsibly. The performance requirements are captured in Table 1.
2.1. Aviation
The aviation industry is very strict when considering the user segment, given the safety-of-life criticality of their application. Because of the raised vulnerabilities of GNSS, pilots are instructed that such instruments should not be used as their primary source of position information. Instead, radar, ground tracking, and even human-derived visual feature recognition should be employed by the pilot.
The user requirements for navigation may be derived by the integrity alert limits by airspace, these being the limit to navigation accuracy uncertainty before an alert is issued. The integrity alert limits for GNSS, derived from the GNSS Manual [33] issued by the International Civil Aviation Organisation, are used in Table 1 as the absolute minimum expected performance for an aviation navigation unit. For most segments of the aeroplane voyage, excluding those of final approach, the user should hold a 500 m confidence in their position.
2.2. Maritime
The maritime industry maintains less strict requirements for navigation than aviation. However, the maritime sector has been subject to some of the most extreme jamming and spoofing attacks of recent years. One such series of event was exposed in a study by the Centre for Advanced Defence Studies [39]. Focusing on GPS spoofing attacks in Russia and Syria, cases were reported in the Black Sea and Syria where cargo ships reported their position several miles outside of Moscow. Similar events have also been reported in the Port of Shanghai, China [40], as well as around the Red Sea [41].
In response to these malicious attacks, as well as other sources of disruption to GNSS, the International Authority of Lighthouse Authorities derived a suggested list of minimum maritime user requirements for each phase of a voyage [34]. The measures also include system integrity requirements, which were discussed in Section 2.1 on aviation. The suggested performances are summarised in Table 1. It should be noted that the cruder performances are permitted during the ocean and coastal phases of a voyage, where accuracies of less than 100 m are required. This is within an absolute frame, and so dead reckoning based systems would not be feasible.
The definition of a back-up system is a key output of [30] a system that ‘ensures continuation of the navigation application, but not necessarily with the full functionality of the primary system and may necessitate some change in procedures by the user.’ By this definition, if GNSS become inoperable, such a backup system must be available to fulfil this need. The back-up system would require 99% availability [34], so terrestrial infrastructure providing a ranging signal would not be suitable.
2.3. Terrestrial space
Most requirements for Earth-orbiting satellites are driven by the technology capability rather than the needs of the application [36]. Performances given in Table 1 consider applications of Synthetic Aperture Radar (SAR), LEO broadband constellations and geostationary communication satellites.
Even if their performances might not be met for the primary mission, back-up or redundant systems are helpful to ensure system reliability. For tracking and monitoring of space traffic, as well as space situational awareness applications, accuracies are typically at the 0.5 km mark [37], achieved through basic ground-based tracking techniques. Supplementing this with an autonomous on-board system would be beneficial to reduce dependency on expensive radar infrastructure, as well as ensuring the system is self-reliant.
An important topic of this paper is the application of visual-based PNT to the delivery of LEO PNT services. This is considered a different category of requirement to those discussed in this section, and so is treated as part of the system analysis in Section 4.
2.4. Lunar space
Lunar navigation requirements have been summarised in recent in-ternational 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) [42], and LunaNet by NASA [38]. These efforts have captured requirements for different mission phases, driven by a motivation that current systems are insufficient.
The requirements treated by NASA’s LunaNet and associated infrastructure for each mission phase are summarised in Table 1 [38]. Most phases require performances up to 100 m, which might be met by the visual-based PNT architecture outlined in Section 3.
The delivery of navigation services from lunar orbit may also utilise visual-based PNT for orbit Determination. Section 4 concentrates on the delivery of terrestrial PNT services, but this might be extrapolated for lunar environments.
3. A proposed alternative
This section evaluates the expected performance and challenges of a visual-based PNT alternative. The proposed technology is considered in context of operational environments discussed in Section 2.
Visual-based refers explicitly to the visual band of the electromagnetic spectrum. Measurements of this kind are typically observed by a camera. Given the nature of visible sunlight, stars and their visible band emissions (450–800 nm), both direct and indirect observations, such as through reflection, can be used as a permanent natural form of navigation reference. These statements should be obvious for the reader, and clearly humans constantly use this type of medium for navigating our own environment. The important point is that this is an alternative to GNSS/RF-based positioning sources, which rely on man-made infrastructure and are more simple to manipulate and deceive [35].
For a spacecraft or ship, disrupting a camera would require a very close or extremely powerful light emitting device to interfere with the observation, and so these navigation references are a powerful alternative. This is not to say they are a replacement. As discussed in Section 2, the focus is to have a resilient back-up to RF-based navigation. It should be note that the current state-of-art visual navigation systems are two orders of magnitude worse than their RF-based equivalents.
Introduced is a proposed architecture for a visual-based navigation alternative. The concept is not novel. As discussed, for the last 60 years, many engineers and scientists have proposed, developed and successfully demonstrated sextants, star and horizon trackers, deep space optical navigation sensors and visual-light ranging devices. However, the adoption of these technologies as an alternative or back-up system for RF-defined environments has not been treated.
Aspects of the approach are assessed by using real space captured image sets, simulated Earth and star lighting environments, and modelling of the orbit trajectory, introducing realistic error parameters. Each analysis independently describes the data used to calculate and present performance of the proposed methodology.
3.1. Concept of operations
The vision-based concept consist of an optical assembly of at least two sensors. Each sensor will point orthogonally, either directed at the celestial body horizon or a star field. The purpose is to capture measurements from each observed object to derive a position reference.
An illustration of the concept is presented in Fig. 1, treating a spacecraft in orbit. ‘Star sense’ operates as an attitude sensor, providing an orientation between the inertial, celestialframe of the stars and the sensor body, and ‘horizon sense’ provides information on the desired body origin reference.
Different terminology is adopted to not confuse the reader with the traditional, separate attitude sensors. This is especially the case for horizon sense, which usually acts as an attitude determination instrument. However, to derive inertial reference frame information, a position in space is also required. The methodology proposed here operates in reverse.
The optical navigation sensor architecture is developed using an initially purposed star tracker made by the University of Sydney. Known as CROSS, a wide field of view optical assembly and baffle supports a high performing attitude determination reference for a CubeSat architecture [43,44]. This same architecture is treated here for the combined star and horizon sening architecture.
The properties of the CROSS star tracker are summarised in Table 2. The same sensor assembly will also be utilised for ‘star sense’. For ‘horizon sense’, a slight increase in FOV is used, from 20◦ to 40◦. A baffle is not necessary for ‘horizon sense’ as observations of the Moon and Earth are desired, and are not treated as stray light sources to observing stars. A picture of CROSS is shown in Fig. 2.
It should be noted that an infrared-band sensor might also be considered, permitting much more sustainable operations in eclipse. It has also been discussed in previous work that the atmosphere is at a near constant height elevation in this band [21]. However, this work is limited to considering the visible light bands utilising the architecture of a star tracker. An infrared sensor is a topic of further work.
3.2. Implementation methodology
The operation algorithms include star tracking alongside attitude determination, horizon identification and position localisation. Measurement are combined within a Kalman filter to improve performance, which is quite substantial. These steps are not presented in detail, but the main ideas and results are outlined. The reader is referred to recent work in the literature with the introduction of each topic.
3.2.1. Attitude determination
The operation of the star tracker within the scope of optical navigation is not discussed in this paper, as the topic is very mature. The reader is referred to state-of-the-art publications on the topic of star trackers [4,5,44,45].
To summarise the core algorithms implemented, the methodology is as follows:
1. Image is captured by star sense.
2. Filter image using a Gaussian/blur kernel.
3. Establish bright pixel/star threshold and search image for stars.
4. Generate regions of interest around each pixel.
5. Calculate star centre by moment method centroid.
6. Identify stars by use of TETRA algorithm [46].
7. Calculate attitude by identified stars celestial frame vectors and measured body vectors by Davenport q-method [47].
The attitude is then combined with the measured horizon edge localisation to produce a position estimate.
It might be considered helpful to include the star centroid estimates directly into the position localisation algorithm, where an output would include both attitude and position information. However, the horizon model also includes orientation information. Even if the horizon identified points are weighted relative to the stars, as the horizon is much less accurate than the star measurements, studies by the authors that the loss in accuracy is significant. So, the process of attitude and position determination is decoupled.
3.2.2. Horizon edge identification
As with star tracking, the topic of horizon sensing for attitude determination is a mature topic. Early horizon sensors approximated the horizon to a flat line, given the planetary geometry measured close to the Earth surface. With leapfrog advances in camera technology and processing, horizon identification and approximation has treated with ever greater detail the observed conic geometry.
Identification and sub-pixel localisation of the point series treated in this work considers the well-developed approach of [18]. This approach is summarised in a series of steps:
1. Identify the direction of sunlight to the planetary body.
2. From the image corners, draw a series of lines running along the direction of illumination. This step is illustrated in Fig. 3.
3. When the line encounters a bright pixel greater than a certain threshold, commence counting to the number of subsequent pixels that also exceed
4. This threshold.
5. If the number of bright pixels exceed a minimum count, then create a region of interest around the pixels.
6. By use of a Sobel-based gradient kernel, identify the pixel in the region where the increase in intensity across pixels is greatest.
7. Create a new region around the desired pixel, and apply a Zernike moment on the region to identify the sub-pixel where intensity change reaches its peak.
To demonstrate the expected performance, an additional step is introduced. A hyperbola is fitted to the located pixel points. The Fitzgibbon conic section fitting technique is used for this [48]. This is combined with a RANSAC outlier rejection methodology [49].
The performance of the horizon edge localisation is assessed using an image sourced from NASA from the orbit of the International Space Station [50]. The image contains the same pixel resolution as the CROSS camera sensor specified in Table 2. Even though the optic assembly is different, the precision demonstrated is assumed comparable.
The results are presented in Fig. 4. The precision of the fit is esti-mated to be approximately 2 px when calculating the root-mean-square error. This error is caused primarily by camera-related noise. This pre-cision will be utilised in the subsequent analysis of Section 3.4.
An important consideration is the atmospheric offset, which might be abstracted from Fig. 4 given the uncertainty in discerning what might be clouds or atmospheric illumination, and what is the horizon body. This is a topic of discussion in Section 3.3.2.
3.2.3. Position localisation
Position estimation using the measured planetary horizon is an often revisited topic. The topic has re-emerged recently as part of recent efforts led by NASA to revisit the Moon. NASA set a requirement for their Orion crewed module that it must operate autonomously in cis-Lunar space. Recent developments and approaches include [9,19].
The measured horizon, as introduced in Section 3.2.2, is either measured as an ellipse, circle, parabola or hyperbola, depending on the orientation of the camera. All are conic sections, and so may be treated by the general form,
3.3. Challenges
This section briefly discusses two major challenges for the proposed system. The first is the calibration of misalignment between the two sensors, and the effect stray light might have. The second is the bias in the observed horizon compared to the planetary ellipsoid, caused by the atmosphere. Both these issues have been ever present in vision-based position determination [9]. Presented are methodologies that hold po-tential to overcome these challenges.
3.3.1. Misalignment calibration and stray light
The implementation of the ‘star sense’ and ‘horizon sense’ combination may suffer from significant misalignment hurdles that impact on accuracy. The intention is that both sensors will be calibrated prior to launch. However, it is well known that during launch and operations, a number of external factors will influence the mechanical alignment between the sensors.
This challenge will be overcome by utilising unbiased star measurements through both sensors. ‘Horizon sense’ may also act as a star tracker, detecting stars instead of identifying the horizon edge. So, by calculating the inertial attitude for both cameras, labelled A and B, the interlock matrix might be calculated by,
A model of a star map and Earth might then be simulated, with the Earth placed in the image corner. The stars irradiance is dependent on the apparent magnitude m, star temperature T and wavelength, written as [53],
where Lo and Mo are the absolute brightness and magnitude of the Sun, β is the conversion factor from parsec to metres, σ, h and k are the Stefan, Planck and Boltzmann constants respectively, and c is the speed of light.
A simulated star map and Earth are illustrated in Fig. 5 using the simulated parameter approach just described. This simulation also successfully identified stars. Using the procedure outlined in Section 2.2.1 for attitude.
Determination from a typical star tracker, the accuracy delivered is 30”.
When introduced to the misalignment correction, this delivers a combined offset of approximately 0.01◦. This misalignment is intro-duced to the full simulation, which is presented as part of Section 3.4.
3.3.2. Atmospheric offset
The atmospheric offset is one of the key challenges for a LEO horizon estimate, or indeed for any planet with an atmosphere. This problem has not been given much study in the literature, with the most recent work by Christian [21].
Christian poses a solution by studying the potential illumination measured by the camera. He calculated an offset of the order of 25 km. However, this is distinctly during daylight operation, and will change during sunset/sunrise and eclipse. It is also dependent on the camera exposure time.
This estimate might be used as an initial estimate to the atmospheric offset. However, the estimate should be validated by use in a least squares filter. The known ellipsoidal parameters of the Earth and the orbit propagation model should provide sufficient information to further refine the horizon estimate.
The atmospheric offset ρ, assuming this is constant to all observed directions of the ellipsoid, may be incorporated in a modified ellipsoidal body matrix,
The EKF parameters are then calculated by the Jacobian. There is no dependence to the atmospheric offset in the orbit propagation.
The atmospheric offset can be reset throughout orbit as the illumination changes from day to night, where the boundary height seen in the image plane ρ raises and lowers.
3.4. Expected performance
The methodology presented in this section are now simulated and compared. They are generated from a scenario of lost-in-space, where no prior position is known by the user. This is a worst case scenario. Horizon points are varied with a 2 px error, as identified in Section 2.2.2, and the ‘star sense’ and ‘horizon sense’ cameras are simulated according to specifications contained within Table 2.
The simulation is run for nearly two orbits. An atmospheric offset ρ is set to 25 km [21], with an initial estimate error at 1 km. The entire filter is run over two orbital periods. The simulation is run on MATLAB.
Given the models seek to aid LEO satellites, orbital altitudes at 300 km, 600 km and 1200 km are compared in Fig. 6. The accuracy and precision (standard deviation) is reported in Table 3. Each result is given by an error and standard deviation for cross-track, along-track and radial error terms.
A steady state is achieved in Fig. 6 after a single orbit, which for a LEO satellite is approximately 90 min. Each of the parameters presented in Table 3 is calculated after the first orbit of 90 min, where it is assumed the solution has converged. The margin of error below 100 m satisfies requirements for some LEO applications reported in Table 1. There ap-pears to be no strong dependence on orbital height at close proximity to the body. The estimated standard deviation indicates strong stability after the solution has converged.
To explore the atmospheric offset correction, the estimated ρ values over the simulation are presented in Fig. 7. The reduction of error is fast, with no noticeable impact to the simulation accuracy. The offset is fast reduced to an approximate 10 m average within 10 min. The standard deviation of the error is also included as a dashed line in this plot.
4. Introduction to navigation infrastructure
As raised in the introduction to this work, not only may visual-based PNT be utilised by spacecraft in-orbit but also as a supporting system for terrestrial and lunar ranging services. Recent plans for LEO mega- constellations [23,24], as well as lunar orbit [25,26,38], envisage the delivery of a new-type of ranging signal. This would be unlike traditional ranging like GPS and Galileo, where the signals are distributed freely, but instead be closed and protected.
Present infrastructure only considers the source of orbit determina-tion to be derived by GNSS or ground infrastructure. Given the restricted availability of tracking stations across the globe, GNSS is even being solely relied upon for the generation of ephemeris on-board the satellites. However, these systems may not be treated as a backup, as they would then be unable to operate if GNSS is denied or unavailable [28]. Thus, a an alternative to GNSS and RF-derived orbit determination should be considered, like the visual-based system treated in this article.
It should be mentioned that what is being proposed is not a replacement but a supporting system to assure that a ranging service may still be delivered in the absence of GNSS. As discussed in Section 2, this is a requirement for both maritime and aviation applications to treat the system as an alternative or back-up. This is also required for a ranging service beyond Earth and on the Moon, as GNSS coverage is very limited.
In Section 3.4, the performance of visual-based PNT for orbit determination was recorded for radial, along- and cross-track. This may be transformed into an equivalent ephemeris error by using the work of Chen in Ref. [54]. The principles are now introduced but only a limited discussion.
Chen considers the probability distribution of ranging signals distributed across the user plane on Earth by a single satellite. The unit vectors of pointing to positions
The GDOP has been reported across MEO GNSS and LEO mega constellations in the pioneering work of Reid et al. [23] that summarises the GDOP expected across each varying orbital geometry.
Upcoming LEO constellations include Teledesic, OneWeb and Star-link. According to Fig. 8, the expected GDOP is on the order of 1.0. Substituting this into (23) using the expected error of 50 m for the user range error σURE, the potential performance for a user position derived by such a ranging signal is 50 m.
Recalling the performances expected for aviation and maritime sectors, this result is promising to be applied across application domain where a back-up system would need to deliver a performance at 100 m. Thus, a vision-based orbit determination may be considered as an alternative technology to RF-based GNSS and ground station tracking for future LEO-based ranging systems. This could also be translated for use in a lunar positioning service, adopting a similar analysis.
5. Conclusions
The work introduces a visual-based PNT system and demonstrates this it is an alternative to GNSS and RF-derived positioning. This system is treated in the framework of being an orbit determination alternative for LEO satellites as well as being a supporting system to new concepts of GNSS in LEO and Lunar environments.
The potential performance delivered by such a system is better than 100 m. This is shown by simulating the orbit of a LEO satellite across multiple altitudes and calculating the standard deviation across along- track, cross-track and radial dimensions. Challenges for LEO operations are also considered, including eclipse and daytime operations as well as atmospheric bias in the observed horizon.
A visual-based PNT system might also be implemented as a form of orbit determination for proposed LEO ranging constellations. It was demonstrated that this can satisfy the requirements of most terrestrial user domains, including maritime and aviation. The results might also be treated in terms of lunar users as part of a lunar navigation service.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors wish to acknowledge the support and expertise of Prof. Daniele Mortari, who has continued to provide extensive advice and review to this research topic at the University of Sydney. This followed from a five month research visit to Texas A&M University.
This research was partially funded by the ARC Training Centre for Cubesats, UAVs and their Applications (CUAVA) – Project ID IC170100023.
The authors would also like extend appreciation to the rest of the CROSS research team, especially Co-Lead Julian Guinane.
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Abbreviations
EKF, Extended Kalman Filter; GDOP, Geometric Dilution of Precision; GNSS, Global Navigation Satellite System; LCNS, Lunar Communication and Navigation Satellites; LEO, Low Earth Orbit; MEO, Medium Earth Orbit; PNT, Position Navigation and Timing; RF, Radio Frequency; SAR, Synthetic Aperture Radar.
First Published by Elsevier Ltd on behalf of IAA. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).
Acta Astronautica 210 (2023) 601–609 © 2023 The Authors.
Republished with authors’ permission.
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