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Onboard Orbit Determination for Deep-Space CubeSats
Abstract
In this work, an orbit determination algorithm suitable for CubeSats onboard implementation is developed, which simulates optical autonomous navigation accomplished by a stand-alone platform. An extended Kalman filter featuring line-of-sight acquisitions of planets is selected as the state estimator, and its performances are tested on a Raspberry Pi, whose characteristics are comparable to a miniaturized onboard computer. An improvement of the solution accuracy is performed by correcting the planetary light-time and aberration effects as well as by exploiting the optimal beacons selection strategy to acquire the external observations. Moreover, the numerical precision of the estimator is improved through the implementation of factorization techniques and nondimensionalization strategies. The results are presented for a sample Earth–Mars transfer, where the time slot for the navigation campaign involves 2 h every 10 days. At final time, the probe position and velocity are estimated with a 3σ accuracy of 360 km and 0.04 m/s, respectively.
... In the framework of autonomous interplanetary navigation, on one side, the state-of-the-art focuses mainly on implementing onboard orbit determination algorithms to estimate the probe state. [12][13][14] On the other side, while a detailed pipeline for Image Processing (IP) at mid-and close-range is available, [15][16][17] few are the works developing an IP pipeline for the extraction of the planet LoS direction, 18,19 and even fewer are the ones presenting a complete navigation cycle. In this context, the present work, framed within the ERC-funded EXTREMA (Engineering Extremely Rare Events in Astrodynamics for Deep-Space Mission in Autonomy) project, 20 wants to propose an exhaustive autonomous vision-based navigation algorithm suited for deep-space miniaturized probes. ...
... The work combines an image processing (IP) pipeline for the extraction of planet information from the image 18 with an extended Kalman filter (EKF) based on the celestial triangulation approach. 10,14,21 In addition, since in interplanetary space light effects, i.e., light-time and light aberration, 10 become significant due to the consistent velocity of the probe and the enormous distance between the spacecraft and the planet, their action is included in the DART Lab sky simulator, 22 and their corrections are implemented in the navigation filter. ...
... Image Generation. The generation of the sky-field images input in the VBN filter is performed by adopting an improved version of the DART Lab 1 sky simulator, 14,22 where the light effects are modeled. 10 On one side, the light-time effect is simply included by projecting the planet position at epoch τ instead of at epoch t, when the signal is received by the probe. ...
A new era of space exploitation is fast approaching. An exponential number of CubeSats, shoe-boxed spacecraft, will be launched into space, owing to their low cost compared to traditional probes. At the current pace, piloting CubeSats from the ground with standard radiometric tracking will become unsustainable. This work tackles the problem from the navigation point of view by developing a fully autonomous vision-based navigation algorithm suited to deep-space miniaturized platforms. An extended Kalman filter featuring planet position extraction from deep-space images is exploited to determine the probe trajectory onboard. Preliminary results show that accuracy of about 1000 km and 0.5 m/s for the position and velocity components can be reached in deep space. Introduction. The space economy is booming. A significant role is played by deep space exploration, whose growth is driven by the increasing number of missions planned by space agencies and by the advent of deep-space CubeSats. These miniaturized probes have triggered a revolution in the way satellites have been launched into space, owing to their low cost and reduced development time compared to traditional spacecraft. 1 Under the propulsive momentum of the new space economy, several deep-space CubeSats applications are foreseen. 2, 3 Yet, their growth is unsustainable with current practice. 4 Operating a deep-space probe involves determining its position , planning its trajectory, and controlling its motion. Currently, the probe position is estimated by exchanging a two-way signal between ground stations and spacecraft. 5 Yet, ground control requires large teams of engineers , takes a large share of the space mission cost, and has a limited number of communication slots which restricts the number of manageable probes. In other terms, the escalation of miniaturized satellites into deep space will soon lead to the saturation of ground-based facilities, and human-in-the-loop navigation for interplanetary missions will quickly become unsustainable. 4 Autonomous navigation alternatives could represent a solution to this problem, such as autonomous X-ray pulsar-based, 6 autonomous radio-based, 7 and vision-based navigation (VBN). Among these approaches, VBN is a cheap and fully ground-independent solution, which enables in-terplanetary CubeSats to determine their position by observing the movement of celestial bodies on images taken by optical sensors, such as cameras or star trackers. In deep space, Solar System bodies, e.g., planets and asteroids , are unresolved, meaning their light falls in one pixel only of the image. 8 In this framework, the celestial body Line-of-Sight (LoS) direction, extracted from the image, can be exploited as information to navigate the
... EXTREMA aims at enabling self-driving interplanetary CubeSats in deep-space cruise. To navigate throughout the Solar System, the probe can exploit the known position of planets at a given epoch and triangulate the spacecraft position when these planets are recognized in on-board camera images [34]. The IP pipeline which provides measurements to the navigation filter is divided in several steps [35]: ...
The increase in number of interplanetary probes has emphasized the need for spacecraft autonomy to reduce overall mission costs and to enable riskier operations without ground support. The perception of the external environment is a critical task for autonomous probes, being fundamental for both motion planning and actuation. Perception is often achieved using navigation sensors which provide measurements of the external environment. For space exploration purposes, cameras are among the sensors that provide navigation information with few constraints at the spacecraft system level. Image processing and vision-based navigation algorithms are exploited to extract information about the external environment and the probe’s position within it from images. It is thus crucial to have the capability to generate realistic image datasets to design, validate, and test autonomous algorithms. This goal is achieved with high-fidelity rendering engines and with hardware-in-the-loop simulations. This work focuses on the latter by presenting a facility developed and used at the Deep-space Astrodynamics Research and Technology (DART) Laboratory at Politecnico di Milano. First, the facility design relationships are established to select hardware components. The critical design parameters of the camera, lens system, and screen are identified and analytical relationships are developed among these parameters. Second, the performances achievable with the chosen components are analytically and numerically studied in terms of geometrical accuracy and optical distortions. Third, the calibration procedures compensating for hardware misalignment and errors are defined. Their performances are evaluated in a laboratory experiment to display the calibration quality. Finally, the facility applicability is demonstrated by testing imageprocessing algorithms for space exploration scenarios.
... The functional layout of Experiment 2 is represented in Fig. 2. The target state and the one estimated by the navigation algorithm [9] are fed as inputs to the Guidance and Control (GC) algorithm, which runs on a Single-Board Computer (SBC). The output of the GC process is used to actuate the cold-gas thruster that is installed on the test bench. ...
As the number of interplanetary space missions keeps increasing thanks to the reduction of spacecraft development and integration costs, there is the urge of avoiding the saturation of the ground infrastructure required to operate satellites. The aim of the EXTREMA project, which has received fundings from the European Research Council, is to solve the aforementioned issue by enabling deep-space autonomous spacecraft. This work presents the EX-TREMA Thruster in The Loop Experiment (ETHILE), a facility under development at the DART laboratory of the Politecnico di Milano. Its aim is to test and validate novel guidance algorithms tailored for satellites traveling autonomously in deep space. Therefore, it shall model the real actuation of low-thrust propulsion systems, measure the produced thrust, and feed the measurements to a high-fidelity numerical propagator. It is worth noting that a true real-time simulation would require an extremely long time: to complete an interplanetary transfers many months or even years are needed. EXTREMA aims at exploiting a scaled model of the physical system, and to correlate the results with the original one thereafter. Through a mapping between the original system and a fast-evolving one, it will be possible to execute the guidance and control simulations in a shorter time frame, which will last only a few hours or days. Once detailing the mapping principle, the paper describes the layout and characteristics of the ETHILE facility, followed by an overview of the guidance and control algorithms, developed in the framework of EXTREMA. Finally, some preliminary results are given and future developments are outlined.
... Because cruise-phase deep space autonomous navigation is still an area of active research [11,8,13,2], and the arguably operational simplicity in terms of guidance and control for the far-approach phase, we abstain from making deep considerations on which profile the spacecraft adopts in that period and concentrate on the scope of this work -much more challenging -that is when the spacecraft is fully autonomously navigating relative to the asteroid without ground supervision, similar to what was made in previous studies [43]. ...
We use nonlinear robust guidance and control to assess the possibility of an autonomous spacecraft fast approaching and orbiting an asteroid without knowledge of its properties. The spacecraft uses onboard batch-sequential filtering to navigate while making a rapid approach with the aim of orbital insertion. We show through conservative assumptions that the proposed autonomous GN\&C architecture is viable within current technology. Greater importance is in showing that an autonomous spacecraft can have a much bolder operational profile around an asteroid, with no need to inherit the conservative and cautious approach of current missions, which rely on ground intervention for firstly constraining uncertainties to a very low level before close-proximity. The results suggest that such paradigm shift can significantly impact costs, and exploration time, which can be very useful for exploring highly populated regions.
... We introduce a random perturbation in the range of [−10 3 , 10 3 ] km on the position variables and in the range of [−10 −3 , 10 −3 ] km/s on the velocity variables, which are conservative values taken from literature on optical-based autonomous navigation systems. 46,47 Since the time of flight changes after each time the trajectory is recomputed, we adjust the number of intervals K to be used for the next optimization such that the function K(t f ) varies linearly with respect to the time of flight. In particular, we define ...
Ballistic capture corridors allow a spacecraft to be temporarily captured about a planet without any thrust firing. They represent a promising approach for future deep-space small-satellites missions, where only limited fuel can be carried onboard. In an effort to enable autonomous interplanetary CubeSats, a guidance algorithm based on convex optimization is exploited to design low-thrust minimum-fuel space trajectories which target ballistic capture corridors at Mars. An Hermite-Legendre-Gauss-Lobatto scheme with nonlinear control interpolation is used to discretize the trajectory. A variable time of flight version of the algorithm is developed and tested in closed-loop guidance simulations, where multiple reference trajectories need to be computed during a simulated interplanetary transfer. The variable time of flight algorithm is of paramount importance when closed-loop guidance is considered to avoid that no feasible solutions are found when the spacecraft is too close to the target celestial body. We show the effectiveness of the variable time of flight algorithm compared to the fixed time of flight one.
A new era of space exploration and exploitation is fast approaching. A multitude of spacecraft will flow in the future decades under the propulsive momentum of the new space economy. Yet, the flourishing proliferation of deep-space assets will make it unsustainable to pilot them from ground with standard radiometric tracking. The adoption of autonomous navigation alternatives is crucial to overcoming these limitations. Among these, optical navigation is an affordable and fully ground-independent approach. Probes can triangulate their position by observing visible beacons, e.g., planets or asteroids, by acquiring their line-of-sight in deep space. To do so, developing efficient and robust image processing algorithms providing information to navigation filters is a necessary action. This paper proposes an innovative pipeline for unresolved beacon recognition and line-of-sight extraction from images for autonomous interplanetary navigation. The developed algorithm exploits the k-vector method for the non-stellar object identification and statistical likelihood to detect whether any beacon projection is visible in the image. Statistical results show that the accuracy in detecting the planet position projection is independent of the spacecraft position uncertainty. Whereas, the planet detection success rate is higher than 95% when the spacecraft position is known with a 3sigma accuracy up to 10^5 km.
Line-of-Sight (LoS) navigation is an optical navigation technique that exploits the direction to visible celestial bodies, obtained from an onboard imaging system, to estimate the position and velocity of a spacecraft. The directions are fed to an estimation filter, where they are matched with the actual position of the observed bodies, retrieved from onboard stored ephemerides. As LoS navigation represents a really promising option for the next-generation deep-space spacecraft, the objective of this work is to provide new insights into the performance. First, the information matrix is analyzed to show the influence of the geometry between the spacecraft and the observed planet(s). Then, a Monte Carlo approach is used to investigate the influence of measurement error (ranging from 0.1 to 100 arcsec), and tracking frequency (ranging from four observations per day to one observation every two days). The effect on navigation performance is quantified by two indicators. The first is the 3D position and velocity Root-Mean-Square-Errors, computed once the estimation is considered to be steady-state. The second is the convergence time, which quantifies the required time for the estimation to reach the steady-state behaviour. The simulation is based on a set of four planets, which do not follow the common heliocentric dynamics but rotate around the Sun with the same (distance-independent) angular velocity of the spacecraft. This approach allows the separation of scenario-dependent behaviours from navigation intrinsic properties, as the same relative geometry between observer and observed objects is maintained during the whole simulation. The results provide a useful guide for the next-generation autonomous navigation system, for both the definition of hardware requirements and the design of an appropriate navigation strategy. Considerations are then applied to Near-Earth Asteroid fly-by mission scenarios for the definition of the navigation strategy and hardware requirements. It is shown the importance of relative angles between the spacecraft and the planets. In the single-planet observation scenario, when the angle between the position vectors of the spacecraft and planet approaches a null value, the estimation error decreases. In the double-planets observation scenario, when the separation angle between the two LoS directions gets close to 90°, the estimation error decreases. The main influence on the performance is driven by the measurement error, which with current technologies is shown to be able to provide a position error in the order of a few hundred kilometers, while with a lower measurement error (0.1 arcsec) it would be possible to have a position error below 100 km. Finally, it is demonstrated that tracking frequency plays a secondary role in the performance, and only influences tangibly the convergence time.
A new space era is fast approaching. In this decade, CubeSats have granted affordable access to space due to their reduced manufacturing costs compared to traditional missions. Although most of miniaturized spacecraft has thus far been deployed into near-Earth orbits, soon a multitude of CubeSats will be employed for deep-space missions as well. By conquering the interplanetary exploration, they will represent a step further in the democratization of space. The current paradigm for deep space mission is based on ground-based guidance, navigation, and control operations, and thus with human-in-the-loop operations. Although this is reliable, ground control slots will saturate soon, so hampering the current momentum in space exploration. The EXTREMA (Engineering Extremely Rare Events in Astrodynamics for Deep-Space Missions in Autonomy) project aims to challenge and revolutionize the current paradigm under which spacecraft are operated. The goal is to enable self-driving CubeSats, capable of traveling in deep space without requiring any control from ground. The project has been awarded a European Research Council (ERC) Consolidator Grant, a prestigious acknowledgement that funds cutting-edge research in Europe. This work gives an overview of EXTREMA, highlighting methodologies and expected results; moreover, the impact on the space sector is also discussed. EXTREMA is built up on three pillars: autonomous navigation, autonomous guidance and control, and ballistic capture. Pillar 1 envisions the development of an optical navigation technique that extracts the line of sight of the celestial bodies to infer the state of the deep-space spacecraft. Pillar 2 deals with the development of a lightweight, robust closed-loop guidance algorithm. Finally, pillar 3 addresses the definition of the corridors for ballistic capture, an extremely rare phenomenon that allows for planetary capture without any energetic effort. The flawless integration of the outcomes from the three pillars into an Orbital Simulation Hub will eventually mark the accomplishment of the EXTREMA objectives. The impact of EXTREMA is expected to be immediately transferrable to bigger, monolithic spacecraft as well, as these are usually equipped with better-performing on-board systems. Thanks to their more generous mission budgets, the impact of the technological transfer is projected to open up new opportunities for the exploitation of interplanetary resources and the exploration of the furthest corners of the Solar System.
The Miniaturised Asteroid Remote Geophysical Observer (M-ARGO) mission is designed to be ESA’s first stand-alone CubeSat to independently travel in deep space with its own electric propulsion and direct-to-Earth communication systems in order to rendezvous with a near-Earth asteroid. Deep-space Cubesats are appealing owing to the scaled mission costs. However, the operational costs are comparable to those of traditional missions if ground-based orbit determination is employed. Thus, autonomous navigation methods are required to favour an overall scaling of the mission cost for deep-space CubeSats. M-ARGO is assumed to perform an autonomous navigation experiment during the deep-space cruise phase. This paper elaborates on the deep-space navigation experiment exploiting the line-of-sight directions to visible beacons in the Solar System. The aim is to assess the experiment feasibility and to quantify the performances of the method. Results indicate feasibility of the autonomous navigation for M-ARGO with a 3 σ accuracy in the order of 1000 km for the position components and 1 m/s for the velocity components in good observation conditions, utilising miniaturized optical sensors.
Future space exploration missions require increased autonomy. This is especially true for navigation, where continued reliance on Earth-based resources is often a limiting factor in mission design and selection. In response to the need for autonomous navigation, this work introduces the StarNAV framework that may allow a spacecraft to autonomously navigate anywhere in the Solar System (or beyond) using only passive observations of naturally occurring starlight. Relativistic perturbations in the wavelength and direction of observed stars may be used to infer spacecraft velocity which, in turn, may be used for navigation. This work develops the mathematics governing such an approach and explores its efficacy for autonomous navigation. Measurement of stellar spectral shift due to the relativistic Doppler effect is found to be ineffective in practice. Instead, measurement of the change in inter-star angle due to stellar aberration appears to be the most promising technique for navigation by the relativistic perturbation of starlight.
CubeSats have become an interesting innovation in the space sector. Such platforms are being used for several space applications, such as education, Earth remote sensing, science, and defense. As of May 31st, 2018, 855 CubeSats had been launched. Remote sensing application is the main sector in which CubeSats are being used, corresponding to about 45% of all applications. This fact indicates the commercial potential of such a platform. Fifty eight countries have already been involved with developing CubeSats. The most used CubeSat configuration is 3U (about 64%), followed by 1U (18%), while 6U platforms account for about 4%. In this paper, we present an analysis of the current situation regarding CubeSats worldwide, through the use of a dataset built to encompass information about these satellites. The overall success rate of the CubeSat missions is increasing over time. Moreover, considering CubeSat missions as a Bernoulli experiment, and excluding launch failures, the current success rate was estimated, as a parameter of a binomial distribution, to be about 75%. By using a logistic model and considering that the launchings keep following the current tendency, one can expect that one thousand CubeSats will be launched in 2021, within 95% certainty.
This study provides a single-point position estimation technique for interplanetary missions by observing visible planets using star trackers. Closed-form least-squares solution is obtained by minimizing the sum of the expected object-space squared distance errors. A weighted least-squares solution is provided by an iterative procedure. The weights are evaluated using the distances to the planets estimated by the least-squares solution. It is shown that the weighted approach only requires one iteration to converge and results in significant accuracy gains compared to simple least squares approach. The light-time correction is taken into account while the star-light aberration cannot be implemented in single-point estimation as it requires knowledge of the observer velocity. The proposed method is numerically validated through a statistical scenario as follows. A three-dimensional grid of test cases is generated: two dimensions sweep through the ecliptic plane and the third dimension sweeps through time from January 1, 2018 to January 1, 2043 in 5-year increments. The observer position is estimated at each test case and the estimate error is recorded. The results obtained show that a large majority of positions are well suited to position estimation by using star trackers pointing to visible planets, and reliable and accurate single-point position estimations can be provided in interplanetary missions. The proposed approach is suitable to be used to initiate a filtering technique to increase the estimation accuracy.
We present a new extensive analysis of the old problem of finding a satisfactory calibration of the relation between the geometric
albedo and some measurable polarization properties of the asteroids. To achieve our goals, we use all polarimetric data at
our disposal. For the purposes of calibration, we use a limited sample of objects for which we can be confident to know the
albedo with good accuracy, according to previous investigations of other authors. We find a new set of updated calibration
coefficients for the classical slope–albedo relation, but we generalize our analysis and we consider also alternative possibilities,
including the use of other polarimetric parameters, one being proposed here for the first time, and the possibility to exclude
from best-fitting analyses the asteroids having low albedos. We also consider a possible parabolic fit of the whole set of
data.
NASA's New Millennium Program consists of a se- ries of missions whose primary purpose is to demon- strate the feasibility of new technologies for space- flight. Deep Space 1 is the first in this series of mis- sions. It was launched on October 24, 1999 and has completed its first leg of the mission - flyby of the asteroid Braille - on July 29, 1999. An additional en- counter is planned with the short period comet Bor- relly in September 2001. The new technologies being demonstrated on DS1 include, among others, an ion propulsion system to provide maneuvering thrust, a combined visible/infrared/ultraviolet imaging in- strument, and an autonomous navigation system. The purpose of this paper is to describe the com- putational elements of the autonomous navigation system and assess its performance in guiding the spacecraft to its first target. Some of the difficul- ties encountered during this leg, and how they were overcome, will also be described.
The Miniaturised Asteroid Remote Geophysical Observer (M-ARGO) is planned to be the first standalone deep-space CubeSat mission to rendezvous with and characterise a near-Earth asteroid. To this aim, it is essential to assess the attainable set of target asteroids. This work presents the initial results of the mission analysis and design of M-ARGO. In particular, the original procedure developed to extract the reachable near-Earth asteroids and the subsequent down-selection process are shown. Hundreds of both time- and fuel-optimal low-thrust trajectory optimisation problems have been solved with an indirect approach, targeting asteroids pre-filtered from the Minor Planet Center Database. The method implements a realistic thruster model, featuring variable input power, thrust, and specific impulse, together with an accurate switching detection technique and analytic derivatives. The analysis shows that approximately 150 minor bodies are found potentially reachable by M-ARGO when departing from the Sun–Earth Lagrange point L2 within a 3-year transfer duration. A manual inspection of the transfer features led to a subset of 41 targets seeming more promising according to mission technological requirements and constraints. Initial results indicate mission feasibility for M-ARGO, which has the potential to enable a completely new class of low-cost deep-space exploration missions.
CubeSats offer a flexible and low-cost option to increase the scientific and technological return of small-body exploration missions. ESA’s Hera mission, the European component of the Asteroid Impact and Deflection Assessment (AIDA) international collaboration, plans on deploying two CubeSats in the proximity of binary system 65803 Didymos, after arrival in 2027. In this work, we discuss the feasibility and preliminary mission profile of Hera’s Milani CubeSat. The CubeSat mission is designed to achieve both scientific and technological objectives. We identify the design challenges and discuss design criteria to find suitable solutions in terms of mission analysis, operational trajectories, and Guidance, Navigation, & Control (GNC) design. We present initial trajectories and GNC baseline, as a result of trade-off analyses. We assess the feasibility of the Milani CubeSat mission and provide a preliminary solution to cover the operational mission profile of Milani in the close-proximity of Didymos system.
Deep-space optical navigation is among the most promising techniques to autonomously estimate the position of a spacecraft in deep space. The method relies on the acquisition of the line-of-sight directions to a number of navigation beacons. The position knowledge depends upon the tracked objects. This paper elaborates on the impact of the observation geometry to the overall performances of the method. A covariance analysis is carried out considering beacons geometry as well as pointing and input errors. A performance index is formulated, and criteria for an optimal beacons selection are derived in a scenario involving two measurements. A test case introducing ten available beacons pairs is used to prove the effectiveness of the developed strategy in selecting the optimal pair, which leads to the smallest achievable error.
Missions to asteroids are now an important component of the space exploration program of major space agencies in the world, with the goal of better understanding the formation of the Solar system and learn about their dynamics to be able to react in case of a possible collision with the Earth. As binary asteroids compose approximately
16% of near Earth asteroids, they are getting more attention from researchers. One mission is currently being planned to binary asteroid system 65803 Didymos. This mission motivates research on the
dynamics of a spacecraft near a binary asteroid. Since the primary bodies of these binary systems have small masses, perturbations like the Solar Radiation Pressure (SRP) or the shape of the primary bodies have a great influence on the dynamics of a spacecraft in their vicinity. Studies that already exist on the effect of the SRP on the dynamics of a spacecraft near binary asteroid systems have mostly used low-fidelity SRP acceleration models, such as the cannonball model or simple flat plate model with a purely reflecting spacecraft. This study shows how the choice of the model influences the strength of the SRP acceleration acting on the spacecraft and how it is possible to take advantage of the choice of the nominal attitude of the spacecraft to influence how the SRP affects the spacecraft dynamics when using a more complex SRP acceleration model. Various types of trajectories are studied, with different results and conclusions.
NASA’s Deep Space 1 mission demonstrated that a spacecraft can be navigated autonomously during deep-space cruise operations using only optical navigation measurements. A methodology is developed to evaluate the feasibility and accuracy of the Deep Space 1 orbit determination approach throughout the solar system as a function of a spacecraft’s imaging capabilities. Feasibility can be addressed by comparing the apparent magnitudes of the known population of asteroids against the imaging system capabilities. An upper limit on the accuracy of the spacecraft position estimate at a given location can be formulated by assuming observations of at least two asteroids simultaneously. Example results are presented for three camera implementations that span the range of capabilities flown in deep space to date using orbit and absolute magnitude data for 50,129 of the brightest known asteroids. Broadly speaking, achievable accuracies range from approximately 200 to 12,000 km (1−σ) interior to the main asteroid belt and from 50 to 2000 km within the main belt, depending strongly on the chosen camera implementation. Between the main belt and Jupiter, only a current state-of-the-art imaging system is consistently capable of kinematic positioning using only asteroids. Beyond Jupiter, there are insufficient known asteroids to support this approach without including images of planets and moons. Although these levels of accuracy are far inferior to those achievable with radiometric navigation, they may yet be sufficient to satisfy cruise-phase requirements for many deep-space missions.
Roger Walker and colleagues consider the potential for sending nanospacecraft into deep space.
Improved equations for computing planetary magnitudes are reported. These formulas model V-band observations acquired from the time of the earliest filter photometry in the 1950s up to the present era. The new equations incorporate several terms that have not previously been used for generating physical ephemerides. These include the rotation and revolution angles of Mars, the sub-solar and sub-Earth latitudes of Uranus, and the secular time dependence of Neptune. Formulas for use in The Astronomical Almanac cover the planetary phase angles visible from Earth. Supplementary equations cover those phase angles beyond the geocentric limits. Geocentric magnitudes were computed over a span of at least 50 years and the results were statistically analyzed. The mean, variation and extreme magnitudes for each planet are reported. Other bands besides V on the Johnson–Cousins and Sloan photometric systems are briefly discussed. The planetary magnitude data products available from the U.S. Naval Observatory are also listed. An appendix describes source code and test data sets that are available online for computing planetary magnitudes according to the equations and circumstances given in this paper. The files are posted as supplementary material for this paper. They are also available at SourceForge under project https://sourceforge.net/projects/planetary-magnitudes/ under the ‘Files’ tab in the folder ‘Ap_Mag_Current_Version’.
The Tracking Link Range and Doppler Information Content Tracking Data Error Sources The GPS Calibration and Tracking System Range and Doppler System Measurement Performance Range and Doppler System Positioning Performance
Traditionally, the space industry produced large and sophisticated spacecraft handcrafted by large teams of engineers and budgets within the reach of only a few large government-backed institutions. However, over the last decade, the space industry experienced an increased interest towards smaller missions and recent advances in commercial-off-the-shelf (COTS) technology miniaturization spurred the development of small spacecraft missions based on the CubeSat standard. CubeSats were initially envisioned primarily as educational tools or low cost technology demonstration platforms that could be developed and launched within one or two years. Recently, however, more advanced CubeSat missions have been developed and proposed, indicating that CubeSats clearly started to transition from being solely educational and technology demonstration platforms to offer opportunities for low-cost real science missions with potential high value in terms of science return and commercial revenue. Despite the significant progress made in CubeSat research and development over the last decade, some fundamental questions still habitually arise about the CubeSat capabilities, limitations, and ultimately about their scientific and commercial value. The main objective of this review is to evaluate the state of the art CubeSat capabilities with a special focus on advanced scientific missions and a goal of assessing the potential of CubeSat platforms as capable spacecraft. A total of over 1200 launched and proposed missions have been analyzed from various sources including peer-reviewed journal publications, conference proceedings, mission webpages as well as other publicly available satellite databases and about 130 relatively high performance missions were downselected and categorized into six groups based on the primary mission objectives including “Earth Science and Spaceborne Applications”, “Deep Space Exploration”, “Heliophysics: Space Weather”, “Astrophysics”, “Spaceborne In Situ Laboratory”, and “Technology Demonstration” for in-detail analysis. Additionally, the evolution of CubeSat enabling technologies are surveyed for evaluating the current technology state of the art as well as identifying potential areas that will benefit the most from further technology developments for enabling high performance science missions based on CubeSat platforms.
Autonomous navigation (AutoNav) for deep space missions is a unique capability that was developed at JPL and used successfully for every camera-equipped comet encounter flown by NASA (Borrelly, Wild 2, Tempel 1, and Hartley 2), as well as an asteroid flyby (Annefrank). AutoNav is the first on-board software to perform autonomous interplanetary navigation (image processing, trajectory determination, maneuver computation), and the first and only system to date to autonomously track comet and asteroid nuclei as well as target and intercept a comet nucleus. In this paper, the functions used by AutoNav and how they were used in previous missions are described. Scenarios for future mission concepts which could benefit greatly from the AutoNav system are also provided. © 2012 by the American Institute of Aeronautics and Astronautics, Inc.
DOI:https://doi.org/10.1103/PhysRev.4.345
In order to reduce the operation cost of the deep space missions, a new autonomous navigation algorithm based on the observed images information of different celestial objects is proposed. First, it uses the directional data from the moon and the earth sensors to determine the initial orbit information of the explorer by geometrical method. Then combination with the observation from the star tracker, a real-time autonomous navigation for the spacecraft is accomplished via UD factorization extended Kalman filter (UD-EKF). Performance and robustness of the algorithm are verified by numerical simulations. The results demonstrate that the algorithm is feasible.
The application of the hyperacuity technique to image processing of star trackers is analysed. An analytical study of the error introduced by the centroiding algorithm is presented and it is shown that a systematic contribution and a random one exist. They result from image processing assumptions and photometric measure uncertainty, respectively. Their behaviour is characterised by means of numerical simulations that are based on optics theoretical point spread functions. The latter ones take into account both defocus and diffraction effects. First, measured star position uncertainty is evaluated as a function of defocus. As a result, a criterion for optimal defocus is presented. Subsequently, an original procedure for systematic centroiding error correction by means of a backpropagation neural network is described. It is also suitable for real hardware calibration. When applied to one of the considered numerical models, the position computation accuracy is improved from 0.01 to 0.005 pixels. © 2002 Elsevier Science Ltd. All rights reserved.
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MarCO: Mars Cube One -Lessons Learned from Readying the First Interplanetary Cubesats for Flight
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The Juventas CubeSat in Support of ESA's Hera Mission to the Asteroid Didymos
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ESA's Hera mission to asteroid Dimorphos
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