Star Tracker System Research Articles

Model-based safety analysis of requirement specifications

Model-based design primarily aims to establish a communication framework throughout a system’s design. Moreover, models with formal semantics allow verification based on rigorous methods, including the analysis of system safety. However, building formal models is a tedious manual process and cannot be easily applied to real problems.A key gap that hinders automation of model development is that there is no systematic way to connect system requirements with the activity of model-based design. In this article, we introduce a workflow to tackle this gap and ultimately automate the analysis of system safety using formal methods.We extend our previous work on boilerplate-based specification of system requirements with ontological semantics towards specifying FDIR (Failure, Detection, Isolation, Recovery) requirements. The workflow is centered around the automated generation of a model skeleton in SLIM, a component-based formal modeling language, from a set of ontology-based requirement specifications. Our approach has been implemented into a dedicated tool, which not only provides visualization of the ontology relations, but also supports traceability of the analysis findings back to the requirements specification. Finally, we provide results on the safety analysis of a real star-tracker system based on a SLIM model derived by minimally changing the auto-generated model skeleton.

Technology Demonstration of Space Situational Awareness (SSA) Mission on Stratospheric Balloon Platform

As the number of resident space objects (RSOs) orbiting Earth increases, the risk of collision increases, and mitigating this risk requires the detection, identification, characterization, and tracking of as many RSOs as possible in view at any given time, an area of research referred to as Space Situational Awareness (SSA). In order to develop algorithms for RSO detection and characterization, starfield images containing RSOs are needed. Such images can be obtained from star trackers, which have traditionally been used for attitude determination. Despite their low resolution, star tracker images have the potential to be useful for SSA. Using star trackers in this dual-purpose manner offers the benefit of leveraging existing star tracker technology already in orbit, eliminating the need for new and costly equipment to be launched into space. In August 2022, we launched a CubeSat-class payload, Resident Space Object Near-space Astrometric Research (RSONAR), on a stratospheric balloon. The primary objective of the payload was to demonstrate a dual-purpose star tracker for imaging and analyzing RSOs from a space-like environment, aiding in the field of SSA. Building on the experience and lessons learned from the 2022 campaign, we developed a next-generation dual-purpose camera in a 4U-inspired CubeSat platform, named RSONAR II. This payload was successfully launched in August 2023. With the RSONAR II payload, we developed a real-time, multi-purpose imaging system with two main cameras of varying cost that can adjust imaging parameters in real-time to evaluate the effectiveness of each configuration for RSO imaging. We also performed onboard RSO detection and attitude determination to verify the performance of our algorithms. Additionally, we implemented a downlink capability to verify payload performance during flight. To add a wider variety of images for testing our algorithms, we altered the resolution of one of the cameras throughout the mission. In this paper, we demonstrate a dual-purpose star tracker system for future SSA missions and compare two different sensor options for RSO imaging.

Systems design results of LunaCube: Dual-satellite lunar navigation system with 6U-CUBESATs

Aiming to establish a long-term presence on the Moon, interest in new and robust communication and navigation capabilities on the lunar surface is greater than ever before. In response, lunar navigation systems (LNS) have been conceptualized and put into action by space agencies. While we expect these services to be fully functional before the late 2020s, many missions are set to begin surface exploration before the initiation of these services. To meet the immediate needs of early missions, our group proposed a small-start technology demonstration mission called the Lunar Navigation CubeSat (LunaCube).The mission aims to demonstrate a LNS transmitter and store-and-forward radio in the vicinity of the Moon and to provide lunar positioning services to lunar surface assets. The project was initiated with funding support from the Japanese Ministry of Education, Culture, Sports, Science, and Technology (MEXT) and completed preliminary design and detailed design in 2021 and 2022 respectively. As a result of the design study, the satellites consist of a 6U-size structure, a 50W-class deployed solar panel, a X-band transponder, three-axis attitude control using a star tracker, sun sensors, gyro, reaction wheels, and reaction control system thruster, as well as orbit control using a water-based resistojet. The total wet mass is less than 14 kg.

AI-Based Real-Time Star Tracker

Many systems on Earth and in space require precise orientation when observing the sky, particularly for objects that move at high speeds in space, such as satellites, spaceships, and missiles. These systems often rely on star trackers, which are devices that use star patterns to determine the orientation of the spacecraft. However, traditional star trackers are often expensive and have limitations in their accuracy and robustness. To address these challenges, this research aims to develop a high-performance and cost-effective AI-based Real-Time Star Tracker system as a basic platform for micro/nanosatellites. The system uses existing hardware, such as FPGAs and cameras, which are already part of many avionics systems, to extract line-of-sight (LOS) vectors from sky images. The algorithm implemented in this research is a “lost-in-space” algorithm that uses a self-organizing neural network map (SOM) for star pattern recognition. SOM is an unsupervised machine learning algorithm that is usually used for data visualization, clustering, and dimensionality reduction. Today’s technologies enable star-based navigation, making matching a sky image to the star map an important aspect of navigation. This research addresses the need for reliable, low-cost, and high-performance star trackers, which can accurately recognize star patterns from sky images with a success rate of about 98% in approximately 870 microseconds.

A real-time calibration method for the systematic errors of a star sensor and gyroscope units based on the payload multiplexed

With the star sensor and gyroscope units integrated for attitude determination, it will provide continuous and accurate attitude information for satellites with a high update rate. This integration could take full advantage of each other. In order to guarantee the accuracy of satellite attitude determination, the calibration of its systematic errors is of critical importance. In this paper, a calibration method for the star tracker and GUs integrated system is proposed based on the satellite payload multiplexed. Firstly, the satellite attitude kinematics model is introduced. Then the measurement model with respect to the systematic errors including the installation errors and GUs drift errors is built for the star sensor, the payload and the GUs. Finally, the state model and observation model are established, according to which the systematic errors are calibrated by a Kalman filter. Simulation results indicate that the proposed method is effective at estimating the systematic errors of the star sensor and GUs integrated system.

An accuracy of better than 200 m in positioning using a portable star tracker

Using a portable star tracking system, the geographical position of the observer, latitude, longitude, and the North direction were obtained. In the previous work, the accuracy of latitude and longitude were obtained as 932 and 1510 m, respectively. The weakest point in the previous work was the installation of the charge-coupled device (CCD) on the inclinometer which had the largest uncertainty in the procedure of positioning. Therefore, a method was presented to calculate the angle between the CCD and the inclinometer. In this work, a new optimization method is applied to improve the accuracy of the calculation of observer position to 147 m in Latitude and 171 m in Longitude. In this method, 80 to 100 stars are used in each picture taken of the sky to apply the optimization method. To obtain the accuracy, 50 nights’ observations were recorded. On each night, 100 quite independent images were taken.

A Comprehensive Calibration Method for a Star Tracker and Gyroscope Units Integrated System.

The integration of a star tracker and gyroscope units (GUs) can take full advantage of the benefits of each, and provide continuous and accurate attitude information with a high update rate. The systematic error calibration of the integrated system is a crucial step to guarantee its attitude accuracy. In this paper, a comprehensive calibration method for the star tracker and GUs integrated system is proposed from a global perspective. Firstly, the observation model of the predicted star centroid error (PSCE) with respect to the systematic errors including the star tracker intrinsic parameter errors, GUs errors and fixed angle errors is accurately established. Then, the systematic errors are modeled by a series of differential equations, based on which the state-space model is established. Finally, the systematic errors are decoupled and estimated by a Kalman filter according to the established state-space model and observation model. The coupling between the errors of the principal point and subcomponents of the fixed angles (i.e., and ) is analysed. Both simulations and experiments indicate that the proposed method is effective at estimating the systematic errors of the star tracker and GUs integrated system with high accuracy and robustness with respect to different star centroid accuracies and gyroscope noise levels.

Automatic Geolocation Correction of Satellite Imagery

Modern satellites tag their images with geolocation information using GPS and star tracking systems. Depending on the quality of the geopositioning equipment, errors may range from a few meters to tens of meters on the ground. At the current state of art, there is no established method to automatically correct these errors limiting the large-scale joint utilization of cross-platform satellite images. In this paper, an automatic geolocation correction framework that corrects images from multiple satellites simultaneously is presented. As a result of the proposed correction process, all the images are effectively registered to the same absolute geodetic coordinate frame. The usability and the quality of the correction framework are demonstrated through a 3-D surface reconstruction application. The 3-D surface models given by original satellite geopositioning metadata, and the corrected metadata, are compared. The quality difference is measured through an entropy-based metric applied to the orthographic height maps given by the 3-D surface models. Measuring the absolute accuracy of the framework is harder due to lack of publicly available high-precision ground surveys. However, the geolocation of images of exemplar satellites from different parts of the globe are corrected, and the road networks given by OpenStreetMap are projected onto the images using original and corrected metadata to demonstrate the improved quality of alignment.

Use of the Comprehensive Inversion method for Swarm satellite data analysis

An advanced algorithm, known as the “Comprehensive Inversion” (CI), is presented for the analysis of Swarm measurements to generate a consistent set of Level-2 data products to be delivered by the Swarm “Satellite Constellation Application and Research Facility” (SCARF) to the European Space Agency (ESA). This new algorithm improves on a previously developed version in several ways, including the ability to process ground-based observatory data, estimation of rotations describing the alignment of vector magnetometer measurements with a known reference system, and the inclusion of ionospheric induction effects due to an a priori 3-dimensional conductivity model. However, the most substantial improvements entail the application of a mechanism termed “Selective Infinite Variance Weighting” (SIVW), which mitigates the effects of non-zero mean systematic noise and allows for the exploitation of gradient information from the low-altitude Swarm satellite pair to determine small-scale lithospheric fields, and an improvement in the treatment of attitude error due to noise in star-tracking systems over previously established methods. The advanced CI algorithm is validated by applying it to synthetic data from a full simulation of the Swarm mission, where it is found to significantly exceed all mandatory and most target accuracy requirements.

Development of a low cost star tracker for the SHEFEX mission

German Aerospace Center (DLR) is designing and developing a novel star tracker to be used as the primary attitude sensor for the SHEFEX mission. The developed star tracker is considered to be a low cost and low accuracy sensor that is suitable for the proposed mission and the attitude accuracy requirements. This sensor is based on an off-the-shelf camera and a PC/104 computer communicating with the navigation computer. The attitude determination software consists of a processing chain including the camera control, the image processing, the star identification and the attitude estimation.The emphasis of the work is on developing a simple but robust system. Therefore, different algorithm concepts for each element of the chain have been implemented, tested and compared. Several night sky tests and star image simulation software have been implemented and used to verify the performance of the sensor in real-time End-to-End tests. The paper presents the star tracker system, details some newly developed algorithms and analyzes the test results.

Improving the Jason-1 Ground Retracking to Better Account for Attitude Effects

After two years of verification and validation activities of the Jason-1 altimeter data, it appears that all the mission specifications are completely fulfilled. Performances of all instruments embarked onboard the platform meet all the requirements of the mission. However, the star tracker system has shown some occasional abnormal behavior leading to mispointing angles out of the range of Jason-1 system specification which states that the altimeter antenna shall be pointed to the nadir direction with an accuracy below 0.2 degree (3 sigma). This article discusses the platform attitude angle and its consequences on the altimetric estimates. We propose improvements of the Jason-1 retracking process to better account for attitude effects. The first star tracker anomalies for the Jason-1 mission were detected in April 2002. The Poseidon-2 algorithms were specified assuming an antenna off-nadir angle smaller than 0.3 degree. For higher values, the current method to estimate the ocean parameters is known to be inaccurate. Thus, the algorithm has to be reviewed, and more specifically, the present altimeter echo model has to be modified to meet the desired instrument performance. Therefore, we derive a second order analytical model of the altimeter echo to take into account attitude angles up to 0.8 degree, and consequently, we adapt the retracking algorithm. This new model is tested on theoretical simulated data using a maximum likelihood estimation. Biases and noise performance characteristics are computed for the different estimated parameters. They are compared to the ones obtained with the current algorithm. This new method provides highly improved estimations for high attitude angles. It is statistically validated on real data by applying it on several cycles of Poseidon-2 raw measurements. The results are found to be consistent with those obtained from simulations. They also fully agree with the TOPEX estimates when flying along the same ground track. Finally, the estimates are also in agreement with the ones available in the current I/GDR (Intermediate Geophysical Data Record) products when mispointing lies in the mission specifications.

The determination of the attitude and attitude dynamics of TeamSat

The second qualification flight of Ariane 5 was launched from the European Space Port in French Guiana on October 30, 1997. It carried on board a small technology demonstration satellite dubbed TeamSat into which five experiments, proposed by various universities and research institutions, were integrated. Among them, the Autonomous Vision System, AVS, a fully autonomous star tracker and vision system. This paper gives a short overview of the TeamSat satellite design, implementation and mission objectives. The AVS is described in more details. The main science objectives of the AVS were to verify, in space, multiple autonomous processes intended for spacecraft applications such as autonomous star identification, attitude determination and identification and tracking of non-stellar objects, imaging and real-time compression of image and science data for further ground analysis. AVS successfully determined the attitude and attitude dynamics of TeamSat.

Taking Earth’s Temperature

This article discusses that starting in 2001, scientists will be able to use the Geoscience Laser Altimeter System (GLAS) to obtain data on the effects of global warming at the north and south poles. GLAS includes a laser system to measure distance, a device to receive signals from Global Positioning System satellites, and a star-tracker altitude-determination system. The laser will transmit four-nanosecond pulses of infrared light at a wavelength of 1064 nanometers and visible (green) light at 532 nm. FEMAP's graphic capabilities allow scientists to provide general views of our finite-element models, animated mode shapes, and 3D assembly views of projects we are working on, such as GLAS.

Description and analysis of an algorithm for star identification, pointing, and tracking systems

Software for star field identification and star pointing and tracking is described. The software will be implemented in the guiding system of UVSTAR, a spectrograph/telescope system for UV astronomy and planetary physics that will operate as a Hitchhiker payload on the Shuttle. The software work with the wide-field CCD camera and an on-board stellar catalog. It is capable of (1) providing high accuracy (better than 2 arcsec) attitude determination from coarse (± 3 deg) initial knowledge of the pointing direction and (2) pointing toward the target. It is capable of tracking at the same high accuracy with a processing time of less than a few hundredths of a second. Simulation of observations and various types of tests are also discussed.

Mapping the world's topography using radar interferometry: the TOPSAT mission

Global-scale topographic data are of fundamental importance to many Earth science studies, and obtaining these data is a priority for the Earth science community. Several groups have considered the requirements for such a data set, and a consensus assessment is that many critical studies would be enabled by the availability of a digital global topographic model with accuracies of 2 and 30 m in the vertical and horizontal directions, respectively. Radar interferometric techniques have been used to produce digital elevation models at these accuracies and are technologically feasible as the centerpiece of a spaceborne satellite mission designed to map the world's land masses, which we denote TOPSAT. A radar interferometer is formed by combining the radar echoes received at a pair of antennas displaced across-track, and specialized data processing results in the elevation data. Two alternative implementations, one using a 2 cm-/spl lambda/ radar, and one using a 24 cm-/spl lambda/ radar, are technologically feasible. The former requires an interferometer baseline length of about 15 m to achieve the required accuracy, and this could be built on a single spacecraft with a long extendible boom. The latter necessitates a kilometers long baseline, and would thus be best implemented using two spacecraft flying in formation. Measurement errors are dominated by phase noise, due largely to signal-to-noise ratio considerations, and attitude errors in determining the baseline orientation. For the 2-m accuracy required by TOPSAT, the orientation must be known to 1 arc-second. For the single-spacecraft approach, where attitude would be determined by star tracking systems, this performance is just beyond the several arc-second range of existing instruments. For the dual-spacecraft systems, though, differential global positioning satellite measurements possess sufficient accuracy. Studies indicate that similar performance can be realized with either system. >

Star trackers, star catalogs, and attitude determination - Probabilistic aspects of system design

Optimizing spacecraft attitude determination systems that use onboard star trackers requires analysis and evaluation of some probabilistic aspects of system design. This paper discusses methods of constructing or compiling optimum star catalogs, which are defined as uniform distributions on a sphere. Both local and global measures of uniformity on a sphere are defined. Application of these methods and measures to a specific problem is also discussed. In addition, Poisson models of star tracker acquisition probabilities are formulated to provide a useful analytical basis for designing and optimizing attitude determination systems. These analytical models and methods lead to rapid and realistic quantitative results and should therefore facilitate making system performance trades. The use of such methods should also reduce the need for performing tedious computer simulations to obtain analogous results. TTITUDE determination of both Earth-orbiting satel- lites, as well as planetary spacecraft, can be performed autonomously using one or more onboard star trackers. An essential part of such an attitude determination system is the onboard star catalog, and the performance of the attitude determination system is closely linked to the characteristics of this catalog. In particular, the total number of stars in the catalog and their spatial distribution largely determine the probability of a given number of stars appearing in a tracker's field of view (FOV); this includes the possibility of there being zero stars from the catalog in the FOV. The purpose of this paper is to apply some analytic methods of probability theory to the following problems: generating optimum star catalogs of any given size and, given such a catalog, evaluating some of the characteristics of the star cata- log/star tracker interaction that are of particular interest when designing attitude determination systems. Evaluating such characteristics will entail some analytical modeling. We shall formulate some simple analytical models that lead to excellent estimates of such quantities as star acquisition probabilities as a function of the number of stars in the catalog, number of operating star trackers, and size of the FOV. Another kind of performance parameter that can be analytically estimated is the duration of intervals during which none of the stars in the catalog appears in a star tracker's FOV. These analytical mod- els should be useful for quantitatively evaluating design and performance trades involving these variables, and for star tracker system engineering in general. Their use may obviate doing tedious computer simulations to obtain quantitative esti- mates of such parameters. Although some related efforts have been reported,1 such efforts have focused more strongly on star tracker hardware than analytical aspects of performance.

A control system for a balloon-borne telescope

This paper deals with a star tracking system for a balloon-borne infrared telescope. A control moment gyro has been adopted for controlling the azimuth angle of the gondola. A CCD image sensor is used in a star field camera. Newly developed on-board microprocessor system is used for supervisory control of on-board equipment.

Balloon-borne ultraviolet stellar spectrograph. I - Instrumentation and observation. II - Highlights of first observational results

A dual star-tracking system and a system including a telescope, an echelle spectrograph, and a SEC vidicon are the chief components of the Balloon-borne Ultraviolet Stellar Spectrograph (BUSS), which has flown four successful missions. The BUSS missions have yielded 81 spectra for 56 stars, recorded with a resolution of 0.1 A in the wavelength range from 2200 to 3400 A. BUSS observations include: profiles of Mg II lines indicating considerable mass flow in early-type supergiants; Mg II features suggesting a cool expanding outer shell above a hotter chromosphere; emission features in Zeta Tau (a shell star) indicating infalling material; and emission features of the Be star Phi Per suggesting mass outflow.

Vidicon Star Tracker

In many applications of star trackers, extremely short acquisition times, as well as accuracy and sensitivity, are required. Tracking systems employing the vidicon as a radiation sensor have been shown to provide the necessary speed of acquisition for such applications. This paper discusses the various theoretical and practical considerations involved in using the vidicon as a sensor in a star tracking system. A typical system configuration including telescope, sensor, and processing electronics is presented. The various optical and sensor parametric relationships required in the design of a vidicon star tracker are fully discussed and analyzed.

Automatic Star-Trackers for Long-Range Navigation

This paper describes development trends of one particular navigational technique (automatic star tracking) and its associated instrumentation methods one of which, the application of pulse code modulation theory to sensor design, is discussed in detail. Plans for the future development of this most promising concept are also included and the effects of military research and development efforts on civilian aircraft requirements are indicated. An appendix provides a glossary of special terms used.Automatic star-tracking systems have been used in military aircraft navigation for position fixing and heading correction for a number of years and the development of the equipment has been actively pursued by the U.S.A.F. since as early as 1946. Basically, star trackers are automatic devices that probe a portion of the celestial sphere for the purpose of detecting, acquiring and tracking stars or other celestial bodies. In using astronomical inputs for cruise vehicle navigation, advantage is taken of the well-known principle that sights on two or more stars when referred to the true vertical and time can be used to provide a position fix. It is the intent of this paper to review techniques used to instrument star trackers, discuss their application to long-range aircraft navigation, indicate development trends and introduce a new concept of employing pulse code modulation theory to the design of a simple, low cost automatic astro-tracker.