Event-based Star Tracking via Multiresolution Progressive Hough Transforms

In this paper, a laboratory model is designed to evaluate the performance of star tracker algorithms for attitude determination of a satellite. Star tracker is the most accurate attitude sensor that determines satellite direction by applying centroiding algorithm, star identification and attitude determination. To utilize such algorithms, first, high quality of star images are needed which should be provided through the star tracker camera. Then, such images are given to processors and it determines the attitude of camera and satellite in three axes based on mentioned algorithms. First, in preliminary design, we define important star tracker parameters, like accuracy, detector, processor and field of view. In this paper, we have considered the range accuracy in yaw/pitch axis less than 20 arcsec and for roll axis less than 100 arcsec. To improve the attitude determination accuracy, we have applied an adaptive structure in centroiding algorithm, as only brightness stars are selected and identification algorithm is done based on them. Another important parameter is speed of identification algorithm which is handled by an ARM processor and improving pyramid algorithm, we reached less than 25 ms. Duo to this time, updating rate would be desired. Also knowing the coordination of bore sight direction that is distance between focal lens and imager is another important parameter that affects the accuracy of attitude and by ground calibration of camera, this parameter could be estimated carefully. Finally, implementation results on real images that are captured by a star tracker demonstrate optimum performance of algorithms.

Star trackers are electro-optical devices that are used to determine the attitude of satellite platforms. The test of star trackers is typically carried out by means of Optical Ground Support Equipment (OGSE). In this paper we present a new prototype of OGSE, the MINISTAR, recently developed by a consortium of Italian enterprises and the Applied Physics Institute of the National Research Council. The MINISTAR is a miniaturized electro-optical device able to generate synthetic images of dynamic star fields for the simultaneous test of up to three star trackers. Their performance can be evaluated in terms of its optics, electronics and on-board attitude software. The MINISTAR is able to perform a dynamic simulation of the apparent motion of the observed scene in order to test the star tracker in a realistic working scenario. It can be placed directly on the star tracker under test and, thanks to its reduced dimensions and weight, the test and validation phase can be performed while the star tracker is assembled on the satellite platform. The MINISTAR is also able to simulate the presence of large objects, such as the Sun, the Earth and the Moon, custom objects and disturbances like cosmic rays and stray light effects. The prototype has been built paying special attention to the employed materials and technology in order to minimize the weight and to ensure its compatibility with most star tracker models available on the market.

There are many devices used today on modern spacecraft to accurately determine their position. Star trackers (space cameras) are the most accurate device in use for determining a spacecraft's position. The star tracker operates automatically, getting images of star patterns within its Field of View (FOV). The stars observed by the camera can then be identified and the orientation of the spacecraft can be calculated. A star tracker is composed of a baffle for removing stray lights, optical system, image sensor, microprocessor and memory. In this paper, basic principles for designing a baffle system, such as determination of baffle dimensions, arrangement of vanes inside the baffle, and coating of surface have been reviewed. We first determined dimensions of a two-stage conical baffle. Then, we calculated positions and height of vane to prohibit diffusely reflected light inside the baffle from entering into the photometer. In order to evaluate performance of the designed baffle system, we have used a ray tracing program using a Monte Carlo method and calculated attenuation factor.

This paper presents a novel approach to the attitude determination problem of space vehicles. The proposed algorithm utilizes a modified Genetic Algorithm (GA) to solve the “lost in space” star pattern recognition problem associated with star tracker attitude determination systems. Characteristics of the stars that are visible within the Field of View (FOV) – reflected on an image taken by the onboard star tracker – are formulated using simple geometric descriptions. The proposed GA minimizes the discrepancy between the characteristics of the stars inside the actual FOV and a candidate FOV selected from the on board stored star map. The global minimum of the discrepancy represents the inertial coordinates of the FOV bore-sight. The concept of a Spiral Genetic Algorithms (SGA) is proposed where the search area decreases for consecutive GA, with consequently tighter constraints, making it converge to the desired location. Also the algorithm presented has the capability of determining the rotational angle between the spacecraft’s coordinate system and that of a real star map. Simulation results indicate competitive results to current star trackers in terms of accuracy.

A robust star identification algorithm with star shortlisting

This paper presents an analysis of star field image features for star field recognition using neural networks during initial acquisition. This is a critical mode in star tracker operation. A learning vector quantization network is investigated. This is an alternative to routines that browse pre-compiled star feature databases for identification because the network structure itself contains the information about star feature vectors. A set of 200 circular sectors, partially overlapping and uniformly distributed over the celestial sphere, was selected as prototypes for recognition during network operation. Then, a number of candidate features was evaluated in each sector. The data have been analyzed to assess feature capability of addressing star field recognition when used as network input. Three basic statistical analyses have been performed: uniformity of distribution, feature cross-correlation, and stability. The most representative and suitable features for the considered application were selected: total number of stars, total radiant flux, four statistics of nearest neighbor angular separations in the field of view (min, max, mean and standard deviation), three second order moments of the star field image. A preliminary validation of feature selection has been performed by running a neural network.

As the growth of the small spacecraft market continues, so does the demand for high-quality data gathered from small spacecraft platforms, such as high-resolution images from Earth observation and astronomy missions or high-speed data transfer by laser communication. This demand, however, imposes stringent jitter requirements on the pointing performance in the range of arcseconds and better. While state-of-the-art Attitude Determination & Control Systems (ADCSs) of small spacecraft are reaching their physical limits, high-pointing accuracy and stability can be provided by dual-stage control system approaches with a payload-in-the-loop configuration in order to further improve the quality of the data. One concept of such a dual-stage control system approach is to combine a currently existing ADCS with a so-called High-Precision Pointing Platform (HPPP). The basic idea of this concept is to separate the low-frequency (< 10Hz) and high-frequency (> 10Hz) content of the pointing disturbances for control. While the spacecraft ADCS suppresses low-frequency disturbances, the HPPP deals with the high-frequency phenomena. This paper will describe two CubeSat scenario’s that benefit from a dual-stage control system approach: (1) an Earth observation mission and (2) an astronomy mission. In both scenario’s the spacecraft ADCS is equipped with a star tracker and a gyro to measure respectively the pointing error and pointing rate error, and reaction wheels to control the pointing error, as this configuration represents the majority of existing small spacecraft missions. For the Earth observation mission, a (fictive) 12U and a 24U CubeSat will be equipped with a Time-Delay Integration (TDI) line-scan camera, enforcing stringent requirements on the absolute and relative pointing error. In this scenario, different HPPP sensor configurations will be considered and analysed in terms of speed and pointing performance. One particular configuration, in which the TDI camera lines are merged, cut into small regions of interest (ROI), and fed to a correlation algorithm, is used as a reference. The disadvantage of the latter sensor output is the relative pointing error which can drift away over time. Therefore, additional information is required to have an absolute measurement, coming from star tracker data, ground control points (GCPs) within images, or a high-accurate gyroscope, … This pointing performance analyses are performed within the framework of the ‘Affordable QUALity Images from Space (AQUALIS)’ SBO 4-year project, funded by the Research Foundation – Flanders (FWO). The consortium of this project exists of the Department of Mech. Eng. of the KU Leuven, VITO, and imec. For the astronomy mission, a 6U CubeSat is equipped with a spectroscopy instrument for which a stringent requirement on the absolute pointing error exist. In this scenario, the HPPP is composed of a fine-guidance sensor (FGS) which senses the deviation of the targeted star, and a fast-steering mirror (FSM) that deviates the light onto both the fine-guidance sensor and the payload via a dichroic beam splitter. In this configuration, the fast and accurate information of the fine-guidance sensor allows to control the fast-steering mirror. This analysis is performed within the PDR and CDR phase of the In-Orbit Demonstration (IOD) CubeSat mission called CubeSpec, funded by BELSPO, the Belgian federal science policy office. The goal of the mission is to demonstrate high-spectral-resolution astronomical spectroscopy from a 6-unit CubeSat. For both scenario’s, simulations are performed first in the frequency domain (Pointing Error Engineering Tool – PEET), allowing for a first estimate of the pointing performance, and time domain (Matlab Simulink), allowing for a more detailed study of the communication between the ADCS and HPPP control loops. This paper will describe both scenario’s (context of the AQUALIS project and context of the CubeSpec mission), the related pointing performance requirements, the simulation models in PEET and Simulink, and their results.

A star-field pattern recognition algorithm has been developed. It is based on matching the stars on a full celestial sphere observed in a CCD-based star tracker and the reference stars, by using the Yale bright star catalog. The correspondence between the observed and the reference star pattern is found by constructing three-star triangles in spherical geometry. Star angular coordinates and stellar magnitudes are matched to build up a celestial region of correspondence. Gaussian errors in the cataloged star coordinates and brightnesses are modeled to test the algorithm against faulty reference data. Random values are selected for the origin and the orientation of the observed star field. The possibility of hardware-introduced stars is modeled by introducing spurious data. The computer simulations and the preliminary experimental results at the Table Mountain Observatory are described.

Spacecraft would be expected to encounter diverse extreme environmental (EE) conditions throughout their mission phases. These EE conditions are often coupled. Star tracker is a high accurate 3-axis attitude measuring instrument used in various spacecrafts. In this paper, an effective scheme to the thermal/optical analysis in optical system of star sensor was described and the concept of thermal optical analysis of star tracker optical system was introduced in detail. Using finite element analysis (FEA) and ray tracing, we can study the relationship of optical properties of optical systems and optical system's temperature distribution . A lens system configuration having six uncemented elements was discussed. The lens system was a 56mm EFL, which was different from common lens used in imaging system that this lens system was required to have a high resolving power in design thoughts. It was designed to determine the attitude of space platform by detecting and mapping the geometric pattern of stars. Based on this system, the FEA models of the optical system were established for temperature distribution calculation and for thermal-elastic structural deformation analysis respectively. Using the models, the steady-state temperature distributions of the tracker were simulated. The rigid body displacements of the optical components under homogeneous temperature changes and certain temperature distributions were derived out. It is convenient to use Zernike polynomials as the data transmission between optical and structural analysis programs. Here, Zernike polynomials and their fitting method are used as an example to determine the thermal induced optical degradations of the optical system.

In this paper a star pattern identification algorithm is addressed. Proposed algorithm is associated in terms of pattern recognition. Each star has related with well-defined pattern that can be determined by the surrounding stars. One of the well-known types related the class is the grid algorithm. The proposed algorithm is based on the algorithm. To enhance the algorithm the modifying methods so called virtual grids and selection multi-reference stars are proposed. This method makes the grid algorithm more accurate and reliable.

Star identification can be accomplished by several different available algorithms that identify the stars observed by a star tracker. However, efficiency and reliability remain key issues and the availability of new active pixel cameras requires new approaches. Two novel algorithms for recursive mode star identification are presented here. The first approach is derived by the spherical polygon search (SP-search) algorithm, it was used to access all the cataloged stars observed by the sensor field-of-view (FOV) and recursively add/remove candidate cataloged stars according to the predicted image motion induced by camera attitude dynamics. Star identification is then accomplished by a star pattern matching technique which identifies the observed stars in the reference catalog. The second method uses star neighborhood information and a catalog neighborhood pointer matrix to access the star catalog. In the recursive star identification process, and under the assumption of "slow" attitude dynamics, only the stars in the neighborhood of previously identified stars are considered for star identification in the succeeding frames. Numerical tests are performed to validate the absolute and relative efficiency of the proposed methods.

An autonomous star tracker (AST) is basically a `star field in, attitude out' device capable of determining its attitude without requiring any a priori attitude knowledge. In addition to this attitude acquisition capability, an AST can perform attitude updates autonomously and is able to provide its attitude `continuously' while tracking a star field. The Lockheed Palo Alto Research Laboratory is developing a reliable, low-cost, miniature AST that has a one arcsec overall accuracy, weighs less than 1.5 kg, consumes less than 7 watts of power, and is sufficiently sensitive to be used at all sky locations. The device performs attitude acquisition in a fraction of a second and outputs its attitude at a 10 Hz rate when operating in its tracking mode. Besides providing the functionality needed for future advanced attitude control and navigation systems, an AST also improves spacecraft reliability, mass, power, cost, and operating expenses. The AST comprises a-thermalized, refractive optics, a frame-transfer CCD with a sensitive area of 1024 by 1024 pixels, camera electronics implemented with application- specific integrated circuits, a compact single board computer with a radiation hard 32 bit RISC processor, and an all-sky guide star database. Star identification is performed by a memory- efficient and highly robust algorithm that finds the largest group of observed stars matching a group of guide stars. An important milestone has recently been achieved with the validation of the attitude acquisition capability through correct and rapid identification of all 704 true-sky star fields obtained at the Lick Observatory, using an uncalibrated prototype AST with a 512 by 1024 pixel frame-transfer CCD and a 50 mm f/1.2 lens that provided an effective 6.5 by 13.2 degree field of view. The overlapping fields cover 47% of the sky, including both rich and sparse areas. The paper contains a description of the AST, a summary of the functions enabled or improved by the device, an overview of the identification algorithm, results obtained with a realistic simulation program, a description of the true-sky star field identification method and a presentation of the results obtained. The AST tolerates the presence of bright objects as was demonstrated by a field that included Jupiter.

We have obtained high-resolution spectropolarimetric data for the planet-hosting star τ Bootis, using the ESPaDOnS spectropolarimeter at the Canada–France–Hawaii Telescope (CFHT). A weak but clear Stokes V signature is detected on three of the four nights of 2006 June during which we have recorded data. This polarimetric signature indicates with no ambiguity the presence of a magnetic field at the star's surface, with intensity of just a few gauss. The analysis of the photospheric lines of τ Boo at ultra-high signal-to-noise ratio reveals the presence of an 18 per cent relative differential rotation. Tentative Zeeman–Doppler imaging, using our spectropolarimetric observations covering only a fraction of the star's rotational phase, indicates a magnetic field with a dominant potential field component. The data are best fitted when a 3.1-d period of modulation and an intermediate inclination are assumed. Considering the level of differential rotation of τ Boo, this implies a rotation period of 3.0 d at the equator and of 3.7 d at the pole, and a topology of the magnetic field where its main non-axisymmetric part is located at low latitudes. The planet is probably synchronized with the star's rotation at intermediate latitudes, while the non-axisymmetric part of the magnetic field seems located at lower latitudes. Our limited data do not provide sufficient constraints on the magnetic field to study a possible interaction of the planet with the star's magnetosphere. Investigating this issue will require data with much better phase coverage. Similar studies should also be performed for other stars hosting close-in giant planets.

Onboard scientific cameras are reused in attitude determination to meet the sub-arcsecond attitude determination accuracy requirements of microsatellites. This approach does not require an additional payload for microsatellites. It involves reusing high-quality optical lenses from the scientific camera and utilizing the peripheral high-quality imaging areas of its square-shaped detector. Separate detectors are placed within these areas as attitude determination detectors to obtain star patterns for closed-loop attitude determination, thereby achieving high-precision attitude determination for microsatellites. The star patterns obtained using this method may pose specific issues due to the relative positions of stars. Through an analysis of the theoretical model that examines the relationship between attitude determination accuracy and the main influencing factors, it is indicated that guide star distribution is one of the main, complex factors determining attitude determination accuracy. A further simulation analysis was conducted on the specific impact of two guide star distribution characteristics—namely, the coverage of guide stars in the attitude determination areas and the proportion of the average field of view occupied by the guide star triangles to the total field of view of the attitude determination areas—on attitude determination accuracy. This study concludes that when the measurement error of the guide stars is bigger than the attitude determination accuracy requirement for its area configuration, four attitude determination areas should be configured. Four attitude determination areas should be prioritized when the measurement error is equal to or smaller than the attitude determination accuracy requirement, followed by the option to configure three attitude determination areas or two symmetric attitude determination areas. When selecting guide stars for star pattern recognition, the guide stars should cover the attitude determination areas as much as possible, and guide stars with a higher proportion of the average field of view occupied by the guide star triangles to the total field of view should be chosen. Finally, experimental validation was conducted using star patterns from dense star fields and sparse star fields. The research results provide an important reference for the optimization of attitude determination area configuration, navigation star catalog construction, and star pattern recognition algorithm research for microsatellites equipped with scientific cameras.

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