Accuracy performance of star trackers - a tutorial

The accuracy of satellite attitude determination depends on the performance of star trackers, which can be improved by careful calibration. Star trackers are initially calibrated on ground. After the launch, because of vibrations, vacuum, thermal cycling and instrument aging, it is common to observe small shifts in calibration parameters. This paper aims to discuss an autonomous on-board calibration technique for star trackers. The approach is especially related to a set of parameters including the focal length, the principal point offset and the focal plane distortions.

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 present results of CCD radiation testing for a proposed Jovian mission. Samples of two candidate star tracker CCDs were irradiated with 10-MeV and 50-MeV electrons at Rensselaer Polytechnic Institute's Gaerttner LINAC. Differences in displacement damage effects on CCD parameters and star tracker performance are discussed for these two energies. Dark current, charge transfer efficiency (CTE), hot pixels, and flat-band voltage shifts are examined. Our electron data is compared to proton irradiation data taken by other experimenters. 10-MeV electron-induced transient data are also discussed.

The autonomous star trackers, using charge couple device CCD camera, or active pixel sensor APS, as natural sensors for optical input, has assumed a permanent position. This is due to their highly accurate attitude determination, small size, light weight and simple functionality, making them devices of choice in nearly all modern space vehicles especially for Nano-satellites. In all star trackers, star centroiding is a fundamental process necessary for pattern recognition. In this paper, a new method is presented, which predicts centers of regions of star locations, in successive image frames, from the current knowledge of boresight direction, which is updated successively. This method is very attractive for hardware implementation using APS imagers known for their random accessibility feature lacked in CCD's. The big advantage of this method is that it does not need pattern recognition, thus making it fast. This reduction of computational budget, power consumption and time, added to the capability of incorporating them in APS imagers, is appealing to Nano-satellites navigational instrumentation.

ABSTRACT: Autonomous star trackers are optical-electronic devices used for attitude determination of artificial satellites, having as a reference for this computation the positions of stars. There is one autonomous star tracker in development at the Aerospace Electronics Division of the Brazilian National Institute for Space Research. The autonomous star tracker imager is a complementary metal-oxide-semiconductor active pixel sensor, consisting of an integrated circuit with an array of them. Each pixel has a photodetector and an active amplifier. Since it has many amplifiers, the active pixel sensor has an additional fixed pattern noise, therefore its characterization is different from the traditional method used for the charge coupled devices. With this experiment, it was observed that the mean value per columns of fixed pattern noise is ~100% greater than the mean value of the pixel one. Taking into account this result, modeling the pixel fixed pattern noise will not be important to improve the autonomous star tracker sensibility. Furthermore, the random noise value was less than 1% of the fixed pattern noise range data, being possible to estimate it. In this work, we presented the fixed pattern noise new parametric model, which has a good agreement when compared with the experimental data. It was calculated Pearson’s product-moment correlation coefficient between the model and the observed data, in order to quantify the model accuracy and it was obtained 99% for flat field and 79% for dark current.

The requirements for the dynamic performance of star trackers are rapidly increasing with the development of space exploration technologies. However, insufficient knowledge of the angular acceleration has largely decreased the performance of the existing star tracking methods, and star trackers may even fail to track under highly dynamic conditions. This study proposes a star tracking method based on multiexposure imaging for intensified star trackers. The accurate estimation model of the complete motion parameters, including the angular velocity and angular acceleration, is established according to the working characteristic of multiexposure imaging. The estimation of the complete motion parameters is utilized to generate the predictive star image accurately. Therefore, the correct matching and tracking between stars in the real and predictive star images can be reliably accomplished under highly dynamic conditions. Simulations with specific dynamic conditions are conducted to verify the feasibility and effectiveness of the proposed method. Experiments with real starry night sky observation are also conducted for further verification. Simulations and experiments demonstrate that the proposed method is effective and shows excellent performance under highly dynamic conditions.

A star sensor is an embedded system used in modern spacecraft for estimating the orientation of the spacecraft. Star trackers capture image of star in the sky, process them and gave highly accurate attitude in all 3 axis. Basically a star tracker is an electronic camera connected to a microcomputer. First generation star trackers are characterized by acquiring and processing few stars information to estimate attitude with limited software modules. The availability of space qualified microcomputers enables generation shift in the star trackers development for attitude determination onboard. Laboratory for Electro-Optics Systems (LEOS) is actively involved in design and development of indigenous star trackers for different ISRO. Current star trackers employs traditional method of acquiring and processing star image and don't meet the many spacecraft requirements in terms of number of stars tracking, accuracy and update rate. In order to meet the current generation spacecraft requirements, LEOS has designed and developed second generation star trackers which are characterized by low weight, volume and power. These sensors are based on ERC-32 processor, here after referred as Mark-II sensor. The essential features expected from onboard software are robustness in operations, run-time and ability to give solutions especially during satellite injection with high angular rate. This paper presents the details of state-of-art software designed and developed for these star trackers to provide high accuracy and higher bandwidth with existing hardware limitations even with harsh space environment with limited resources and constraints.

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 currently the most accurate spacecraft attitude sensors. As a result, they are widely used in remote sensing satellites. Since traditional charge-coupled device (CCD)-based star trackers have a limited sensitivity range and dynamic range, the matching process for a star tracker is typically not very sensitive to star brightness. For active pixel sensor (APS) star trackers, the intensity of an imaged star is valuable information that can be used in star identification process. In this paper an improved brightness referenced star identification algorithm is presented. This algorithm utilizes the k-vector search theory and adds imaged stars' intensities to narrow the search scope and therefore increase the efficiency of the matching process. Based on different imaging conditions (slew, bright bodies, etc.) the developed matching algorithm operates in one of two identification modes: a three-star mode, and a four-star mode. If the reference bright stars (the stars brighter than three magnitude) show up, the algorithm runs the three-star mode and efficiency is further improved. The proposed method was compared with other two distinctive methods the pyramid and geometric voting methods. All three methods were tested with simulation data and actual in orbit data from the APS star tracker of ZY-3. Using a catalog composed of 1500 stars, the results show that without false stars the efficiency of this new method is 4∼5 times that of the pyramid method and 35∼37 times that of the geometric method.

Precession–nutation correction for star tracker attitude measurement of STECE satellite

This research is aimed to improve star tracker performance in presence of dynamic conditions. It offers an assessment of various image thresholding and centroiding algorithms to improve star tracker centroiding accuracy at moderate slew rates (< 10 0=s). Star trackers generally have arc-second accuracy in stationary conditions, however their accuracy degrades as slew rate increases. In dynamic conditions, blur effects add to the challenges of star detection. This work presents an image processing algorithm for star images that preserves star tracker detection accuracy and is able to detect dim stars up to slew rates less than 10 0=s. A number of algorithms from literature were evaluated and their performance in motion and simulations were measured. The primary performance metrics are false positive ratio, and false negative ratio of star pixels. This Work introduced a new algorithm for star acquisition in moderate slew rates that combines positive features of existing algorithms.

Jena-Optronik GmbH (JOP) has a strong heritage in the development of cameras for numerous space-based applications. So far, our focus has been on cameras working in the visible & near-infrared range of the spectrum. The main application case for these cameras is the use as autonomous star trackers being part of a satellite’s Guidance, Navigation & Control System. JOP has been very successful with these cameras –for a long time and is the world market leader in providing such sensors to satellite prime manufactures. Investigating the possible applications of cameras in space, one realizes that thermal or long wave infrared (IR) cameras are necessary for specific applications. One major field for several of such applications is the field of Space Situational Awareness (SSA). SSA has been attracting more and more attention over the past years especially for space objects, natural debris as well as man-made threats & disturbances such as military conflicts. Two further application fields for IR cameras are formation flying and docking. The first rendezvous and docking with a non-cooperative satellite (Intelsat 901) in geostationary orbit by Northrop Grummans MEV-1 was a key milestone for docking capabilities. Additionally, the recent years have shown that a transition from few big and multi-purpose satellites towards small, medium or even large constellations consisting of numerous small satellites is taking place. Especially for constellations, a key aspect is formation flying which usually requires relative navigation. The relative angles between the satellites can be easily provided by IR cameras as they detect the satellites reliably and independently of local lighting conditions due to their elevated temperature against the cold space background. Based on the very successful ASTRO product range of space proven cameras, ASTROtir (tir = thermal infra-red) will extend JOPs product capabilities into the thermal / long wave infrared (LWIR) wavelength range to cover all of the applications cases listed above. Following a successful ESA co-funded first evaluation, the ASTROtir development project has been kicked-off in December 2022 in cooperation with ESA. Target of this project is to demonstrate TRL8 of ASTROtir. Future applications are formation flying (relative navigation), approach and docking with a non-cooperative space object as well as detailed image generation of near satellite objects. Currently, no European solution for an IR camera covering the application cases and mission scenarios is available as off-the-shelf product, which further increases ASTROtir’s already promising market potential. As the market demand, especially in the field of SSA, is rising further in the coming years, its development will be closely followed and its market entry is eagerly awaited. Jena-Optronik will present the preliminary design and development status of ASTROtir. As ASTROtir aims primarily at applications on small and medium satellites, its target mass budget of 300g is a driving requirement. Following our intermediate / preliminary design review scheduled for August 2023, Jena-Optronik aims at presenting first results from ASTROtir’s system analyses as well as the related plans for the EM and EQM campaigns.

Star trackers based on charge-coupled device (CCD) or complementary metal-oxide semiconductor (CMOS) sensors, use a brightness independent star identification strategy that requires highly accurate measurements of star spot position. Therefore, precise calibration of the measurement model is crucial. Generally, ground-based real night sky observation is a specific and costly approach. In this work, an optical laboratory method for star tracker calibration is proposed. This method is based on ordinary instruments, laser autocollimation adjustment, and image processing techniques. The calibration issues of the star tracker with a brightness independent star identification strategy are analyzed. A new laboratory calibration method is introduced, and its results on an active pixel sensor (APS) star tracker are discussed. This method proves to be practical and adequate in the development of a star tracker with wide field of view.

Owing to changes in the space thermal environment, the optical axis angle between the camera and star tracker (Cam-ST) changes as well, resulting in regular low-frequency attitude errors and a decline in the geometric positioning accuracy of the images. In this study, a star-observation-based low-frequency attitude error correction method is proposed. First, the star was used as the control point to be observed by satellite from different latitudes in an orbit. The star information is extracted using a priori attitude to obtain the camera pointing in inertial coordinates. Second, combined with the optical axis pointing value of the star tracker, the angle change between the camera and two star trackers (Cam-2STs) was calculated. A polynomial model was used to fit the angle change, and the fitting model and camera optical axis pointing compensation algorithm were used to compensate for the camera optical axis. Third, the regular low-frequency attitude error of the camera was realized. The experiment used 20 groups of star observation data from two missions of the Jilin-1 07 video satellite. After compensation, the camera pointing maximum root mean square error was reduced from 30.08" to 7.70", the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> -axis attitude error was reduced from 13.26" to 7.09", and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y</i> -axis from 29.48" to 7.36". The geometric positioning accuracy of Jilin-1 ground images was 25.63 m after correction. The experimental results showed that the proposed method effectively improved the attitude measurement accuracy. This method can thus effectively improve the direct geometric positioning accuracy of a single image.

After the successfully launched hypersonic SHarp Edge Flight EXperiment (SHEFEX) in 2005, DLR has scheduled a second re-entry experiment SHEFEX 2 for 2010. The novel flight control system based on steerable canard fins requires a precise knowledge of the inertial spacecraft attitude. For this purpose, a star tracker is to be conceived and integrated in an inertial navigation system, updating the attitude information before re-entry. 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 PC104 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. Furthermore, star image simulation software has been developed, allowing performance and speed tests of the single blocks and the processing chain as a unit. The paper presents the star tracker system, details some newly developed parts and discusses the test results.