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A star tracker is a widely used celestial sensor in astronomical navigation systems, which calculates the spacecraft's high-precision attitude by observing stars in space to obtain several star vectors. Existing star identification algorithms typically require the selection of a specific anchor star (e.g., the nearest neighbor star), using the line connecting the target star and the anchor star as the rotational reference axis to achieve rotation invariance in the star identification algorithm. However, this approach makes the entire identification algorithm overly dependent on the anchor star, resulting in insufficient identification accuracy in cases of excessive positional noise or a high number of false stars. In this paper, we adopt the angles between any neighboring stars and the distances ratio between neighboring stars and the observed star as the initial matching criteria. We then calculate the matching with each navigation star using the accumulated angle in the counterclockwise direction based on this criterion. The navigation star with the highest matching is identified. Unlike other identification algorithms that require selecting the nearest neighbor star which can be easily affected by interference as the rotational reference axis, our method effectively achieves rotation invariance in star identification by leveraging angle information. Therefore, it exhibits better tolerance to positional noise, magnitude noise, and false stars, particularly demonstrating higher robustness against focal length variations. [ABSTRACT FROM AUTHOR]

This paper reports the successful application of a self-developed, miniaturized, low-power nano-star tracker for precise attitude measurement of a 5-m-long satellite extension boom. Such extension booms are widely used in space science missions to extend and support payloads like magnetometers. The nano-star tracker, based on a CMOS image sensor, weighs 150 g (including the baffle), has a total power consumption of approximately 0.85 W, and achieves a pointing accuracy of about 5 arcseconds. It is paired with a low-cost, commercial lens and utilizes automated calibration techniques for measurement correction of the collected data. This system has been successfully applied to the precise attitude measurement of the 5-m magnetometer boom on the Chinese Advanced Space Technology Demonstration Satellite (SATech-01). Analysis of the in-orbit measurement data shows that within shadowed regions, the extension boom remains stable relative to the satellite, with a standard deviation of 30′′ (1σ). The average Euler angles for the "X-Y-Z" rotation sequence from the extension boom to the satellite are [−89.49°, 0.08°, 90.11°]. In the transition zone from shadow to sunlight, influenced by vibrations and thermal factors during satellite attitude adjustments, the maximum angular fluctuation of the extension boom relative to the satellite is approximately ±2°. These data and the accuracy of the measurements can effectively correct magnetic field vector measurements. [ABSTRACT FROM AUTHOR]

Abstract Global Navigation Satellite System (GNSS) can provide an approach for spacecraft autonomous navigation in earth–moon space to make up for the insufficiency of earth-based tracking, telemetry, and control systems. However, its weak power and poor observation geometry near the moon causes new problems. After the GNSS signal characteristics and satellite visibility were evaluated in Phasing Orbit and Lunar Transfer Orbit, we proposed an adaptive Kalman filter based on the Carrier-to-Noise ratio (C/N 0) and innovation vector to weaken the influence of GNSS accuracy attenuation as much as possible. The experimental results show that the spacecraft position and velocity accuracy are better than 10 m and 0.1 m/s near the Earth, and better than 50 m and approximately 0.2 m/s near the moon use GNSS with the proposed adaptive algorithms. Additionally, because of the deterioration of navigation performance based on the orbit filter during orbital maneuvering, we used accelerometer data to compensate for the dynamic model to maintain navigation performance. The results of the experiment provide a reference for subsequent studies.

In this work, when calculating the star blur trajectory, geometric distortion in the accumulated images is taken into account in two ways: analytical and numerical. The analytical approach uses a model of direct distortion correction, which makes it possible to obtain a new differential equation for the blur trajectory in the image plane with distortion. The numerical approach uses a model of reverse distortion correction that converts points of a trajectory calculated in the ideal image plane into the image plane with distortion. This approach makes it possible to preserve the structure of the subpixel accumulation and star detection algorithms previously obtained for an ideal image. An example of allowing for the radial distortion parameters obtained by calibrating a real camera is given.

Global Navigation Satellite System (GNSS) can provide an approach for spacecraft autonomous navigation in earth–moon space to make up for the insufficiency of earth-based tracking, telemetry, and control systems. However, its weak power and poor observation geometry near the moon causes new problems. After the GNSS signal characteristics and satellite visibility were evaluated in Phasing Orbit and Lunar Transfer Orbit, we proposed an adaptive Kalman filter based on the Carrier-to-Noise ratio (C/N0) and innovation vector to weaken the influence of GNSS accuracy attenuation as much as possible. The experimental results show that the spacecraft position and velocity accuracy are better than 10 m and 0.1 m/s near the Earth, and better than 50 m and approximately 0.2 m/s near the moon use GNSS with the proposed adaptive algorithms. Additionally, because of the deterioration of navigation performance based on the orbit filter during orbital maneuvering, we used accelerometer data to compensate for the dynamic model to maintain navigation performance. The results of the experiment provide a reference for subsequent studies. [ABSTRACT FROM AUTHOR]

To determine the attitude from the image of a star field obtained by a digital camera, it is necessary to detect images of individual stars and determine their coordinates with subpixel resolution. This problem is relatively easy to solve if the image of the star field is obtained by a stationary camera observing a clear night sky. The difficulty arises when the stars are observed by the rotating camera against the background of the daytime sky. The blurred images of stars are almost impossible to detect in the background noise in one frame. This difficulty can be overcome by accumulating a certain number of consecutive frames after the matched blur filtering has been performed. This paper considers an algorithm for accumulating the sequence of frames, implemented as a multichannel accumulator, consisting of several accumulative channels of the same type, and operating in parallel. The plane of the accumulated image in each channel coincides with the plane of the first frame of the accumulated sequence. Subpixel resolution in determining the coordinates of detected star images is achieved by introducing intrapixel discretization in the first frame. The orientation of the current frame relative to the first one is calculated from the measurements of the gyroscopes of the astroinertial sensor. When synthesizing the impulse responses of the blur-matched filters for the current frame, the attitude of this frame and the location of the intrapixel discretization nodes of the first frame are taken into account. Calculation formulas are given for determining the number of accumulated frames depending on the angular velocity of the camera rotation, the background intensity and the brightness of the observed stars. The simulation results show the possibility of detecting blurred images of fairly dim stars against the background of the daytime sky and determining their coordinates with subpixel resolution.

The airborne star tracker is crucial in aircraft navigation systems, with its tracking performance directly impacting navigation accuracy. Under airborne conditions, the performance of its tracking control will be compromised by various disturbances. Moreover, the limitation in computational resources is another issue that must be addressed. Assuming that the existing studies on this application did not consider these two aspects of the effects simultaneously, this study proposes a novel event-triggered sliding mode control (ET-SMC) scheme considering the known input time delay for star tracking control to address these two issues. First, an extended state observer (ESO) is presented to estimate the disturbance generated by airborne conditions. Second, the ET-SMC scheme further enhances the robustness and improves resource utilization, thus easing the processor burden. An ET mechanism related to the disturbance estimation triggering error in the ESO is introduced to ensure that the system input is only updated when necessary. A novel, easy-to-implement sliding gain is also proposed to increase system adaptability and reduce inherent chattering. The reachability of the sliding surface and the existence of a practical sliding mode of the system are ensured based on the Lyapunov theory. The ultimate upper bound of system states considering the known input time delay is also proven, thereby confirming the stability of the proposed design. The exclusion of Zeno behavior validates the feasibility of the proposed ESO-based ET-SMC. Finally, the effectiveness of the proposed method is verified using comparative simulations and target-tracking experiments. The experimental results demonstrate that the proposed method excels in robustness, disturbance attenuation, high tracking accuracy, and computational resource efficiency. These enhancements are anticipated to result in a more stable tracking performance for the star tracker, thereby contributing to precise aircraft navigation. • The problem of target tracking in the star tracker considering the input delay is addressed. • A novel extended state observer (ESO) based event-triggered sliding mode control (ET-SMC) is proposed. • The stability and feasibility of the proposed method considering the known input delay is verified. • Comparative simulation and target tracking experiments are conducted to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This study introduces an innovative approach aimed at enhancing the accuracy of attitude determination through the computation of star observation quality. The proposed algorithm stems from the inherent invariance of singular values under attitude transformations, leveraging the concept of assessing error magnitude through the deviation of singular values. Quantization becomes imperative to employ this error magnitude as a weighting factor within the attitude determination process. To fulfill this purpose, this study applies p-value hypothesis testing to calculate quantized error levels. Simulation results validate that the calculated weights derived from the proposed algorithm lead to a discernible enhancement in attitude determination performance. [ABSTRACT FROM AUTHOR]

Star trackers are devices that determine high-accuracy attitude by observing stars. As aerospace technology develops, the dynamic performance of the star tracker becomes increasingly important. In the star images taken under high dynamic conditions, the star spots will be tailed or fractured. It will cause a sharp decrease in Signal-to-Noise Ratio (SNR) and make it a challenge to extract and position star spots. In this paper, an Object-to-Pixel star spots extraction and positioning method based on pixel association was proposed, which is a breakthrough compared to the existing Pixel-to-Object extraction method. In the proposed method, rough extraction of star spots is carried out by the Radon transform and image entropy. Precise positioning of star spots is carried out by Gaussian mixture model (GMM) and maximum likelihood estimation (MLE). Experimental results indicate that the proposed method can achieve reliable extraction for star spots with SNR less than 3 or even close to 1. Meanwhile, the positioning accuracy can be improved by at least twice compared with the conventional threshold method. [ABSTRACT FROM AUTHOR]

Small satellite attitude angles are estimated using measurements of star trackers and rate gyros in this study. The issue related to gyro drifts is overcome by adding the bias terms into the state vector in order to estimate them. As an estimation method, two-stage non-traditional filter is used. In the first stage, singular value decomposition (SVD) is used for determining the attitude measurements. As a second stage, an extended Kalman filter (EKF) is designed based on linear attitude measurements. These two stages are integrated for the whole estimation algorithm in order to have estimations with high accuracy, and it is called SVD-Aided EKF. The proposed SVD-Aided EKF is used with two attitude models of satellite: only the kinematics model which does not include the dynamics of a satellite, and both kinematics and dynamics relations. Several scales of uncertainties on the principal moment of inertia of the satellite are considered in order to determine the level when estimation error of the kinematics and dynamics-based filter exceeds the error of the case using only kinematics relations. [ABSTRACT FROM AUTHOR]

The problem of the individual calibration of five elements of the intrinsic orientation of the digital camera of a star tracker is examined: the focal distance of the objective, two coordinates of the principal image point, and two second order coefficients of second-order radial distortion. These elements of the internal orientation form a set of parameters for a mathematical model of digital images of stars taken by a star tracker camera. Stars observed from the earth's surface by the camera being calibrated are used as the calibration test object. The coordinates of the stars are cataloged with very high accuracy, which made it possible to avoid complicated calibration equipment and reduce the calibration problem to a particular problem of digital processing of images of stars. It is shown that the effects of distortion of stars observed from the earth's surface owing to velocity aberration and atmospheric refraction can be taken into account by introducing distortions in the directional vectors of stars taken from the star catalog. Two approaches to solving the calibration problem are considered which take the unknown orientation relative to the earth of the camera to be calibrated into account in different ways. It is established experimentally that the two approaches yield the same results. The discrepancy in the results of the calibration measurements after calibration is reduced by a factor of 32 to a value on the order of the unremovable angular error in determining the visible position of a star in a turbulent atmosphere. The results of an individual calibration of the elements of internal orientation of the camera are used in the program software for the star tracker to correct the systematic error in the measurements of the orientation based on the stars. [ABSTRACT FROM AUTHOR]

Static thresholding-based or filtering and windowing-based star detection algorithms are the most commonly ones implemented on satellite-onboard star trackers. In this investigation, a new star detection algorithm is proposed. It segments stellar images using an adaptive dynamic thresholding approach, instead of a static one. Therefore, it allows the elimination of the non-uniform random noise in stellar images, and thus facilities and improves the detection of stars in such considered data. Another advantage of the proposed algorithm is that the processing is carried out on-line, which results in a reduced processing time. The performance of the designed algorithm is evaluated by means of established criterion, and obtained results are compared to those achieved by some tested literature approaches. For such a purpose, a set of stellar images is generated. This one deals with numerous types of random noise and different scenarios that can be encountered in space. The obtained results show that the proposed algorithm is more robust, faster and has a better ability to detect stars, compared to the tested literature methods. [ABSTRACT FROM AUTHOR]

Abstract Star detection is an important part of the spacecraft attitude determination performed by star trackers. The current advanced star detection algorithms can effectively extract star points in complex backgrounds. However, there are still two problems: first, the parameters of the star detection algorithm are not adaptive, which limits its reliability and robustness; second, the high performance and low computational time of algorithms usually cannot be achieved simultaneously. In this work, a rapid star detection algorithm utilizing dyadic wavelet transform (SDDWT) was developed based on the à Trous algorithm. The authors constructed a suitable dyadic wavelet basis and applied the dyadic wavelet transform to the star image. The maximum wavelet coefficients at a certain scale were binarized according to a threshold value to separate stars from the background. The threshold was adaptively determined according to the white Gaussian noise (WGN) power. Finally, a method for separating individual stars was developed. Experiments indicated that the proposed algorithm was able to ensure a low false alarm rate and high detection rate by adaptively threshold value. Moreover, for a star image of 1024×1024, the computational time of the SDDWT algorithm was stable within 0.3 s, which was smaller than other algorithms.

The algorithm for star identification is a crucial technology for determining the orientation of spacecraft using star sensors. Traditional star identification algorithms achieve matching by seeking a unique or a few optimal solutions. However, in high-noise environments, some solutions may be lost, which could result in matching failure. A new lost-in-space architecture algorithm aimed at rapid identification under high star position noise conditions by directly using star positions for final matching is proposed in this paper. The main idea of this algorithm is to construct sufficiently redundant navigation triangles, fully utilizing the physical relationships of the features and forming a screening method from high to low dimensions and from loose to strict. During identification, a multi-layer joint screening matching method is adopted to screen triangles as a whole, narrowing the range of matches quickly while retaining error tolerance. In a series of simulation experiments, this algorithm achieved identification rates of 99.51%, 99.06%, and 98.42% for 2.0 pixel star position noise, 1.0 Mv star magnitude noise, and 5 false stars, respectively. In terms of practical application, all 1000 star images taken by the star sensor in orbit have been successfully identified, and it only takes 28ms to identify each image. In addition, star images taken by consumer-grade cameras from the ground also show that the algorithm has strong robustness to star position noise, magnitude error and false star interference in more severe environments. This method provides partial algorithmic reference for non-specialized design of star sensors for low-cost, large-scale satellites in the future.

Space situational awareness (SSA) refers to collecting, analyzing, and keeping track of detailed knowledge of resident space objects (RSOs) in the space environment. With the rapidly increasing number of objects in space, the need for SSA grows as well. Traditional methods rely heavily on imaging RSOs from large, narrow field-of-view (FOV), ground-based telescopes. This research outlines the technology demonstration payload, Resident Space Object Near-space Astrometric Research (RSONAR)—a star tracker-like, wide FOV camera combined with commercial off-the-shelf (COTS) hardware to image RSOs from the stratosphere, overcoming the disadvantages of ground-based observations. The hardware components and software algorithm are described and evaluated. The eligibility of the payload for SSA is proven by the image processing algorithms, which detect the RSOs in the images captured during flight and the survival of the COTS components in the near-space environment. The payload features a low-resolution, wide FOV camera coupled with a Field Programmable Gate Array (FPGA)-based platform that houses the altitude and time-based image capture algorithm. The newly developed payload in a 2U-CubeSat form factor was flown as a space-ready payload on the CSA/CNES stratospheric balloon research platform to carry out algorithm and functionality tests in August 2022. [ABSTRACT FROM AUTHOR]

We propose a unique dataset with star images, their centroids, and a new centroid algorithm based on machine learning, that significantly improves star image centroid performance. The centroid of the star image is the subpixel coordinates on the image plane corresponding to the assumed point source of the light (a star). We have compiled and open-sourced an unparalleled dataset of 50000 images of bright stars with their sub-pixel coordinates. It can be used by scientists to refine various techniques and algorithms related to photogrammetry, astrometry, and photometry. Data for this dataset are obtained from the Gaia space observatory, the most recent generation of space astrometric missions. The proposed algorithm outperforms the classical Center of gravity method by almost an order of magnitude. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Angular rate is a piece of useful information for the attitude control of a spacecraft. The star tracker as a space optical sensor can be used to measure the angular rate of a spacecraft. In this paper, a novel approach is proposed to improve the measurement accuracy of the angular rate during spacecraft rotation. The electronic rolling shutter (RS) imaging mode of the complementary metal-oxide semiconductor (CMOS) image sensor in a star tracker is applied to obtain much higher sampling frequency for reducing the change of the angular rate between the sampling interval. The optic flow vector on the imaging plane is approximated within the second order using three successive star images to reflect the nonlinear effect from the variable angular rate. The experiment is performed to demonstrate the advantage of the new approach for variable angular rate measurement. [ABSTRACT FROM AUTHOR]

This paper presents an attitude error model of a star tracker, which is induced from the optical system errors, and proposes an attitude Kalman filter considering the star tracker errors. Though it can be calibrated before and after launches, it is impossible to obtain error-free star tracker parameters in practice, which generates non-white noise errors in the star tracker outputs. Moreover, star tracker error models are usually a business secret for the manufacturers, so it is hard to estimate them online on the spacecraft bus. We model the attitude bias caused by the error of the optical parameters as colored noise using the camera model parameters and their covariance. A recursive form of the colored noise is derived based on a vector autoregressive model, and a colored noise Kalman filter is proposed to estimate the attitude error along with the spacecraft attitude and gyro bias. The proposed method only needs three additional states to be estimated and does not contain sensitive information for a star tracker manufacturer, which can ease the burden of its applications. The simulations illustrate the stability and reliability of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The rapid increase of space debris poses a risk to space activities, so it is vital to develop countermeasures in terms of space surveillance to prevent possible threats. The current Space Surveillance Network is majorly composed of radar and optical telescopes that regularly observe and track space objects. However, these measures are limited by size, being able to detect only a tiny amount of debris. Hence, alternative solutions are essential for securing the future of space activities. Therefore, this paper proposes the design of a payload camera breadboard for space surveillance to increase the information on debris, particularly for the under-catalogued ones. The device was designed with similar characteristics to star trackers of small satellites and CubeSats. Star trackers are attitude devices usually used in satellites for attitude determination and, therefore, have a wide potential role as a major tool for space debris detection. The breadboard was built with commercial off-the-shelf components, representing the current space-camera resolution and field of view. The image sensor was characterized to compute the sensitivity of the camera and evaluate the detectability performance in several simulated positions. Furthermore, the payload camera concept was tested by taking images of the night sky using satellites as proxies of space debris, and a photometric analysis was performed to validate the simulated detectability performance. [ABSTRACT FROM AUTHOR]

The paper studies the blur trajectory, i.e. the motion of a point light source projection along the image plane. It occurs when the digital camera and the observed scene move relative to each other during exposure. The blur trajectory is calculated by solving a set of differential equations of the point plane motion kinematics, written in terms of the measurements of velocity and specific force vectors. The formulated problem is called the special problem of inertial navigation in order to emphasize its differences from the problem of strapdown inertial navigation in the conventional sense. The set of equations of the special problem is obtained in the image plane coordinates. Model examples of blur trajectories calculation are presented for two limiting cases: a distant star and a close motionless target. In the first case, the possibility of increasing the probability of the star blurry image detection in noise is shown. Also, it is discussed how to eliminate the unpredictable systematic error in measuring the star's coordinates. [ABSTRACT FROM AUTHOR]

Measuring resident space objects (RSOs) by star trackers has become a research hotspot in space situational awareness. However, the arc length measured by star trackers is too short to complete the high-precision orbit determination of the RSO. In this paper, a staring–tracking measurement (STM) method is proposed to obtain a sufficiently long arc. Firstly, the three-axis attitude calculation model of the satellite is established for tracking RSOs during the staring process. Secondly, an observation method of the RSO location is proposed based on the principle of the angular distance invariance and the imaging mapping function of the star tracker. Finally, the numerical simulations and the ground experiment were conducted to verify the proposed algorithm. Simulation results show that the acquisition time of the measurable arcs is longer than 6 min, and the accuracy of the declination and the ascension can meet the standard for RSO orbit determination. The physical experiment shows that the acquisition time is consistent with that in the simulation. Our work provides a new idea for the realization of high-precision space-based optical measurement. [ABSTRACT FROM AUTHOR]

Space systems play an integral role in every facet of our daily lives, including national security, communications, and resource management. Therefore, it is critical to protect our valuable assets in space and build resiliency in the space environment. In recent years, we have developed a novel approach to Space Situational Awareness (SSA), in the form of a low-resolution, Wide Field-of-View (WFOV) camera payload for attitude determination and Resident Space Object (RSO) detection. Detection is the first step in tracking, identification, and characterization of RSOs, including natural and artificial objects orbiting the Earth. A space-based dual-purpose camera that can provide attitude information alongside RSO detection can enhance the current SSA technologies which rely on ground infrastructure. A CubeSat form factor payload with real-time attitude determination and RSO detection algorithms was developed and flown onboard the CSA/CNES stratospheric balloon platform in August 2023. Sub-degree pointing information and multiple RSO detections were demonstrated during operation, with opportunities for improvement discussed. This paper outlines the hardware and software architecture, system design methodology, on-ground testing, and in-flight results of the dual-purpose camera payload.

Star detection is an important part of the spacecraft attitude determination performed by star trackers. The current advanced star detection algorithms can effectively extract star points in complex backgrounds. However, there are still two problems: first, the parameters of the star detection algorithm are not adaptive, which limits its reliability and robustness; second, the high performance and low computational time of algorithms usually cannot be achieved simultaneously. In this work, a rapid star detection algorithm utilizing dyadic wavelet transform (SDDWT) was developed based on the à Trous algorithm. The authors constructed a suitable dyadic wavelet basis and applied the dyadic wavelet transform to the star image. The maximum wavelet coefficients at a certain scale were binarized according to a threshold value to separate stars from the background. The threshold was adaptively determined according to the white Gaussian noise (WGN) power. Finally, a method for separating individual stars was developed. Experiments indicated that the proposed algorithm was able to ensure a low false alarm rate and high detection rate by adaptively threshold value. Moreover, for a star image of 1024×1024, the computational time of the SDDWT algorithm was stable within 0.3 s, which was smaller than other algorithms. [ABSTRACT FROM AUTHOR]

Star trackers are currently the most accurate sensors for determining the attitude of a spacecraft. These sensors comprise not only highly capable optical detectors and processor units but also complicated software solvers. One of the main solvers employed in star trackers is image segmentation. In this study, the aim is to develop a hybrid image segmentation method which is a combination of both global thresholding and density-based spatial clustering of applications with noise (DBSCAN) method to increase detection probability of the stars in heavy noise. Secondly, a sorting algorithm is added to list the detected stars in terms of their brightness to increase the efficiency of the star tracking algorithm. Then, this new approach and two different conventional segmentation methods are applied to the Orion star constellation image polluted with Gaussian, salt and pepper, and uneven background noises. The resulting images of these segmentation methods are compared in terms of denoising capabilities. Although computationally more expensive, the proposed DBSCAN-based hybrid method displays a background pixel recovery performance of 99.5%, compared to Otsu global thresholding and adaptive thresholding methods' 73.5% and 79.9% recovery values, respectively. Additionally, it has been demonstrated that the sorting algorithm successfully listed the detected stars in accordance with their brightness. [ABSTRACT FROM AUTHOR]

The ESA Swarm mission, launched on 22 November 2013, consists of three spacecraft each equipped with a Micro Advanced Stellar Compass (μ ASC) from the Technical University of Denmark (DTU). Each μ ASC features three Camera Head Units (CHUs) orientated orthogonally to optimize system accuracy performance and avoid simultaneous blinding. The image sensors inside the CHUs are sensitive to ionizing radiation. When an energetic particle impacts the image sensor, electrons are liberated along the particle's ionizing track and appear on the source image as white dots dubbed 'energetic particle detection' (EPD) events. For star tracker applications EPDs are normally supressed to support nominal attitude operation. However, in early 2018 software was uploaded to the μ ASCs on-board Swarm, which on top of using the EPD measurements to improve the image for star tracking, is reporting the EPD count to the telemetry to ground. This added functionality enables detection and monitoring of high energy particles. By taking advantage of the sample rates (1-2 Hz), the orientation of the camera heads and simultaneous measurements from all three spacecraft spatial derivatives of the EDP aligned to electric and magnetic fields can be determined. Furthermore, since the Swarm spacecraft are in circular, near-polar orbits at an altitude of 450-510 km the spacecraft continuously monitor and map high energy particles at the South Atlantic Anomaly (SAA) of relevance for future mission planning as well as provide detailed time-radiation relations from charge injections processes from e.g. Coronal Mass Ejections (CMEs). In this work we present processes and analysis of four years of high energy radiation data obtained from the Micro Advanced Stellar Compass (μ ASC) on board ESA's Swarm mission, from February 2018 to February 2022. [ABSTRACT FROM AUTHOR]

The rolling shutter effect decreases the accuracy of the attitude measurement of star trackers when they work in rolling shutter exposure mode, especially under dynamic conditions. To solve this problem, a rolling shutter effect correction method based on particle swarm optimization is proposed. Firstly, a collinear reverse installation method between the star tracker and the satellite is proposed, which simplifies the relationship between the velocity of the star centroid and the star tracker angular velocity. Next, the centroid error model is obtained by the star centroid velocity. Based on the centroid error model and angular distance invariance, the loss function of the centroid error is proposed. Then, the particle swarm optimization algorithm is used to determine the star tracker angular velocity by minimizing the loss function. Finally, the simulation and experiments are carried out to verify the proposed method. The experimental results show that the convergence times of the algorithm are less than 50 and the root mean square error (RMSE) of the angular velocity is better than 0.02°/s when the angular velocity of the star tracker is no more than 5°/s. [ABSTRACT FROM AUTHOR]

The literature since Apollo contains exhaustive material on attitude filtering, usually treating the problem of two sensors, a combination of state measuring and inertial devices. More recently, it has become popular for a sole attitude determination device to be considered. This is especially the case for a star tracker given its unbiased stellar measurement and recent improvements in optical sensor performance. The state device indirectly estimates the attitude rate using a known dynamic model. In estimation theory, two main attitude filtering approaches are classified, the additive and the multiplicative. Each refers to the nature of the quaternion update in the filter. In this article, these two techniques are implemented for the case of a sole star tracker, using simulated and real night sky image data. Both sets of results are presented and compared with each other, with a baseline established through a basic linear least square estimate. The state approach is more accurate and precise for measuring angular velocity than using the error-based filter. However, no discernible difference is observed between each technique for determining pointing. These results are important not only for sole device attitude determination systems, but also for space situational awareness object localisation, where attitude and rate estimate accuracy are highly important. [ABSTRACT FROM AUTHOR]

The authors of this paper propose a robust star identification algorithm for a 'Lost-In-Space'-mode star tracker for lost-cost CubeSat missions. A two-step identification framework and an embedded validation mechanism were designed to accelerate the process. In the first step, a masked distance map is designed to provide a shortlist of stars, and the embedded fast validation process enables the direct output of validated stars before the second step. In the second step, local similarity is utilized to select a set of stars from those shortlisted, and the final validation procedure rejects all unsatisfactory stars. This algorithm can provide reliable and robust recognition even when the captured star images include severe star positioning errors, missing stars and false stars. The proposed algorithm was verified by a simulation study under various conditions. As low-cost star sensors face harsh and unknown environments during deep space CubeSat missions such as asteroid exploration, the proposed algorithm with high robustness will provide an important function. [ABSTRACT FROM AUTHOR]

Planetary rover navigation frequently relies on dead reckoning and external infrastructure such as orbiting satellites. Celestial navigation techniques combine measurements of the Sun, stars, and gravity to provide autonomous absolute localization. This study examines the performance of digital star sextants (DSS)—a suite of sensors combining a star tracker and an inclinometer— on estimating position on the planetary surface. In particular, we discuss the estimation, calibration, and error analysis for an elevation-only measurement formulation that does not rely on ground-truth heading information. Field tests and Monte Carlo simulations provide validation of the proposed techniques. The real-world performance of the experimental system gives a mean single-orientation error of 296 m. The relative agreement between the predicted and observed error reveals a clear roadmap to help evaluate the impact of prospective sensor improvements on DSS performance. [ABSTRACT FROM AUTHOR]

The star tracker is a prerequisite device to realize high-precision attitude determination for a spacecraft. However, due to the errors in optical lens machining, optical path assembly, and temperature alternation, optical instruments suffer from some amount of optical geometric distortion, resulting in declining star tracker accuracy. The on-orbit distortion correction of star images is indispensable for precise performance. In this paper, a novel single-layer 2D Legendre neural network (2DLNN) to automatically correct the geometric distortion of the star tracker is proposed. An offline training method grounded on batch star images and an online training algorithm based on sequential star images are designed, respectively. The 2DLNN realizes the ground-based and on-orbit online correction of optical geometric distortion for the star tracker. The 2DLNN features self-learning, lifelong learning, and good adaptability. The single-layer neural network is simple, quick convergence, which is suitable for on-orbit implementation. The simulations demonstrate that the average distortion error can be reduced to less than 0.04 px after ground-based training. In the earth-orientation mode of the LEO satellite, the on-orbit sequential training algorithm can converge in 2500 star images under 1 frame/s. The proposed 2DLNN can achieve high-precision correction at the sub-pixel level, effectively improving the star tracker's attitude determination accuracy. [ABSTRACT FROM AUTHOR]

Star identification algorithms based on triangular-pattern are more suitable for low-cost star trackers since they require less star density in the field of view to operate effectively. In this paper, we propose a modified star pattern recognition algorithm based on the triangular-based algorithm of “LIEBE”. The main contribution of the proposed work is twofold. First, a new strategy for the selection of star triplets is proposed for database construction. Second, new selection criteria of the reference star are considered for pattern generation process. A sky simulation program is developed to assess mainly the robustness against different conditions of noise. The obtained results show an improvement in the overall identification rate, more robustness towards missing stars, and more efficiency towards magnitude noise. Furthermore, our proposed algorithm shows comparable robustness with the recently proposed triangular algorithms despite their reliance on more accurate camera and a validation process. To assess the algorithm performance, the algorithm is implemented on a prototype of Data Processing Unit (DPU) based on ARM Cortex-M4 processor. In this part, we discuss the major design decisions and we present the hardware architecture of DPU. The algorithm shows promising running time at a reduced on-board database when implemented on ARM platform.

Stellar atmospheric refraction imaging error, as the optical imaging variation of starlight before and after passing through Earth’s atmosphere, is one of the key issues for terrestrial star trackers to obtain accurate attitude measurement results. To resolve the problem, a refraction surface-based stellar atmospheric refraction correction method is presented in this paper. Different from existing correction methods, a new atmospheric refraction feature, i.e., stellar atmospheric refraction surface, is proposed to represent the random irregular optical phenomena of starlight, and avoids the limitations of theoretical atmospheric models and empirical formulas. On the basis of the principles of “collinear refraction surfaces”, “invariable refraction surface”, the proposed model successfully realizes the accuracy atmospheric refraction correction by the sensor itself, without external atmospheric parameters. Then, by analyzing the error factors parallel and perpendicular to the atmospheric refraction surface, the atmospheric refraction correction error estimation model is established to forecast the attitude accuracy after correction. Numerical simulations and night sky experiments validate the reliability of our atmospheric refraction correction method and error estimation model. The average angular distance error of the test star tracker is reduced from $31.1310''$ into $1.7705''$ , which is significantly decreased by 94.31%. [ABSTRACT FROM AUTHOR]

A star tracker provides accurate space positioning and reference for satellites, intercontinental strategic missiles, and other spacecrafts. However, the main imaging unit of the star sensor – the image sensor – is affected by the space radiation environment and, in turn, affects the precision with which the star is located by the star tracker. In this study, the parameter degradation of a CMOS image sensor (CIS) after proton irradiation with different fluences was investigated. An outfield test platform for star map collection was built using the star sensor lens and image collection system. The influence of dark current, dark-current nonuniformity, and photo-response nonuniformity of the irradiated CIS on the star diagonal distance measurement error and star-point centroid position detection accuracy was studied. The results showed that with increasing proton fluences, the CIS noise increased, leading to an increase in the error in the measured diagonal distance of the star and a decrease in the star's position detection accuracy. Among these parameters, the dark current plays the greatest role in influencing the measurement accuracy of the star tracker. Furthermore, when a tracker is exposed to space radiation with fluences that are same as those used in this experiment, it is beneficial to reduce the integration time. This reduction in the time will decrease the noise and improve the position measurement accuracy. [ABSTRACT FROM AUTHOR]

Star identification is the foundation of star trackers, which are used to precisely determine the attitude of spacecraft. In this paper, we propose a novel star identification approach based on spectral graph matching. In the proposed approach, we construct a feature called the neighbor graph for each main star, transforming the star identification to the problem of finding the most similar neighbor graph. Then the rough search and graph matching are cooperated to form a dynamic search framework to solve the problem. In the rough search stage, the total edge weight in the minimum spanning tree of the neighbor graph is selected as an indicator, then the k-vector range search is applied for reducing the search scale. Spectral graph matching is utilized to achieve global matching, identifying all stars in the neighbor circle with good noise-tolerance ability. Extensive simulation experiments under the position noise, lost-star noise, and fake-star noise show that our approach achieves higher accuracy (mostly over 99%) and better robustness results compared with other baseline algorithms in most cases. [ABSTRACT FROM AUTHOR]

The rapid increase of space debris poses a risk to space activities, so it is vital to develop countermeasures in terms of space surveillance to prevent possible threats. The current Space Surveillance Network is majorly composed of radar and optical telescopes that regularly observe and track space objects. However, these measures are limited by size, being able to detect only a tiny amount of debris. Hence, alternative solutions are essential for securing the future of space activities. Therefore, this paper proposes the design of a payload camera breadboard for space surveillance to increase the information on debris, particularly for the under-catalogued ones. The device was designed with similar characteristics to star trackers of small satellites and CubeSats. Star trackers are attitude devices usually used in satellites for attitude determination and, therefore, have a wide potential role as a major tool for space debris detection. The breadboard was built with commercial off-the-shelf components, representing the current space-camera resolution and field of view. The image sensor was characterized to compute the sensitivity of the camera and evaluate the detectability performance in several simulated positions. Furthermore, the payload camera concept was tested by taking images of the night sky using satellites as proxies of space debris, and a photometric analysis was performed to validate the simulated detectability performance.

Measuring resident space objects (RSOs) by star trackers has become a research hotspot in space situational awareness. However, the arc length measured by star trackers is too short to complete the high-precision orbit determination of the RSO. In this paper, a staring–tracking measurement (STM) method is proposed to obtain a sufficiently long arc. Firstly, the three-axis attitude calculation model of the satellite is established for tracking RSOs during the staring process. Secondly, an observation method of the RSO location is proposed based on the principle of the angular distance invariance and the imaging mapping function of the star tracker. Finally, the numerical simulations and the ground experiment were conducted to verify the proposed algorithm. Simulation results show that the acquisition time of the measurable arcs is longer than 6 min, and the accuracy of the declination and the ascension can meet the standard for RSO orbit determination. The physical experiment shows that the acquisition time is consistent with that in the simulation. Our work provides a new idea for the realization of high-precision space-based optical measurement.

The guide star catalog is an important component of star identification algorithms for star sensors that indirectly determines their identification rate and other performance characteristics. Currently, star identification algorithms based on triangle features have high identification rates and strong anti-interference abilities. However, this type of method usually requires a large-size guide triangle catalog. Without proper construction, many triangles in the catalog are barely used in the pattern recognition process. In this paper, a guide triangle catalog generation method for star identification based on triangle density and utilization is proposed. First, a model of the star density and triangle density distribution in the celestial sphere is established. Then, considering factors such as the sizes and shapes of the triangles and the brightness levels of the stars, a triangle utilization model is established. Based on these models, a high-triangle-utilization, low-size guide triangle catalog is generated by eliminating low-utilization triangles to the greatest extent possible under the premise of ensuring a minimum triangle density. Some experiments were conducted to prove the performance of the proposed method. Compared with the existing methods under the same conditions, the size of the catalog constructed by the proposed method can be reduced by 70%–90%. Because the selected triangles are different, the proposed catalog exhibits a higher identification rate than other catalogs of the same size. [ABSTRACT FROM AUTHOR]

The Algerian Space Agency has been active in the field of microsatellite engineering for more than 15 years and has successfully developed microsatellites under several know-how transfer technology programs, six to date. This paper presents the flight results and lessons learned from the attitude determination and control system (ADCS) flown on the ALSAT-2B satellite, an Earth observation microsatellite, by analysing the behaviour of the satellite from the initial attitude acquisition through the coarse pointing mode then the nominal mode, where the payload is first tested, and finally the orbit control mode. The spacecraft was launched on 26 September 2016 and placed into a 670km Sun-synchronous orbit with a solar local time at an ascending node of 22:15. The ADCS performance presented here mainly focuses on the launch and early operation results. ALSAT-2B includes four reaction wheels in a pyramidal configuration, three gyros, three Sun sensors, three magneto-torquers, one magnetometer, and one star tracker for agile and accurate attitude control. In addition, a propulsion system based on four 1N hydrazine thrusters is also used on board the microsatellite. The main new development in this platform compared with previous ones of the same type is the fusion of the star tracker and measurements by the three gyroscopes into one gyrostellar estimator that was implemented for the first time on ALSAT-2B, and the pyramidal configuration of the wheels, aiming to increase the angular momentum. The results obtained from the early launch operations for different ADCS modes are very encouraging and fulfil all the requirements set during design and testing. Currently, the satellite has accomplished its fourth year in orbit and is still operational and producing high-quality images. [ABSTRACT FROM AUTHOR]