Star Tracker Research Articles

The Components of Cepheid Systems: The FN Vel System* * Based on observations with the NASA/ESA Hubble Space Telescope obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS5-26555.

Cepheid masses continue to be important tests of evolutionary tracks for intermediate-mass stars as well as important predictors of their future fate. For systems where the secondary is a B star, Hubble Space Telescope ultraviolet spectra have been obtained. From these spectra a temperature can be derived, and from this a mass of the companion M 2. Once Gaia DR4 is available, proper motions can be used to determine the inclination of the orbit. Combining mass of the companion, M 2, the mass function from the ground-based orbit of the Cepheid and the inclination produces the mass of the Cepheid, M 1. The Cepheid system FN Vel is used here to demonstrate this approach and what limits can be put on the Cepheid mass for inclination between 50° and 130°.

Design of Exterior Orientation Parameters Variation Real-Time Monitoring System in Remote Sensing Cameras

The positional accuracy of satellite imagery is essential for remote sensing cameras. However, vibrations and temperature changes during launch and operation can alter the exterior orientation parameters of remote sensing cameras, significantly reducing image positional accuracy. To address this issue, this article proposes an exterior orientation parameter variation real-time monitoring system (EOPV-RTMS). This system employs lasers to establish a full-link active optical monitoring path, which is free from time and space constraints. By simultaneously receiving star and laser signals with the star tracker, the system monitors changes in the exterior orientation parameters of the remote sensing camera in real time. Based on the in-orbit calibration geometric model, a new theoretical model and process for the calibration of exterior orientation parameters are proposed, and the accuracy and effectiveness of the system design are verified by ground experiments. The results indicate that, under the condition of a centroid extraction error of 0.1 pixel for the star tracker, the EOPV-RTMS achieves a measurement accuracy of up to 0.6″(3σ) for a single image. Displacement variation experiments validate that the measurement error of the system deviates by at most 0.05″ from the theoretical calculation results. The proposed EOPV-RTMS provides a new design solution for improving in-orbit calibration technology and image positional accuracy.

Research on Precise Attitude Measurement Technology for Satellite Extension Booms Based on the Star Tracker

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.

Grayscale Iterative Star Spot Extraction Algorithm Based on Image Entropy

Star trackers are susceptible to interference from stray light, such as sunlight, moonlight, and Earth atmosphere light, in the space environment, resulting in an overall improvement in the star image grayscale, poor background uniformity, low star extraction rate, and high number of false star spots. In response to these challenges, this paper proposes a grayscale iterative star spot extraction algorithm based on image entropy. The implementation of the algorithm is mainly divided into two steps: (1) The algorithm conducts multiple grayscale iterations, effectively utilizing the prior information on the local contrast of star spots to filter out stray light backgrounds to a certain extent. (2) By establishing an inner–outer template, the image entropy algorithm is employed to obtain the real star targets to be extracted, which further suppresses the background clutter and noise. Numerical simulations and experimental results demonstrate that, compared to traditional detection algorithms, this algorithm can effectively suppress background stray light, enhance star extraction rates, and reduce the number of false star spots, and it exhibits superior detection performance in complex backgrounds across various scenarios.

Design and tests of filtering actions for an AI-based RSOs detection and tracking algorithm

Space debris represent a huge threat for the actual and future space traffic. The continuous monitoring of the space environment around the Earth and the build-up, maintenance of Resident Space Objects (RSOs) catalogue are essential to enhance the space segment safety. In the last few years, trend towards Space Based Space Surveillance (SBSS) missions was relevant. In particular, the monitoring of space debris through on-board Star Trackers (STs) coupled with Artificial Intelligence (AI) based algorithms is being studied, modeling RSOs as clear streaks on a dark background. This work presents the advances in the development of an AI-based algorithm for streaks-like RSOs Detection & Tracking for on-board optical sensors applications like STs. The initial design of the RSOs monitoring algorithm (Mastrofini et al., 2022) is extended and tested for what concerns the tracking part with new filtering actions. The goal is the improvement of the tracking outputs quality and reliability when multiple RSOs passages occur, with different configurations. Tests both on real and simulated images from STs are shown and discussed.

Embedded Star Catalog Calculation Tool for Autonomous Star Trackers

Autonomous star trackers are crucial attitude sensors for spacecraft three-axis control. They are the most accurate commercial-off-the-shelf sensors available. An autonomous star tracker is an optoelectronic device that autonomously determines the spacecraft’s attitude, using an embedded star catalog that is compared to in-orbit images to perform stellar field recognition. This work presents a computational tool to calculate the embedded star catalog for any specified star sensor. To optimize the star sensor design, the tool developed provides users with sensor accuracy analysis regarding the observed starfield.

Toward a Comprehensive Grid of Cepheid Models with MESA. I. Uncertainties of the Evolutionary Tracks of Intermediate-mass Stars

Helium-burning stars, in particular Cepheids, are especially difficult to model, as the choice of free parameters can greatly impact the shape of the blue loops—the part of the evolutionary track at which the instability strip is crossed. Contemporary one-dimensional stellar evolution codes, like Modules for Experiments in Stellar Astrophysics (MESA), come with a large number of free parameters that allow us to model the physical processes in stellar interiors under many assumptions. The uncertainties that arise from this freedom are rarely discussed in the literature despite their impact on the evolution of the model. We calculate a grid of evolutionary models with MESA, varying several controls, like solar mixture of heavy elements, mixing-length theory prescription, nuclear reaction rates, the scheme to determine convective boundaries, atmosphere model, and temporal and spatial resolution, and quantify their impact on age and location of the evolutionary track on the H-R diagram from the main sequence until the end of core helium burning. Our investigation was conducted for a full range of masses and metallicities expected for classical Cepheids. The uncertainties are significant, especially during core helium burning, reaching or exceeding the observational uncertainties of logTeff and logL for detached eclipsing binary systems. For ≥9 M ⊙ models, thin convective shells develop and evolve erratically, not allowing the models to converge. A careful inspection of Kippenhahn diagrams and convergence study is advised for a given mass and metallicity, to assess how severe this problem is and to what extent it may affect the evolution.

LONEStar: The Lunar Flashlight Optical Navigation Experiment

This paper documents the results from the highly successful Lunar flashlight Optical Navigation Experiment with a Star tracker (LONEStar). Launched in December 2022, Lunar Flashlight (LF) was a NASA-funded technology demonstration mission. After a propulsion system anomaly prevented capture in lunar orbit, LF was ejected from the Earth-Moon system and into heliocentric space. NASA subsequently transferred ownership of LF to Georgia Tech to conduct an unfunded extended mission to demonstrate further advanced technology objectives, including LONEStar. From August to December 2023, the LONEStar team performed on-orbit calibration of the optical instrument and a number of different OPNAV experiments. This campaign included the processing of nearly 400 images of star fields, Earth and Moon, and four other planets (Mercury, Mars, Jupiter, and Saturn). LONEStar provided the first on-orbit demonstrations of heliocentric navigation using only optical observations of planets. Of special note is the successful in-flight demonstration of (1) instantaneous triangulation with simultaneous sightings of two planets with the LOST algorithm and (2) dynamic triangulation with sequential sightings of multiple planets.

Navigation performance analysis of Earth–Moon spacecraft using GNSS, INS, and star tracker

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.

Stray light analysis and suppression of high-resolution camera line-of-sight variation real-time monitoring system (LoS Var RTMS)

Due to environmental disturbances during emission and operation processes, the line-of-sight of a high-resolution camera is highly prone to variation, resulting in a significant decrease in image positioning accuracy. To address this issue, we propose a line-of-sight variation real-time monitoring system (LoS Var RTMS). A full-link active optical monitoring system is established using laser, and a high-resolution camera is coupled to a star tracker, thereby enhancing the on-orbit calibration and image positioning accuracy of the camera. However, the high-resolution camera LoS Var RTMS belongs to a high stray light sensitivity system. Stray light entering the star tracker from the high-resolution camera through the relay reflective system can significantly affect the imaging of the star tracker, leading to the failure of the monitoring system. Therefore, a comprehensive and accurate analysis of the stray light propagation path in the monitoring system is necessary to ensure its normal operation. In response to this issue, this article proposes a stray light analysis method based on the surface subdivision method, and utilizes inverse ray tracing to meticulously analyze the propagation path of stray light. Additionally, to address the impact of stray light on laser light in the LoS Var RTMS, an inner baffle polarization filtering system is designed to effectively suppress the influence of external strong stray light on the monitoring system. The results demonstrate that the stray light analysis method based on the surface subdivision method not only enhances the integrity and accuracy of the analysis of stray light propagation paths within the monitoring system, but also significantly improves the precision of stray light analysis. It provides a reference for the analysis of stray light in high stray light sensitive systems. Moreover, the design of the inner baffle polarization filtering system effectively distinguishes between lasers and stray light, suppressing stray light within the high-resolution camera LoS Var RTMS and ensuring its normal operation.

Effects of phase angle and sensor properties on on-orbit debris detection using commercial star trackers

The recent proliferation of resident space objects (RSOs) in low Earth orbit (LEO) threatens the sustainability of space as a resource and requires persistent monitoring to avoid collisions involving valuable space assets. State-of-the-art ground-based space surveillance techniques, due to their susceptibility to atmosphere, weather, and lighting conditions, tend to focus on RSOs with characteristic length greater than 10 cm or 1 dm. Consequently, millions of smaller LEO RSOs remain untracked by ground-based methods, which reduces overall space situational awareness. Onboard satellite sensors offer a space-based method for tracking RSOs. Prior research has investigated the feasibility of using commercial star trackers (CSTs) — optical sensors prevalent on most active spacecraft — to observe, detect, and estimate the position and velocity of RSOs larger than 10 cm. In a recent effort, we expanded on these feasibility studies by assessing the capabilities of CSTs to detect debris particles smaller than 10 cm in characteristic length. We modeled the particles as Lambertian spheres with zero phase angle and ten percent reflectivity and found that typical CSTs can detect properly illuminated debris of characteristic length between 1 cm and 10 cm even at distances of tens of kilometers. More sensitive CSTs can characterize decimeter-scale RSOs hundreds of kilometers away; alternatively, they can track centimeter-scale and smaller RSOs at closer distances. In this paper, we summarize these key results and extend our previous study by relaxing its zero-phase-angle assumption and characterizing the effect of Sun-RSO-CST phase angle on debris detection range. We identify a number of representative CSTs with publicly available optical characteristics and consider the effects of properties such as pixel pitch, focal length, aperture diameter, and field of view (FOV) on the capability of each CST to detect debris at a given distance and relative velocity (in the form of streak speed). We find that, for debris particles modeled as diffuse Lambertian spheres, Sun-RSO-CST phase angles as high as 57° result in no more than 20% reduction to the useful RSO-CST detection range. In addition, we find that pixel pitch and focal length, rather than aperture diameter, tend to determine the capability of a given CST to resolve two distinct RSOs. Furthermore, streak speed may serve as a stronger limiting factor for detection of smaller debris particles than for larger ones. Despite these limitations, the overall results indicate that CSTs have the potential to substantially enhance space-based debris detection capability.

Qualification of bracket design for star tracker: numerical and experimental evaluation

Qualification of bracket design for star tracker: numerical and experimental evaluation

Continuous adaptive nonlinear model predictive control using spiking neural networks and real-time learning

Model predictive control (MPC) is a prominent control paradigm providing accurate state prediction and subsequent control actions for intricate dynamical systems with applications ranging from autonomous driving to star tracking. However, there is an apparent discrepancy between the model’s mathematical description and its behavior in real-world conditions, affecting its performance in real-time. In this work, we propose a novel neuromorphic (brain-inspired) spiking neural network for continuous adaptive non-linear MPC. Utilizing real-time learning, our design significantly reduces dynamic error and augments model accuracy, while simultaneously addressing unforeseen situations. We evaluated our framework using real-world scenarios in autonomous driving, implemented in a physics-driven simulation. We tested our design with various vehicles (from a Tesla Model 3 to an Ambulance) experiencing malfunctioning and swift steering scenarios. We demonstrate significant improvements in dynamic error rate compared with traditional MPC implementation with up to 89.15% median prediction error reduction with 5 spiking neurons and up to 96.08% with 5,000 neurons. Our results may pave the way for novel applications in real-time control and stimulate further studies in the adaptive control realm with spiking neural networks.

Dynamic accuracy measurement method for star trackers using a time-synchronized high-accuracy turntable

Star trackers are typically used in a spacecraft to provide absolute attitude information to the on-board attitude control system so as to promote high accuracy. The performance of the star tracker is rather important. Attitude incorrectness provided by star trackers may lead to bad navigation with big deviations, even failure of satellites. Therefore, how to realize and verify the accuracy is crucial. As a matter of fact, it is difficult to validate accuracy of star trackers on the ground, especially for star trackers under highly dynamic conditions. In this paper, an accuracy measurement method for star trackers under dynamic conditions is proposed, utilizing a high-accuracy swing table to provide reference to compare. To this end, a swing table, star tracker, and the test equipment are synchronized, in order to reduce systematic errors. As the motion trajectory of the swing table can be set beforehand, the initial attitude of the star tracker can be predicted through a set of coordinate transformations. As a result, the star tracker is able to keep tracking, regardless of the angular velocity of the swing table. This makes the statistical sample points more sufficient and the results more reliable. Moreover, it can evaluate the angular velocity of star trackers up to 20°/s. In comparison with the conventional method with simulated stars, this method utilizes real navigation stars as observation targets making the measurement results much closer to the on-orbit performance. Lastly, but much more importantly, it can also verify the performance of a star tracker in one experiment, such as sensitivity, static performance, capture probability, and so on. Experimental results demonstrate that the proposed method is effective, especially for highly dynamic star trackers. Such a measurement environment is close to the in-orbit conditions, and it can satisfy the stringent requirement for star trackers under high dynamics.

On the Maximum Black Hole Mass at Solar Metallicity

In high-metallicity environments the mass that black holes (BHs) can reach just after core collapse widely depends on how much mass their progenitor stars lose via winds. On one hand, new theoretical and observational insights suggest that early-stage winds should be weaker than what many canonical models prescribe. On the other hand, the proximity to the Eddington limit should affect the formation of optically thick envelopes already during the earliest stages of stars with initial masses M ZAMS ≳ 100 M ⊙, hence resulting in higher mass-loss rates during the main sequence. We use the evolutionary codes MESA and Genec to calculate a suite of tracks for massive stars at solar metallicity Z ⊙ = 0.014, which incorporate these changes in our wind-mass-loss prescription. In our calculations we employ moderate rotation, high overshooting, and magnetic angular momentum transport. We find a maximum BH mass MBH,max=28.3 M ⊙ at Z ⊙. The most massive BHs are predicted to form from stars with M ZAMS ≳ 250 M ⊙, with the BH mass directly proportional to its progenitor’s M ZAMS. We also find in our models that at Z ⊙ almost any BH progenitor naturally evolves into a Wolf–Rayet star due to the combined effect of internal mixing and wind mass loss. These results are considerably different from most recent studies regarding the final mass of stars before their collapse into BHs. While we acknowledge the inherent uncertainties in stellar evolution modeling, our study underscores the importance of employing the most up-to-date physics in BH mass predictions.

Quaternary pulse width modulation based ultra-high frame rate scene projector used for hard-ware-in-the-loop testing.

The scene projector (SP) can provide simulated scene images with same optical characteristics as the real scenes to evaluate imaging systems in hard-ware-in-the-loop (HWIL) simulation testing. The single scene generation device (SGD) based SP typically projects 8-bit images at 220 fps, which is insufficient to fulfill the requirements of ultra-high frame rate imaging systems, such as star trackers and space debris detectors. In this paper, an innovative quaternary pulse width modulation (PWM) based SP is developed and implemented to realize the ultra-high frame rate projection. By optically overlapping modulation layers of two digital micro-mirror devices (DMDs) in parallel, and illuminating them with light intensities, a quaternary SGD is built up to modulate quaternary digit-planes (QDs) with four grayscale levels. And the quaternary digit-plane de-composition (QDD) is adopted to decompose an 8-bit image into 4 QDs. In addition, the exposure time of each QD is controlled by quaternary PWM, and the base time is optimized to 8 µs. The experimental results prove that the total exposure time of all QDs sequentially modulated by quaternary PWM is approximately 760 µs, namely projecting 8-bit images at 1300 fps. The quaternary PWM using two DMDs in parallel dramatically improves the grayscale modulation efficiency compared to the existing projection technologies, which provides a new approach for the SP design with ultra-high frame rate.

Use of thermal data to estimate satellite rotation rate in the UPMSat-2

Attitude determination is a fundamental task of the Attitude Determination and Control Subsystem (ADCS). It involves determining the spacecraft’s orientation with respect to a reference system and calculating its angular velocity, which is essential for understanding where the payload is pointing and the spacecraft’s stability. The determination of the attitude is obtained using sensors such as Sun sensors, Nadir sensors, or Star trackers. Regarding the spacecraft angular velocity, gyroscopes or MEMs can be used to measure the angular velocity of the satellite, but in their absence the velocity can be derived from the attitude data of the other sensors. However, this method requires a sampling rate to be twice the frequency of the movement, otherwise the angular velocity cannot be calculated with traditional methods. To address this issue, this study proposes a thermal analysis of the external temperatures of a rotating satellite to obtain its rotation rate. This method is especially useful for satellites with low or limited data sample rates. The proposed methodology is used in the UPMSat-2 case to demonstrate the functionality of its experimental ADCS.

A two-dimensional perspective of the rotational evolution of rapidly rotating intermediate-mass stars

Context. Recently, the first successful attempt at computing stellar structure and evolution models in two dimensions was presented with models that include centrifugal deformation and self-consistently compute the velocity field. Aims. The aim of the present study is to explore the rotational evolution of two-dimensional models of stars rotating at a significant fraction of their critical angular velocity. From the predictions of these models, we aim to improve our understanding of the formation of single Be stars. Methods. Using the ESTER code, which solves the stellar structure of a rotating star in two dimensions with time evolution, we computed evolution tracks of stars of between 4 and 10 M⊙ for initial rotation rates ranging between 60 and 90% of the critical rotation rate. Furthermore, we compute models for both a Galactic metallicity and an SMC metallicity. Results. A minimum initial rotation rate at the start of the main sequence is needed to spin up the star to critical rotation within its main sequence lifetime. This threshold depends on the stellar mass, and increases with increasing mass. The models do not predict any stars above 8 M⊙ to reach (near-)critical rotation during the main sequence. Furthermore, we find the minimum threshold of initial angular velocity is lower for SMC metallicity than for Galactic metallicity, which is in agreement with the increased fraction of observed Be stars in lower metallicity environments. The strong difference in the rotational evolution between different masses is not predicted by any one-dimensional stellar evolution models. Conclusions. Our self-consistent two-dimensional stellar evolution models provide further insight into the rotational evolution of intermediate-mass stars, and our predictions are consistent with observations of velocity distributions and the fraction of Be stars amongst B-type stars. We find that stars with a mass above 8 M⊙ do not increase their fraction of critical rotation during the main sequence. As a fraction of stars above 8 M⊙ have been observed to display the Be phenomenon, other processes or formation channels must be at play, or, alternatively, critical rotation is not required for the Be phenomenon above this mass.

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

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

Tracking scheme of airborne star tracker based on event-triggered sliding mode control with known input delay

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.