Star Vector Research Articles

Robust and adaptive star identification algorithm based on linear assignment for multiple large field of view visual imaging systems

The integration of the visual imaging system and the self-attitude determination system in on-orbit space projects necessitates robust star identification algorithms. However, disturbances in the on-orbit environment pose a challenge to the accuracy and efficiency of star identification algorithms. This paper introduces a novel star identification algorithm, to the best of our knowledge, designed for multiple large field of view (FOV) visual imaging systems, providing stability in the presence of the noise types, including position noise, lost-star noise, and fake-star noise. We employ the dynamic simulated star images generation method to construct simulated star image libraries suitable for various cameras with different FOV angles. Our algorithm comprises two parts: the star edge matching for coarse matching of interstellar angular distances based on linear assignment, and the star point registration for precise matching of star vectors. This innovative combination of local edge generation and global matching approach achieves an impressive 97.83% identification accuracy, maintaining this performance even with a standard deviation of one pixel in image plane errors and up to five missing stars. A comprehensive approach involving both simulated and empirical experiments was employed to validate the algorithm’s effectiveness. This integration of the visual imaging system and the self-attitude determination system offers potential benefits such as reduced space equipment weight, simplified satellite launch processes, and decreased maintenance costs.

Analysis of Stator-Slot and Rotor-Pole Combinations of Axial Modular-Flux Reversal Permanent Magnet Machine

This paper investigates the influence of stator-slot and rotor-pole combinations on torque performances in axial modular-flux reversal permanent magnet (AM-FRPM) machines. Based on the slot-conductor back-EMF star vector theory, the winding factors of all stator-slot and rotor-pole combinations are improved by adopting toroidal windings. In addition, based on a magnetomotive-force and permeance model, the candidates of stator-slot and rotor-pole combinations with higher torque capacity can be determined by analyzing the harmonic combinations between the PM and armature reaction field. Besides, the cogging torque is suppressed by selecting the corresponding angle between rotor modules for different stator- slot and rotor-pole combinations. Finally, an electromagnetic performance comparison between a conventional FRPM machine and three AM-FRPM machines candidates with attractive torque performances is conducted, and the experiments are constructed to verify the theoretical analysis.

Rigorous and integrated self-calibration model for a large-field-of-view camera using a star image

This paper proposes a novel self-calibration method for a large-FoV (Field-of-View) camera using a real star image. First, based on the classic equisolid-angle projection model and polynomial distortion model, the inclination of the optical axis is thoroughly considered with respect to the image plane, and a rigorous imaging model including 8 unknown intrinsic parameters is built. Second, the basic calibration equation based on star vector observations is presented. Third, the partial derivative expressions of all 11 camera parameters for linearizing the calibration equation are deduced in detail, and an iterative solution using the least squares method is given. Furtherly, simulation experiment is designed, results of which shows the new model has a better performance than the old model. At last, three experiments were conducted at night in central China and 671 valid star images were collected. The results indicate that the new method obtains a mean magnitude of reprojection error of 0.251 pixels at a 120° FoV, which improves the calibration accuracy by 38.6% compared with the old calibration model (not considering the inclination of the optical axis). When the FoV drops below 20°, the mean magnitude of the reprojection error decreases to 0.15 pixels for both the new model and the old model. Since stars instead of manual control points are used, the new method can realize self-calibration, which might be significant for the long-duration navigation of vehicles in some unfamiliar or extreme environments, such as those of Mars or Earth’s moon.

GMM-Based Adaptive Extended Kalman Filter Design for Satellite Attitude Estimation under Thruster-Induced Disturbances.

Star images from star trackers are usually defocused to capture stars over an exposure time for better centroid measurements. While a satellite is maneuvering, the star point on the screen of the camera is affected by the satellite, which results in the degradation of centroid measurement accuracy. Additionally, this could result in a worse star vector outcome. For geostationary satellites, onboard thrusters are used to maintain or change orbit parameters under orbit disturbances. Since there is misalignment in the thruster and torque is generated by an impulsive shape signal from the torque command, it is difficult to generate target torque; in addition, it also impacts the star image because the impulsive torque creates a sudden change in the angular velocity in the satellite dynamics. This makes the noise of the star image non-Gaussian, which may require introducing a method for dealing with non-Gaussian measurement noise. To meet this goal, in this study, an adaptive extended Kalman filter is implemented to predict measurement vectors with predicted states. The GMM (Gaussian mixture model) is connected in this sequence, giving weighting parameters to each Gaussian density and resulting in the better prediction of measurement vectors. Simulation results show that the GMM-EKF exhibits a better performance than the EKF for attitude estimation, with 30% improvement in performance. Therefore, the GMM-EKF could be a more attractive approach for use with geostationary satellites during station-keeping maneuvers.

On Robust Expansiveness for Sectional Hyperbolic Attracting Sets

We prove that sectional-hyperbolic attracting sets for $C^1$ vector fields are robustly expansive (under an open technical condition of strong dissipative for higher codimensional cases). This extends known results of expansiveness for singular-hyperbolic attractors in $3$-flows even in this low dimensional setting. We deduce some converse results taking advantage of recent progress in the study of star vector fields: a robustly transitive attractor is sectional-hyperbolic if, and only if, it is robustly expansive. In a low dimensional setting, we show that an attracting set of a $3$-flow is singular-hyperbolic if, and only if, it is robustly chaotic (robustly sensitive to initial conditions).

Star centroid error compensation based on the star triangle internal angles for celestial navigation with aero-optical degradation

In this paper, to solve the correction problem of star vector error induced by the aero-optic effect under hypersonic conditions, and to improve the navigation accuracy further, a novel method of star centroid error correction is proposed. The method is based on the star triangle internal angles, which can effectively use the prior information to estimate the aero-optical star centroid error. The method is verified by the Monte Carlo simulation and Hardware-In-Loop simulation. According to Hardware-In-Loop simulation, the star centroid error can be reduced by approximately 27%, and the attitude error can be reduced by approximately 14%. Therefore, the presented method is significant for the application of celestial navigation with hypersonic conditions.

Accelerometer Bias and Star Sensor Installation Error Joint Calibration for the SINS/CNS Integrated Navigation System Using Attitude Maneuver

The integrated strap-down inertial navigation system/celestial navigation system (SINS/CNS) is an important autonomous navigation method with effective concealment and high precision. Both accelerometer bias and star sensor installation error are important factors that affect the performance of this navigation system, which need to be calibrated and compensated. A new accelerometer bias and star sensor installation error joint calibration method for the SINS/CNS integrated navigation system is proposed. In this newly proposed method, the installation error of star sensor is augmented to the state vector, and the star vector, nadir angle, horizontal position error and velocity error are used as measurements to calibrate the two errors mentioned above. Simulations show that both accelerometer bias and star sensor installation error can be calibrated effectively.

Domains of the adsorbed benzene monolayer on graphene

We consider the adsorbed benzene monolayer on graphene and show that the monolayer’s structure can be very complicated even for benzene, the simplest representative of the cyclic hydrocarbons. We base this on previous the first principal investigations, which found different energy states of the adsorbed benzene molecule. We find the existence of the six domains (star domains) for the stable molecular monolayer. The representatives of these domains (grains) at the graphene hexagonal layer are star vectors that describe transitions from symmetric high energy state into the stable low symmetric position. In the hexagon lattice of any benzene close pack domain, we introduce the primitive unit vectors, which are twice longer than the graphene primitive unit ones. The symmetry elements of the adsorbed benzene monolayer on graphene are found, left and right domains are introduced. Besides, half-translation of the benzene domains on the graphene primitive unit vectors leads to a further increase in the variety of the domain types. We introduce the selection procedure to decrease the number of the possible domains, find zero-block cells, and the complete number of the benzene domains — eight. We find all types of the structural domains and show their relation with the graphene unit cell construction.

Comprehensive Comparison of Two Fault Tolerant Axial Field Modular Flux-Switching Permanent Magnet Machines with Different Stator and Rotor Pole-Pairs Combinations

This paper gives a comprehensive comparison among two fault-tolerant axial field modular flux-switching (AFFSPM) machines with different stator modular segments (U- and E-core) and stator-slots/pole-pairs combinations. The topologies of two AFFSPM machines are introduced, each with two feasible stator slots and rotor pole-pairs combinations with high winding factors based on the slot-conductor back-EMF star vectors theory. Then, the static performance including the air-gap flux density, flux linkage, back-electromagnetic force (back-EMF), and electromagnetic torque are analyzed and compared. Moreover, the fault-tolerant capability is then investigated by the torque performance under one- and two-phase open-circuit conditions in which the corresponding fault-tolerant control strategies are applied. The predicted results confirm that the 6-stator slot/11-rotor-pole-pair E-core AFFSPM machine exhibits the best performance of the four candidates.

Minimal differential lateral acceleration configurations for starshade stationkeeping in exoplanet direct imaging

Exoplanet imaging missions utilizing an external occulter (starshade) for starlight suppression require precise alignment between the telescope and starshade, necessitating maintenance of the starshade orbit during observations. Differential lateral acceleration between the two spacecraft serves as a proxy for fuel use and number of required thruster firings, which may interrupt the observation. Comparison against results from high fidelity simulations of stationkeeping validates the use of this easy-to-compute proxy. Among starshade positions constrained to the surface of a sphere centered about the telescope, minima of differential lateral acceleration lie on a great circle and its corresponding poles. We present a closed expression for telescope to star vectors requiring minimal stationkeeping for observation from a telescope at an arbitrary position. This proxy metric along with analytical knowledge of optimal observations facilitates computationally efficient design of exoplanet imaging missions employing a starshade.

Neural Network Calibration of Star Trackers

To maintain ideal performance, star trackers must be able to predict the direction of incident starlight to within a few arcseconds across the entire instrument field of view. Parametric camera models are commonly employed to calculate star vectors from camera images and correct for aberrations in the instrument optics. This conventional approach can be quite effective, but systematic errors can be difficult to eliminate and the proper selection of calibration basis functions is often difficult to determine. This study explores using supervised machine learning approaches such as Radial Basis Function networks (RBFNs) and Support Vector Machines (SVMs) for star tracker calibration as an alternative to conventional aberration formulations. These networks can be formulated either as a correction to a low-order camera model or complete replacement for the whole model. When applied to the instrument calibration of a dozen Sinclair Interplanetary ST-16RT2 sensors the RBFN formulation offers 27% reduction in the calibration residuals and almost 12% reduction in the validation residuals over conventional formulations.

Starlight-inertial integrated navigation based on single star vector

Starlight-inertial integrated navigation based on single star vector

Measures of intermediate entropies for star vector fields

We prove that all star vector fields, including Lorenz attractors and multi-singular hyperbolic vector fields, admit the intermediate entropy property. To be precise, if X is a star vector field with htop(X) > 0, then for any h ∈ [0, htop(X)), there exists an ergodic invariant measure μ of X such that hμ(X)= h. Moreover, we show that the topological entropy is lower semi-continuous for star vector fields.

The Stellar-INS Navigation Performance Influence Mechanism of Star Vector Orientation in the Field of View

The star sensor field of view varies from several arc-minutes to 20 degrees, which directly determines the star vector orientation in the field of view (FOV). Although the relationship between star vector orientation in the FOV and attitude accuracy has been revealed, the influence mechanism of star vector orientation on the integrated navigation performance of a stellar inertial navigation system has not been analysed. In order to improve the integrated accuracy, the main errors such as star sensor installation error, gyro error and initial platform angle error should be estimated online. It is significant to study the influence mechanism of star vector orientation on estimation of the above errors. In this paper, the star sensor sensitivity and the geometry factor are defined to feature the difference between the optical axis direction and the non-optical axis direction. The formulised mechanism and quantification results between star vector orientation and integration attitude and error estimation accuracy are clearly given. Simulation and ground testing were conducted and it was found that the larger the star vector orientation along the optical axis, the better the error estimation accuracy. In contrast, the attitude accuracy is weakly sensitive to the orientation of the star vector in conditions of appropriate posture adjustment and star observation scheme. This conclusion can offer universal guidance for the design and evaluation of stellar inertial navigation systems with narrow field of view or large field of view star sensors.

INS/CNS integrated filtering technique based on celestial calibration

This paper analyzes the filtering mode and working characteristics of INS/CNS system according to application features of celestial equipment. In view of combination mode of gyro drift calibrated by CNS, this paper establishes corresponding filtering model according to different measurement information selected by INS/CNS system. The error of inertia component is compensated by virtue of star vector estimate value so as to guarantee the long-term precision of inertial navigation. Simulation analysis verifies that this method may improve adaptability of INS/CNS system to environment, and effectively guarantee the navigation precision in long-time operation of the system.

A Star Sensor On-Orbit Calibration Method Based on Singular Value Decomposition

The navigation accuracy of a star sensor depends on the estimation accuracy of its optical parameters, and so, the parameters should be updated in real time to obtain the best performance. Current on-orbit calibration methods for star sensors mainly rely on the angular distance between stars, and few studies have been devoted to seeking new calibration references. In this paper, an on-orbit calibration method using singular values as the calibration reference is introduced and studied. Firstly, the camera model of the star sensor is presented. Then, on the basis of the invariance of the singular values under coordinate transformation, an on-orbit calibration method based on the singular-value decomposition (SVD) method is proposed. By means of observability analysis, an optimal model of the star combinations for calibration is explored. According to the physical interpretation of the singular-value decomposition of the star vector matrix, the singular-value selection for calibration is discussed. Finally, to demonstrate the performance of the SVD method, simulation calibrations are conducted by both the SVD method and the conventional angular distance-based method. The results show that the accuracy and convergence speed of both methods are similar; however, the computational cost of the SVD method is heavily reduced. Furthermore, a field experiment is conducted to verify the feasibility of the SVD method. Therefore, the SVD method performs well in the calibration of star sensors, and in particular, it is suitable for star sensors with limited computing resources.

A high-accuracy autonomous navigation scheme for the Mars rover

High-accuracy, autonomous and reliable navigation systems are important foundations for Mars rovers to achieve exploration missions successfully. Based on the motion characteristics and working environment of the rover, the paper shows a high-accuracy strapdown inertial navigation system/visual navigation system/celestial navigation system (SINS/VNS/CNS) integrated navigation scheme suitable for the rover with long-time and long-distance motion. According to the feature point positions in the camera frame at adjacent time obtained by the binocular visual odometry, its velocity in the camera frame and the attitude are calculated, then a subsystem model of SINS/VNS integrated navigation is established. In addition, using the star vectors measured by the large field-of-view star sensor, a high-accuracy attitude matrix of the rover in the inertial frame can be obtained, and a SINS/CNS subsystem model is established. Furthermore, in order to make full use of the complementary advantages of the two subsystems in attitude and position estimation, an interacting multiple model filter is developed. By updating the model probabilities of the subsystems separately in real time, the filter can output accurate navigation information of the rover. Simulation results show that the proposed navigation scheme can significantly improve the estimation accuracy of attitude, position and velocity simultaneously.

Spacecraft angular velocity estimation method using optical flow of stars

Angular velocity is a crucial parameter for spacecraft navigation, which, at present, is mainly obtained by using gyroscopes. Several studies have been performed on angular velocity estimation using star sensors when data from gyroscopes are not available. Most of the previous angular velocity estimation methods using star sensors are based on information on the attitude or star vector measurements. In this paper, an angular velocity estimation method using the optical flow (OF) directly from the star images is proposed, which, unlike the previous methods, requires star coordinates in two consecutive images only. Because the procedure of star identification is eliminated, the corresponding high computation requirement is reduced. Simulations demonstrate that the proposed method has a robust performance in terms of computational cost and the number of stars in the field of view (FOV) compared with the previous methods. Finally, certain affecting factors are analyzed, including lens distortion, star senor instantaneous FOV (IFOV), star number, and accuracy of the star sensor.

A Markley Variables-based Attitude Estimation Method Using Optical Flow and a Star Vector for Spinning Spacecraft

Markley variables have advantages of slow variation, easy numerical integration and high precision in describing the attitude of spinning spacecraft. Previous attitude estimation methods based on Markley variables for spinning spacecraft usually employ a sun vector from the sun sensor, a magnetic vector from the magnetometer, or the angular rate from the gyro as the measurement. This paper proposes a Markley variables-based attitude estimation method using optical flow and a star vector from a star sensor as the measurement, where optical flow provides rate information and the star vector provides direction information. This method can estimate the direction of the spin axis and spin angular rate very well by using only one star sensor. In addition, the star sensor has higher accuracy than the traditional sun sensor and magnetometer, and the star sensor can also replace the gyro in case the gyro is out of action. The impact factors of this method are also analysed, which include spin angular rate, spin axis orientation and spacecraft moment of inertia tensor error.

Spacecraft angular velocity estimation algorithm for star tracker based on optical flow techniques

An integrated navigation system often uses the traditional gyro and star tracker for high precision navigation with the shortcomings of large volume, heavy weight and high-cost. With the development of autonomous navigation for deep space and small spacecraft, star tracker has been gradually used for attitude calculation and angular velocity measurement directly. At the same time, with the dynamic imaging requirements of remote sensing satellites and other imaging satellites, how to measure the angular velocity in the dynamic situation to improve the accuracy of the star tracker is the hotspot of future research. We propose the approach to measure angular rate with a nongyro and improve the dynamic performance of the star tracker. First, the star extraction algorithm based on morphology is used to extract the star region, and the stars in the two images are matched according to the method of angular distance voting. The calculation of the displacement of the star image is measured by the improved optical flow method. Finally, the triaxial angular velocity of the star tracker is calculated by the star vector using the least squares method. The method has the advantages of fast matching speed, strong antinoise ability, and good dynamic performance. The triaxial angular velocity of star tracker can be obtained accurately with these methods. So, the star tracker can achieve better tracking performance and dynamic attitude positioning accuracy to lay a good foundation for the wide application of various satellites and complex space missions.