Star Tracker Research Articles

Blind Compensation of Angle Jitter for Satellite-Based Ground-Imaging Lidar

Space-based ground-imaging lidar has become increasingly feasible with recent technological advances. Compact fiber-optic lasers and single-photon-sensitive Geiger-mode detector arrays push designs toward low pulse energies and high pulse rates. A challenge in implementing such a system is imperfect pointing knowledge caused by angular jitter, exacerbated by long distances between satellite and ground. Without mitigation, angular jitter would cause significant blurring of the 3-D data products. Reducing the error in pointing knowledge to avoid such problems might require extreme mechanical isolation, advanced inertial measurement units (IMUs), star trackers, or auxiliary passive optical sensors. These mitigations can increase cost and size, weight, and power considerably. An alternative approach is demonstrated, in which the two-axis jitter time series is estimated using only the lidar data. Simultaneously, a single-surface model of the ground is estimated as nuisance parameters. Expectation–maximization is used to separate signal and background detections while maximizing the joint posterior probability density of the jitter and surface states. The resulting estimated jitter, when used in coincidence processing or image reconstruction, can reduce the blurring effect of jitter to an amount comparable to the optical diffraction limit.

Modification and hardware implementation of star tracker algorithms

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

Observation angular distance error modeling and matching threshold optimization for terrestrial star tracker.

Observation angular distance error, as the difference between the actual observation angular distance and the reference angular distance, is an important parameter that affects the identification success rate, attitude measurement accuracy, and real-time performance of a terrestrial star tracker. It is the criterion to determine whether stars are identified in star identification but is still unclarified to date. To resolve the problem, the observation angular error model is presented in this work. This model determines the variation range of the observation angular distance error by analyzing the factors of astrometric transformations. Then, the optimal angular distance matching threshold expression for a terrestrial star tracker is presented on the basis of the proposed model for the optimal efficiency in star identification. Numerical simulations and a night sky experiment demonstrate that the differences between the theoretical model, simulation and actual experiment results are less than 0.5'' and thereby validate the reliability of our conclusions.

The Formation of Subdwarf A-type Stars

Abstract Subdwarf A-type stars (sdAs) are objects that have hydrogen-rich spectra with surface gravity similar to that of hot subdwarf stars but effective temperature below the zero-age horizontal branch. They are considered to be metal-poor main-sequence (MS) stars or extremely low-mass white dwarfs (ELM WDs). In this work, using the stellar evolution code Modules for Experiments in Stellar Astrophysics, we investigate the sdAs formed both by the evolution of (pre-)ELM WDs in double-degenerate systems and metal-poor MS stars with single evolution models. We find that both of the evolutionary tracks of ELM WDs and metal-poor MS stars can explain the observation properties of sdAs. However, the proportions between these two populations are uncertain. In this work, we adopt the method of binary population synthesis of both ELM WDs in the disk and metal-poor MS stars in the halo to obtain their populations at different stellar population ages and calculate their proportions. We find that the proportion of metal-poor MS stars to sdAs for a stellar population of 10 Gyr is ∼98.5%, which is consistent with the conclusion that most sdAs (>95%) are metal-poor MS stars. And the proportion of ELM WDs (metal-poor MS stars) to sdAs increases (decreases) from 0.1% (99.9%) to 20% (80%) with stellar population ages from 5 to 13.7 Gyr.

Star identification robust to angular rates and false objects with rolling shutter compensation

This paper addresses the problem of star identification in the presence of high slew rates, false objects and image deformations introduced by the rolling shutter. These problems can affect the operating life of star trackers and worsen the nominal performances. The proposed methodology relies on a technique named Improved Multi-Poles Algorithm, especially designed for robustness to false objects and slew rates. Angular velocities up to five degrees per second are considered so that stars are seen no more as near-circular spots but appear as streaks. The image deformation due to the rolling shutter of modern active pixel sensor detectors is compensated by means of a mathematical model based on a first order approximation of problem. A star tracker high fidelity simulator generates the input images considering typical noises due to the electronics and space environment. The reported results show that the proposed approach guarantees a reliable star identification and attitude determination with angular velocity from zero to five degrees per second.

A Novel Two-Step Validation Algorithm for Lost-in-Space Star Identification

Since star identification algorithms most likely yield multiple matching candidates, validation algorithms are required for star trackers. Traditional validation is performed in an iteratively cascaded way by incrementally introducing new star points for help, costing plenty of inefficient lookups and complex combinations, but leading to nondeterministic results only. Focusing on this problem, this paper considers a novel validation idea that the attitude estimate perturbation caused by bounded measuring noises should be bounded as well. As a result, a two-step validation algorithm is proposed following a noniterative deterministic structure. Theoretical analyses and simulation examples are both given to demonstrate the algorithm.

A test and calibration environment for the Brazilian star tracker

For many spacecraft to accomplish their mission goals there is a need to have an accurate control of their spatial orientation (attitude), so that instruments aboard the spacecraft, such as remote sensing cameras, telescopes, and other scientific payload be correctly pointed to their targets. For that purpose, many spacecraft employ sophisticated attitude control systems, fed by a variety of attitude sensors: sun sensors, horizon sensors, gyroscopes, star trackers, etc. Among the attitude sensors capable of providing an absolute attitude measurement, star trackers are considered the most accurate. This work presents an overview of the test and calibration infrastructure built for an autonomous star tracker (AST) being developed by the Electro-Optics group of INPE, result of an effort to increase the competence of the country in attitude control systems.

Monocular-based pose determination of uncooperative space objects

Vision-based methods to determine the relative pose of an uncooperative orbiting object are investigated in applications to spacecraft proximity operations, such as on-orbit servicing, spacecraft formation flying, and small bodies exploration. Depending on whether the object is known or unknown, a shape model of the orbiting target object may have to be constructed autonomously in real-time by making use of only optical measurements. The Simultaneous Estimation of Pose and Shape (SEPS) algorithm that does not require a priori knowledge of the pose and shape of the target is presented. This makes use of a novel measurement equation and filter that can efficiently use optical flow information along with a star tracker to estimate the target's angular rotational and translational relative velocity as well as its center of gravity. Depending on the mission constraints, SEPS can be augmented by a more accurate offline, on-board 3D reconstruction of the target shape, which allows for the estimation of the pose as a known target. The use of Structure from Motion (SfM) for this purpose is discussed. A model-based approach for pose estimation of known targets is also presented. The architecture and implementation of both the proposed approaches are elucidated and their performance metrics are evaluated through numerical simulations by using a dataset of images that are synthetically generated according to a chaser/target relative motion in Geosynchronous Orbit (GEO).

The Ice, Cloud, and Land Elevation Satellite – 2 mission: A global geolocated photon product derived from the Advanced Topographic Laser Altimeter System

The Ice, Cloud, and land Elevation Satellite – 2 (ICESat-2) observatory was launched on 15 September 2018 to measure ice sheet and glacier elevation change, sea ice freeboard, and enable the determination of the heights of Earth's forests. ICESat-2's laser altimeter, the Advanced Topographic Laser Altimeter System (ATLAS) uses green (532 nm) laser light and single-photon sensitive detection to measure time of flight and subsequently surface height along each of its six beams. In this paper, we describe the major components of ATLAS, including the transmitter, the receiver and the components of the timing system. We present the major components of the ICESat-2 observatory, including the Global Positioning System, star trackers and inertial measurement unit. The ICESat-2 Level 1B data product (ATL02) provides the precise photon round-trip time of flight, among other data. The ICESat-2 Level 2A data product (ATL03) combines the photon times of flight with the observatory position and attitude to determine the geodetic location (i.e. the latitude, longitude and height) of the ground bounce point of photons detected by ATLAS. The ATL03 data product is used by higher-level (Level 3A) surface-specific data products to determine glacier and ice sheet height, sea ice freeboard, vegetation canopy height, ocean surface topography, and inland water body height.

Quality assurance of the linear accelerator device using Star Track and Perspex

In this study, the quality assurance of the linear accelerator available at the Baghdad Center for Radiation Therapy and Nuclear Medicine was verified using Star Track and Perspex. The study was established from August to December 2018. This study showed that there was an acceptable variation in the dose output of the linear accelerator. This variation was ±2% and it was within the permissible range according to the recommendations of the manufacturer of the accelerator (Elkta).

The application of star trackers in radio telescope pointing measurement

The large radio telescope reacquires rigorous pointing performance, and its pointing performance can be influenced by much more factors due to its large scale. The conventional pointing measurement method would be time-consuming because of the telescope’s large inertia. An accurate direction measurement of the receiver cabin structure can transform the pointing measurement and correction problem into some less complex problems. The star tracker can provide pointing measurement data of sub-arcsecond precision at several Hz update rate, which satisfies the measurement needs well. We introduced the scheme to pointing the telescope with assistance of star trackers, and presented application examples of them on some radio telescopes. At last, we discussed some specific requirements of the star tracker used on large radio telescopes and the possibility of low-cost solutions with commercial cameras.

Alfvén Wave-driven Wind from RGB and AGB Stars

Abstract We develop a magnetohydrodynamical model of Alfvén wave-driven wind in open magnetic flux tubes piercing the stellar surface of red giant branch (RGB) and asymptotic giant branch (AGB) stars, and investigate the physical properties of the winds. The model simulations are carried out along the evolutionary tracks of stars with initial mass in the range of 1.5–3.0 M ⊙ and initial metallicity Z ini = 0.02. Setting the surface magnetic field strength to 1 G, we find that the wind during the evolution of the star can be classified into the following four types: the first is wind with velocity higher than 80 km s−1 in the RGB and early AGB (E-AGB) phases, the second is wind with outflow velocity less than 10 km s−1 seen around the tip of the RGB or in the E-AGB phase, the third is the unstable wind in the E-AGB and thermally pulsing AGB (TP-AGB) phases, and the fourth is the stable massive and slow wind with mass-loss rate higher than 10−7 M ⊙ yr−1 and outflow velocity lower than 20 km s−1 in the TP-AGB phase. The mass-loss rates in the first and second types of wind are two or three orders of magnitude lower than the values evaluated by an empirical formula. The presence of a massive and slow wind of the fourth type suggests the possibility that the massive outflow observed in TP-AGB stars could be attributed to Alfvén wave-driven wind.

Refinining the Drift Model of a Strapdown ESG for Orbital Spacecraft

Refinement of the electrostatic gyroscope (ESG) drift model aboard an orbital maneuverable satellite for remote sensing of the Earth’s surface is considered. Some changes of the drift model also hold for the ESG ground-based applications. The paper also analyzes the quasi-continuous correction mode of the ESG-based strapdown inertial attitude reference system (SIARS) using raw (unsmoothed) data from the star tracker and the extended Kalman filter (EKF) algorithm. A special feature of solving the problem of SIARS output data correction and the calibration problem in this mode is rejection of incorrect measurements. The algorithm for this problem solution is described. The ESG drift model is given both for the SIARS calibration mode in order to ensure an adequate prediction of ESG drifts over a long time interval and for the quasi-continuous correction mode under spacecraft maneuvering conditions. The results of data processing of the flight tests of the SIARS and the star tracker aboard one of the spacecraft are discussed.

Geometric Inverse Problem of Radiative Heat Transfer as Applied to the Development of Alternate Spacecraft Orientation Systems

At present, the angular position of small spacecraft is determined using solar sensors, magnetometers, and angular-velocity pickups as a rule, whereas star trackers are used for complicated problems requiring high accuracy. Each individual system has its advantages and disadvantages. Therefore, combined systems are used to avoid them. Also, to improve the reliability of a craft, recourse to redundancy of the sensors must be had. All these subtleties result in the increased materials intensity and in the complicated mutual synchronization of the systems. In the present work, the authors analyze the possibilities of creating and using the main or alternative orientation system for small spacecraft with radiative-heat-flux sensors on the basis of the methodology of inverse heat-transfer problems. This system will allow checking and correcting the craft's angular position.

GOCE gradiometer data calibration

The GOCE mission provides a unique gravity gradient dataset, which is used by most state-of-the-art global gravity field models. The quality of the gravity gradients of previous data releases degraded during the mission lifetime, which was often attributed to the increasing drag forces towards the end of the mission due to the approaching solar maximum and also, starting in August 2012, a sequence of five orbit lowerings. An imperfect calibration of the gravity gradiometer data was often suspected as root cause for the degradation. We present the novel method for the calibration of the GOCE gravity gradiometer data that was used for the official reprocessing of the GOCE gravity gradients in 2018. It is based on a comprehensive calibration model that includes quadratic factors and angular acceleration couplings as new calibration parameters. The calibration parameters are estimated from star tracker angular rates, gravity gradients calculated from a GRACE gravity field model and the condition that the three gradiometer arms measure the same non-gravitational acceleration. In addition to the GOCE data generated during science mode operations, we also use the data collected during satellite shaking mode operations. We demonstrate that applying the new method removes systematic errors to a large extent and, consequently, yields gravity gradients of superior and constant quality compared to previous data releases.

Performance Analysis of GNSS-Aided Inertial Navigation Systems on Spinning Flight Vehicles

Inertial navigation on spin-stabilized sounding rockets and missiles is challenging due to the high spin rate about the longitudinal axis. Especially the scale factor error of the roll axis gyroscope causes an accumulating roll angle error, which may subsequently transform to the lateral axes if, for example, the rocket is actively reoriented. This orientation error leads to growing position and velocity estimation errors whenever propulsion or aerodynamic forces act on the rocket. Specialized inertial platforms were developed in the 1970s with gimbaled inertial measurement units isolating the sensors from the high spin rate. Because these platforms are rarely available on the market today, ongoing research focuses on integrated navigation systems with strap-down inertial measurement units and additional aiding sensors such as satellite navigation receivers, Sun sensors, or star tracker. Because satellite navigation receivers are well-established on sounding rockets for range safety anyway, this paper investigates to what extent position, velocity, and particularly orientation errors can be estimated with satellite navigation aiding only. Using the example of SHEFEX-2, the paper discusses the observability of translational and rotational navigation errors by translational aiding measurements along a typical trajectory of a two-staged and actively reoriented sounding rocket both qualitatively and quantitatively.

The study of unclassified B[e] stars and candidates in the Galaxy and Magellanic Clouds†

ABSTRACT We investigated 12 unclassified B[e] stars or candidates, 8 from the Galaxy, 2 from the Large Magellanic Cloud (LMC), and 2 from the Small Magellanic Cloud (SMC). Based on the analysis of high-resolution spectroscopic (FEROS) and photometric data, we confirmed the presence of the B[e] phenomenon for all objects of our sample, except for one (IRAS 07455-3143). We derived their effective temperature, spectral type, luminosity class, interstellar extinction and, using the distances from Gaia DR2, we obtained their bolometric magnitude, luminosity, and radius. Modelling of the forbidden lines present in the FEROS spectra revealed information about the kinematics and geometry of the circumstellar medium of these objects. In addition, we analysed the light curves of four stars, finding their most probable periods. The evolutionary stage of 11 stars of our sample is suggested from their position on the HR diagram, taking into account evolutionary tracks of stars with solar, LMC, and SMC metallicities. As results, we identified B and B[e] supergiants, B[e] stars probably at the main sequence or close to its end, post-AGB and HAeB[e] candidates, and A[e] stars in the main sequence or in the pre-main sequence. However, our most remarkable results are the identification of the third A[e] supergiant (ARDB 54, the first one in the LMC), and of an ‘LBV impostor’ in the SMC (LHA 115-N82).

On Period Distribution of RR Lyr Type Variables in the Globular Cluster M3

Evolutionary calculations of population II stars with chemical composition of the globular cluster M3 were carried out under various assumptions about the initial stellar mass ($0.809M_\odot\le M_\mathrm{ZAMS} \le 0.83M_\odot$) and the mass loss rate parameter in the Reimers formula ($0.45\le\eta_\mathrm{R}\le 0.55$). In general, 30 evolutionary tracks of the horizontal branch stars were computed. Selected models of evolutionary sequences were used as initial conditions for solution of the equations of hydrodynamics that describe radial stellar oscillations. Hydrodynamic models of RR Lyr type stars were computed for the core helium burning stage as well as for the preceding pre--ZAHB stage. Analytic relations for the effective temperature of the instability strip edges as a function of stellar luminosity are obtained. Theoretical histograms of the period distribution of RR Lyr type variables were produced for each evolutionary sequence using Monte--Carlo simulations based on the consistent stellar evolution and nonlinear stellar pulsation calculations. A satisfactory agreement with observations (i.e. the greater number of RRab variables) was found for the evolutionary sequence $M_\mathrm{ZAMS} = 0.811M_\odot$, $\eta_\mathrm{R}=0.55$ with the number fraction of fundamental mode pulsators $\approx 75\%$. At the same time the mean period of fundamental mode pulsators ($\langle\Pi\rangle_0=0.79$ day) is substantially greater compared to the observational estimate of $\langle\Pi\rangle_\mathrm{ab}$.

Attitude-correlated frames adding approach to improve signal-to-noise ratio of star image for star tracker.

When applied inside Earth's atmosphere, the star tracker is sensitive to sky background produced by atmospheric scattering and stray light. The shot noise induced by the strong background reduces star detection capability and even makes it completely out of operation. To improve the star detection capability, an attitude-correlated frames adding (ACFA) approach is proposed in this paper. Firstly, the attitude changes of the star tracker are measured by three gyroscope units (GUs). Then the mathematical relationship between the image coordinates at different time and the attitude changes of the star tracker is constructed (namely attitude-correlated transformation, ACT). Using the ACT, the image regions in different frames that correspond to the same star can be extracted and added to the current frame. After attitude-correlated frames adding, the intensity of the star signal increases by n times, while the shot noise increases by n~n/2 times due to its stochastic characteristic. Consequently, the signal-to-noise ratio (SNR) of the star image enhances by a factor of n~2n. Simulations and experimental results indicate that the proposed method can effectively improve the star detection ability. Hence, there are more dim stars detected and used for attitude determination. In addition, the star centroiding error induced by the background noise can also be reduced.

Rocket Investigation of Current Closure in the Ionosphere (RICCI): A novel application of CubeSats from a sounding rocket platform

The Rocket Investigation of Current Closure in the Ionosphere (RICCI) sounding rocket mission concept will use the novel deployment of multiple CubeSats as miniature sub-payloads to obtain the first direct in-situ measurement of ionospheric closure currents. These ionospheric currents are critical to understanding the nature of atmosphere-ionosphere-magnetosphere coupling and have relevance to space weather parameters such as ionospheric densities, thermospheric heating, and satellite drag. Previous attempts to measure these ionospheric closure current in-situ have been limited by poor attitude knowledge resulting in large uncertainties in the magnetic field measurement that compromise the ability to measure the gradient of the magnetic field beyond the precision necessary to resolve the current densities. To address this, RICCI uses dedicated star trackers and currently-available CubeSat subsystems to obtain the high-precision attitude knowledge necessary to directly measure these elusive currents.