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Large Field-of-View Infrared Horizon Sensor Attitude Correction for Earth’s Oblateness
The analysis of satellite coverage to determine the visibility of ground targets from satellites has been extensively studied, particularly through geometric-based methods that provide analytical results. However, there exists a key limitation that these methods do not precisely consider the elevation-angle constraint. To address this limitation, this article provides a geometric approach for computing the visibility considering the elevation-angle constraint. First, the mathematical model of the elevation-angle constraint is established, and the elevation-element equation describing the geometrical relationship between satellite and ground target satisfying the elevation-angle constraint is deduced. Additionally, based on the analytical solution to the elevation-element equation, a two-dimensional map, named the elevation mapping, is proposed. Subsequently, the presented geometric approach is established by incorporating the elevation-angle constraint model into the satellite-target visibility model, and an extended field mapping is proposed to rapidly compute access intervals while adhering to the elevation-angle constraint. Specifically, it achieves this by converting the task into a straightforward problem involving the intersection of a set of lines with the time-invariant regions generated by the extended field mapping. Furthermore, the extended constellation field mapping is presented, which can simplify the multisatellite coverage problem into an easier single-satellite coverage problem, enabling it to solve the constellation coverage problem considering elevation-angle constraints analytically and rapidly. Simulation results demonstrate that the proposed intuitive methodology can accurately and rapidly compute access intervals while considering the elevation-angle constraint, which suggests its wide applications in satellite coverage analysis.
The paper describes how the attitude of a sounding rocket, launch vehicle or satellite with respect to the Earth can be estimated from camera images of the Earth horizon. Details about detecting the horizon in the camera image, fitting hyperbolae or ellipses to the detected horizon curve and deriving the Earth nadir vector and the corresponding error covariance from the fitted conic section are given. The presented method works at low heights, where the projected horizon mostly appears to be hyperbolic, as well as at large heights, where the projected horizon mostly appears to be elliptic and it is irrelevant if the Earth is fully or only partially in the field of view of the camera. The method can be universally used to estimate the direction vectors and attitude with respect to any spherical celestial body such as the Sun or Moon. Using the example of a sounding rocket mission with two cameras aboard, it is illustrated how the estimates of the Earth nadir and the Sun direction vectors are fused with the measurements of a strapdown inertial measurement unit and a GPS receiver to obtain an accurate and continuous estimate of the three-dimensional orientation of the sounding rocket with respect to the Earth.
Images of a nearby celestial body collected by a camera on an exploration spacecraft contain a wealth of actionable information. This work considers how the apparent location of the observed body’s horizon in a digital image may be used to infer the relative position, attitude, or both. When the celestial body is a sphere, spheroid, or ellipsoid (as is the case for most large bodies in the Solar System), the projected horizon in an image is a conic—usually an ellipse at large distances and a hyperbola at small distances. This work develops non-iterative and analytically exact methods for every case (all combinations of unknown state parameters and quadric shapes), completely superseding older horizon-based methods that are iterative, approximate, or both. Some of the analytic methods presented in this work are new. Recognizing that these developments build on techniques that may be unfamiliar to many spacecraft navigators, this work is fashioned as a tutorial. Descriptive illustrations and numerical examples are provided to make concepts clear and to validate the proposed algorithms.
Infrared Earth sensors are widely used in attitude-determination and control systems of satellites. The main deficiency of static infrared Earth sensors is the requirement of a small field of view (FOV). A typical FOV for a static infrared Earth sensor is about 20° to 30°, which may not be sufficient for low-Earth-orbiting micro-satellites. A novel compact infrared Earth sensor with an FOV of nearly 180° is developed here. The Earth sensor comprises a panoramic annular lens (PAL) and an off-the-shelf camera with an uncooled complementary-metal-oxide-semiconductor (CMOS) infrared sensor. PAL is used to augment FOV so as to obtain a complete infrared image of the Earth from low-Earth-orbit. An algorithm is developed to compensate for the distortion caused by PAL and to calculate the vector of the Earth. The new infrared Earth sensor is compact with low power consumption and high precision. Simulated images and on-orbit infrared images obtained via the micro-satellite ZDPS-2 are used to assess the performance of the new infrared Earth sensor. Experiments show that the accuracy of the Earth sensor is about 0.032°.
The preliminary design and validation of a novel, high accuracy horizon-sensor for small satellites is presented, which is based on the theory of attitude determination from ellipsoid observations. The concept consists of a multi-head infrared sensor capturing images of the Earth limb. By fitting an ellipse to the imaged limb arcs, and exploiting some analytical results available from projective geometry, a closed form solution for computing the attitude matrix is provided. The algorithm is developed in a dimensionless framework, requiring the knowledge of the shape of the imaged target, but not of its size. As a result, the solution is less sensitive to the limb shift caused by the atmospheric own radiance. To evaluate the performance of the proposed method, a numerical simulator is developed, which generates images captured in low Earth orbit, including also the presence of the atmosphere. In addition, experimental validation is provided due to a dedicated testbed, making use of a miniature infrared camera. Results show that our sensor concept returns rms errors of few hundredths of a degree or less in determining the local nadir direction.
A method is proposed to calibrate the long-wave infrared ultra-wide-angle camera in this paper. In addition, a novel calibration chessboard is designed and an advanced chessboard corner positioning method is adopted to improve the calibration precision. The designed calibration chessboard can achieve high thermal infrared contrast and exhibits outstanding stability, which is made of a thermoelectric semiconductor refrigeration device. The proposed subpixel corner positioning method can accurately locate the corners on the calibration chessboard according to the characteristics of the infrared image and the checkerboard pattern. Both the principle of the proposed infrared chessboard and the subpixel corner positioning procedure were presented, and the calibration experiment showed that the mean reprojection error and the root mean square error were reduced to 0.32 pixel and 0.39 pixel, respectively. Comparison studies were also performed to verify the calibration effect of the proposed method, and the possibilities of camera calibration error of the proposed method were analyzed.
A study was conducted to consider the systematic error caused by oblateness for a dual cone sensor (DCS) and present the orbit and attitude corrections for the Earth's oblateness. The problem was transferred from the roll and pitch angle errors' correction to nadir vector determination around the oblate Earth. An algorithm determining the nadir vector that accounted for the Earth's oblateness, was derived with the Gauss-Newton method according to the principle of measurement. The nadir vector information, combined with the measurements of other sensors, was used for orbit and attitude determination. The nadir vector determination algorithm was verified and the orbit and attitude corrections for the Earth's oblateness was demonstrated by an integrated algorithm of least-squares orbit determination and two-vector attitude determination based on the orientation information of the sun, Earth, and moon.
Fish-eye lenses are convenient in such applications where a very wide angle of view is needed, but their use for measurement purposes has been limited by the lack of an accurate, generic, and easy-to-use calibration procedure. We hence propose a generic camera model, which is suitable for fish-eye lens cameras as well as for conventional and wide-angle lens cameras, and a calibration method for estimating the parameters of the model. The achieved level of calibration accuracy is comparable to the previously reported state-of-the-art.
Inadequate geometric accuracy of cameras is the main constraint to improving the precision of infrared horizon sensors with a large field of view (FOV). An enormous FOV with a blind area in the center greatly limits the accuracy and feasibility of traditional geometric calibration methods. A novel camera calibration method for infrared horizon sensors is presented and validated in this paper. Three infrared targets are used as control points. The camera is mounted on a rotary table. As the table rotates, these control points will be evenly distributed in the entire FOV. Compared with traditional methods that combine a collimator and a rotary table which cannot effectively cover a large FOV and require harsh experimental equipment, this method is easier to implement at a low cost. A corresponding three-step parameter estimation algorithm is proposed to avoid precisely measuring the positions of the camera and the control points. Experiments are implemented with 10 infrared horizon sensors to verify the effectiveness of the calibration method. The results show that the proposed method is highly stable, and that the calibration accuracy is at least 30% higher than those of existing methods.
Infrared Earth horizon sensors are capable of providing attitude knowledge for satellites in low Earth orbit by using thermopile measurements of the Earth’s infrared emission to locate the Earth’s horizon. Because some small satellites, such as CubeSats, have limited resources, a framework was developed that improves the attitude determination performance of an Earth horizon sensing system consisting of inexpensive thermopiles in static dual-mount configurations by leveraging mission geometry properties and improving sensor models. This paper presents an analytical approach to generate an estimate of the nadir vector in the satellite’s body frame from Earth horizon sensor measurements. On-orbit telemetry data from the Microsized Microwave Atmospheric Satellite (MicroMAS) during limb-crossing events were used to assess our model of sensor readings in response to Earth horizon detection. To quantify the expected attitude estimation performance of our method, a detailed simulation of a low-Earth-orbiting satellite was developed with Earth horizon sensors in similar configurations to the MicroMAS sensor system. Our attitude determination method returns an error of 0.16° on average (root-mean-square error of 0.18°) in nadir estimation under a periodic low-frequency attitude disturbance of 4°. A sensitivity analysis was conducted, which takes mounting uncertainty and position error into account, resulting in an additional attitude error of 0.3° for a mounting offset of 0.2° and up to 0.13° error for a 10-km position knowledge error.
This paper focuses on the autonomous orbit determination accuracy of Beidou MEO satellite using the onboard observations of the star sensors and infrared horizon sensor. A polynomial fitting method is proposed to calibrate the periodic error in the observation of the infrared horizon sensor, which will greatly influence the accuracy of autonomous orbit determination. Test results show that the periodic error can be eliminated using the polynomial fitting method. The User Range Error (URE) of Beidou MEO satellite is less than 2 km using the observations of the star sensors and infrared horizon sensor for autonomous orbit determination. The error of the Right Ascension of Ascending Node (RAAN) is less than 60. μrad and the observations of star sensors can be used as a spatial basis for Beidou MEO navigation constellation.
The use of images for spacecraft navigation is well established. Although these images have traditionally been processed by a human analyst on Earth, a variety of recent advancements have led to an increased interest in autonomous imaged-based spacecraft navigation. This work presents a comprehensive treatment of the techniques required to navigate using the lit limb of an ellipsoidal body (usually a planet or moon) in an image. New observations are made regarding the effect of surface albedo and terrain on navigation performance. Furthermore, study of this problem led to a new subpixel edge localization algorithm using Zernike moments, which is found to outperform existing methods for accurately finding the horizon's location in an image. The new limb localization technique is discussed in detail, along with extensive comparisons with alternative approaches. Theoretical results are validated through a variety of numerical examples.
ZDPS-2, the 2nd generation nano-satellites designed and manufactured by Microsat Research Center of Zhejiang University, were successfully launched by the new generation rocket CZ-6 on Sep 20th, 2015. They are two 20 kg identical nano-satellites (ZDPS-2-A and ZDPS-2-B) with a large deployable mechanism with a truss structure. The main mission of these two satellites is on-orbit demonstration of several new technologies, including large lightweight and flexible deployable mechanisms, a custom-designed panoramic wide field of view micro camera Sun sensor and infrared Earth sensor, and a micro-propulsion system as well as dual-satellite formation flying technology. The satellite is a 25 cm cube with a deployable mechanism, whose fundamental frequency is only approximately 0.13 Hz. This brings several challenges to attitude control. Flexible structure dynamics and its influence on attitude stabilization must be taken into consideration. A rubust control scheme is developed by fully utilizing environmental torques with limited control actuator capability. On-orbit performance verified this design. ZDPS-2 satellites have successfully achieved rate damping, sun-pointing control and 3-axis stabilized Earth-pointing control, with a control accuracy of 5 ° (3σ) and stability superior to 0.1 °/s (3σ). This paper demonstrates the flexible attitude dynamics modeling, illustrates the attitude control system design of ZDPS-2 and presents the on-orbit performance as well.
A strapdown inertial navigation system and celestial navigation system integrated autonomous navigation scheme is proposed in this paper, using the navigation information obtained from Earth sensors and star sensors. To eliminate the adverse effect caused by the asymmetry of Earth infrared radiance, the relationship between Earth infrared radiance brightness and effective horizon height is found. According to the relationship as well as the measuring principle of the Earth sensor, this paper derives a function to correct the measurement of the Earth sensor. Then, the angle-distance of stars can be calculated, and using this information, we can estimate the navigation information of a ballistic missile by least square estimation. The simulation results show that the error of Earth infrared radiance has a great effect on the navigation precision, and by using the correction scheme, this adverse effect can be greatly mitigated. This correction scheme is available and effective.
Recent interest in sending humans to the moon, Mars, or other destinations beyond low Earth orbit has created an increased need for autonomous spacecraft navigation. Because traditional navigation approaches rely on ground-based tracking, new onboard techniques are necessary for the crew to safely return to Earth in the event of a communication systems failure. This paper investigates how images of a planet or moon may be used to perform autonomous navigation through the centroid and apparent diameter measurement type. If a planet is modeled as a triaxial ellipsoid, then it will project to an ellipse in an image. A new approach, which allows estimation of the spacecraft position relative to the observed planet using the full set of parameters describing an ellipse that is fit to points along the planet's lit horizon, is presented. The performances of a number of different ellipse-fitting algorithms are also evaluated. Finally, the covariance of the solution is derived, and simulation results are presented.
Earth-oriented satellites typically use horizon sensors to estimate and correct their roll and pitch errors with respect to the local vertical. A low earth orbit (LEO) satellite can achieve roll and pitch attitude determination accuracy on the order of 0.1 deg using a single scanning horizon sensor. However, the sensor accuracy is limited by errors arising from various sources. From these various sources, the earth oblateness contributes significant effects on the sensor measurement errors, which propagate directly to the satellite attitude estimates. Several authors have studied the horizon sensors and impact of oblate Earth on the attitude errors. Most of the results, however, have been limited in scope and scattered in the open literature and internal technical documents. In the note, we show a complete and simple method to determine and correct roll and pitch errors caused by earth oblateness for single and scanning type horizon sensor configurations.
In the immediate aftermath of Sputnik, the Transit system (a.k.a. Navy Navigation Satellite System, NNSS, NAVSAT) was invented by F. T. McClure, W. H. Guier, and G. C. Weiffenbach. Under the leadership of R. B. Kershner, the system was developed at the Johns Hopkins University Applied Physics Laboratory over the six-year period of 1958-1964. The system pioneered the use of satellites for ocean navigation and land surveying and reduced the arts of surveying and navigation to a solved technical problem with a firm scientific basis. This paper is intended to sketch how the system works - its undergirding principles - and to describe the early (1958-64) development of the system.