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Imaging-Based Attitude Determination Algorithm for Small Satellites: Design and The Preliminary Results
Abstract
Limitations for small satellite missions encourages researchers and engineers to use on-board equipment for multiple tasks. Thus, both space can be saved and the equipment redundancy can be prevented. For Earth-imaging satellites a prominent equipment that can be used for multiple purposes is the camera. Other than the observation, the taken images can be used as measurements for determining the absolute or relative attitude of the spacecraft. Depending on also the content of the image (e.g. stars, Earth, Moon) a camera can be an alternate attitude sensor that is capable of providing high accuracy attitude measurements in low cost. This research aims at designing an attitude estimation algorithm, which can aid the coarse attitude estimates with the attitude information extracted from Earth images. Whenever an image is available to be used for attitude estimation, reference Earth data is matched with the ellipsoid that Earth image forms on the sensor frame to estimate the three-axis attitude of the spacecraft. This estimated attitude is fed to a multiplicative extended Kalman filter (MEKF) algorithm that runs as the main block of the attitude estimator. The measurements from the conventional attitude sensor block, which is formed of a three-axis magnetometer and Sun sensor, are pre-processed with QUEST algorithm to unify the measurement update process of the filter. This paper introduces the architecture of the proposed algorithm together with the details on possible methods to extract the attitude information from the obtained Earth images. Preliminary results to demonstrate the success of the algorithm are presented.
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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.
Earth orbiting satellites come in a wide range of shapes and sizes to meet a diverse variety of uses and applications. Large satellites with masses over 1000 kg support high-resolution remote sensing of the Earth, high bandwidth communications services, and world-class scientific studies but take lengthy developments and are costly to build and launch. The advent of commercially available, high-volume, and hence low-cost microelectronics has enabled a different approach through miniaturization. This results in physically far smaller satellites that dramatically reduce timescales and costs and that are able to provide operational and commercially viable services. This paper charts the evolution and rise of small satellites from being an early curiosity with limited utility through to the present where small satellites are a key element of modern space capabilities.
This paper presents a method of improving the attitude determination accuracy for nanosatellites with the aid of the camera sensor. In typical mission, the star tracker is usually used as an optical sensor for the precise attitude pointing for the nanosatellite. However, mostly, the star tracker cannot be affordable for most of the missions because of its cost. Instead of using the star tracker, the low cost MEMS camera module was used for providing the angular velocity vector of the satellite. The angular velocity from the camera module was put into the Extended Kalman Filter as a measurement. The simulation results showed that the attitude determination accuracy using the angular velocity from the camera module was improved compared with the results without the camera module. For the simulation, the spacecraft dynamics and the space environments were modeled for the verification. The precise camera model and the tracking of the stars in the camera images will be conducted in the future.
A simple and fast ellipse estimation method is presented based on optimisation of the Sampson distance serving as a measure of the quality of fit between a candidate ellipse and data points. Generation of ellipses, not just conics, as estimates is ensured through the use of a parametrisation of the set of all ellipses. Optimisation of the Sampson distance is performed with the aid of a custom variant of the Levenberg–Marquardt algorithm. The method is supplemented with a measure of uncertainty of an ellipse fit in two closely related forms. One of these concerns the uncertainty in the algebraic parameters of the fit and the other pertains to the uncertainty in the geometrically meaningful parameters of the fit such as the centre, axes, and major axis orientation. In addition, a means is provided for visualising the uncertainty of an ellipse fit in the form of planar confidence regions. For moderate noise levels, the proposed estimator produces results that are fully comparable in accuracy to those produced by the much slower maximum likelihood estimator. Due to its speed and simplicity, the method may prove useful in numerous industrial applications where a measure of reliability for geometric ellipse parameters is required.
This paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution. We define detection and localization criteria for a class of edges, and present mathematical forms for these criteria as functionals on the operator impulse response. A third criterion is then added to ensure that the detector has only one response to a single edge. We use the criteria in numerical optimization to derive detectors for several common image features, including step edges. On specializing the analysis to step edges, we find that there is a natural uncertainty principle between detection and localization performance, which are the two main goals. With this principle we derive a single operator shape which is optimal at any scale. The optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a Gaussian-smoothed image. We extend this simple detector using operators of several widths to cope with different signal-to-noise ratios in the image. We present a general method, called feature synthesis, for the fine-to-coarse integration of information from operators at different scales. Finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge.
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.
This work develops a star-based attitude propagator that uses relative motion of stars in an imager's field of view to infer the motion of a satellite by calculating relative attitude estimates in three degrees of freedom. Algorithms to perform the star detection, correspondence using the random sample consensus (RANSAC), and attitude propagation are presented. The work presented here overviews the approach, describes the developed algorithms, evaluates experimental results, and offers component selection for a CubeSat imaging system.
This paper contains a critical comparison of estimators minimizing Wahba's loss function. Some new results are presented for the QUaternion ESTimator (QUEST) and EStimators of the Optimal Quaternion (ESOQ and ESOQ2) to avoid the computational burden of sequential rotations in these algorithms. None of these methods is as robust in principle as Davenport's q method or the Singular Value Decomposition (SVD) method, which are significantly slower. Robustness is only an issue for measurements with widely differing accuracies, so the fastest estimators, the modified ESOQ and ESOQ2, are well suited to sensors that track multiple stars with comparable accuracies. More robust forms of ESOQ and ESOQ2 are developed that are intermediate in speed.
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