High-resolution space debris image

Litter is not just a problem on Earth. According to NASA, there are currently millions of pieces of space debris in the altitude range from 200 to 2,000 kilometers above the Earth’s surface, known as the Earth’s lower orbit (LEO). Most of the rubbish is made up of man-made materials, such as pieces of an old spaceship or useless satellites. This space debris can reach speeds of up to 18,000 miles per hour, and is a major threat to the 2,612 satellites currently operating at LEO. Without effective tools for monitoring space debris, parts of LEO can even be too dangerous for satellites.

In a paper published today in the SIAM Journal of Image Sciences, Matan Leibovich (University of New York), George Papanicolaou (Stanford University), and Chrysoula Tsogka (University of California, Merced) introduce a new method for high-resolution images of fast-moving and rotating objects in space, such as satellites or debris in LEO. They created an image process that first uses a state-of-the-art algorithm to estimate the speed and angle at which an object in space rotates, then applies these estimates to a high-resolution image. of the target development.

Leibovich, Papanicolaou, and Tsogka used a theoretical model of a space imaging system to construct and test their imaging process. The model features a fast-moving piece of debris as a collection of very little reflective material that represents the strong reflective edges of an object in orbit, such as the solar panels on a satellite. The gathering of meditators all moves together with the same speed and direction and revolves around a common center. In the model, several sources of radiation on the Earth’s surface – such as ground control stations of global navigation satellite systems – emit pulses emitted by target pieces of space debris. A set of scattered receivers then detects and records the signals that kick from the targets.

The model focuses on sources that emit radiation in the X-band, or from 8 to 12 gigahertz frequencies. “It is known that resolution can be improved by using higher frequencies, such as the X-band,” Tsogka said. “Higher frequencies, however, lead to movements in the image due to environmental variations from atmospheric effects.” Signals are moved by turbulent air as it travels from the target to receivers , and this can make images of objects in LEO very challenging. So the first step of the authors ’imaging process was to link the data taken at different receivers, which will help reduce the impact of these distortions.

The diameter of the area covered by the receivers is called the physical opening of the picture system – in the model, this is about 200 kilometers. Under normal image conditions, the size of the physical aperture determines the resolution of the resulting image; a larger opening gives a sharper picture. However, the rapid movement of the target can create images relative to the captures synthetic aperture opening, in which the signals detected by multiple receivers as the target was moving across their field of view are correspondingly synthesized. This configuration can effectively improve the resolution, as if the imaging system had a wider aperture than the physical one.

Objects in LEO can spin on time frames ranging from full motion every few seconds to every few hundred seconds, which makes the imaging process difficult. So it’s important to know – or at least be able to estimate – some details about the movement before you develop the image. The authors therefore had to estimate the parameters associated with the rotation of the object before transmitting the data from different receivers. While it is only possible to examine all possible parameters to see which ones give the most technically sharpest image, a lot of computing power would be required. Instead of using this brutal force approach, the authors developed a new algorithm that can analyze the image data to estimate the rotation speed of the object and the direction of its axis.

After describing the rotation, the next step in the authors’ imaging process was to analyze the data to develop a picture of the space debris that would hopefully be as accurate and accurate as possible. . One method that researchers often use for this type of images of fast-moving objects is one-point migration of joints. Although atmospheric variables do not usually have a significant effect in this way, it does not have a very high resolution. A different imaging method, commonly used called Kirchhoff migration, can achieve high resolution, as it benefits from a non-inverted synthetic aperture arrangement; however, the trade-off is that it is mitigated by changes in atmosphere. With the aim of creating an image scheme that does not cause excessive changes in atmosphere but still maintains high resolution, the authors proposed a third approach: an algorithm that has a product called a status-1 image. “The inclusion of the status-1 image and its solution analysis for fast-moving and orbiting objects is the most recent part of this study,” Leibovich said.

To compare the performance of the three image schemes, the authors provided each with symbolic data of rotating material in LEO and compared the images they produced. Interestingly, the status-1 image was much more accurate and well-resolved as a result of one-point migration. Its features were also similar to the product of Kirchhoff’s migration method. But this result was not entirely surprising, given the design of the problem. “It is important to note that the status-1 image benefits from the rotation of the object,” Papanicolaou said. While a rotating object generates more complex data, one can integrate this additional information into the image processing method to improve its resolution. Circulation at certain angles can also increase the size of the synthetic aperture, which greatly improves the resolution for Kirchhoff migration and status-1 imaging.

Further simulations showed that the status-1 image is not easily reduced by errors in the new algorithm for estimating rotation parameters. It is also more resistant to atmospheric effects than Kirchhoff’s migratory image. If captures capture data for full movement of the object, the status-1 image can achieve even the best image resolution. Due to its good performance, this new imaging method could improve the image accuracy of LEO satellites and space debris. “Overall, this study shed light on a new way of making images of fast-moving and orbiting objects in space,” Tsogka said. “This is critical to ensuring the safety of the LEO band, which is the backbone of global remote sensing.”

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Source article: Leibovich, M., Papanicolaou, G., & Tsogka, C. (2021). Correlation-based image for rotating satellites. SIAM J. Think. Sci., 14(1), 271-303.