We track the satellite so that the stars are trails and the satellites circles. This helps to a) increase the signal-to-noise ratio of the satellite, allowing us to observe fainter objects and b) it improves the measured satellite position as the center of a gaussian-like circle can be found more precisely than a potentially faint and potentially discontinuous trail.
In order to apply coordinates to each image, the star trails must be identified and then matched with known catalog stars.
After coordinates are applied, the satellite is identified and measured.
Our pipeline produces satellite positions accurate to within 0.8 arcseconds.
Measuring the centers of star trails
The center of each star trail is the position of that particular star at the middle of the observation, i.e. at 2 seconds into a 4 second exposure. To find the centers, we cross-correlate the image data with a kernel that looks like a trail. All of the trails in the image should be of the same length, rotated by the same amount, and the point spread function (PSF) should have the same full-width-at-half-maximum (FWHM). We can measure and/or calculate these values for each image, and use them to make the kernel. See an example kernel above.
A cross-correlation searches for objects in the data that look like the kernel used. In this case, we search for trails that have the specified parameters. The peaks of the cross-correlation correspond to the centers of the trails.
As each pixel is 1.16 arcseconds, these centers are correct to somewhere within that span. We refine them by computing the centroid of the entire trail.
These refined centers are then passed to astrometry.net, which applies coordinates to the image by matching the positions found to known stars.
Finding the satellite in the image
To identify what is a satellite and what is a star, we categorize each object, or source, found in the image by its ellipticity using SExtractor. There is a clear separation between the low ellipticities of satellites and the high ellipticities of stars, as shown in the histogram. A cutoff is defined, below which any object is designated a satellite.