Analysis of the multi-hypothesis test for determining pointing angles for telescopes

Abstract

To catalog space objects, the position and angular rate of the detected object must be determined; however, the quality of this data is restricted by the capability to determine the telescope’s pointing azimuth and elevation. The commonly used Binary Hypothesis Test (BHT) determines whether an object is present in an image or not by calculating the ratio of the probability of whether an object is present in each pixel to the probability of an object not being present. If this ratio exceeds a specified threshold, an object has been detected. The Multiple Hypothesis Test (MHT) operates similarly to the BHT but includes the additional step of correlating the image data against sampled Point Spread Functions (PSF). These PSFs appear differently based on the sub-pixel location of the object. The PSF with the strongest correlation to the image data indicates that the detected object is likely in the same sub-pixel location. Using the MHT can improve the ability to determine the telescope’s azimuth and elevation by observing objects at known locations. The data will be gathered through projecting a star map and using a telescope to locate the objects. This experimental data will provide verification and quantification of the improved accuracy of using the multi-hypothesis test.