# Detection and Tracking of Weak Exoatmospheric Target with Elliptical Hough Transform
###### Abstract
They typically use unthresholded data or thresholded data with significantly lower thresholds and operate on measurement data over several scans in a batch-processing fashion. As a consequence, this usually requires more computational load and has the drawback of not being real-time compared to that of recursive tracking families. Since \"a sophisticated software can save sensor hardware\" [6], to detect and track low SNR targets at ranges greater than that of a traditional recursive processing mode, it is very important to employ some sophisticated algorithms to extend radar performance under stressful circumstances. There have been many TBD approaches highlighting detecting weak infrared targets and aircraft targets; however, not many of them have been applied for exoatmospheric applications, especially for those Hough transform ones. The Hough transform is a classical method that has been widely used in radar tracking fields, such as in track initiation [36; 37] and joint detection and tracking [15; 16; 17; 18], but very few results have been reported on exoatmospheric applications. The reason partly lies in that the exoatmospheric target often follows a parabolic curve (or more precisely elliptical curve); therefore, the standard Hough transform (SHT) [38] which is intended to detect straight lines, cannot be expected to have better performance. If the accumulation time is sufficiently short, a straight line is a good approximation of an exoatmospheric target trajectory, and the SHT works well. However, it is not the case for long time accumulation (such as the entire midcourse time); in the latter case, the SHT may work badly due to the inherent mismatch of the model. Therefore, one must resort to some innovations wherein the HT can have better detection performance. Note that when restricted to a two-body problem, the motion of an exoatmospheric target is essentially a part of an elliptical orbit, governed by the Keplerian motion equation [39]. What is more natural and rational, as well as practice, is to develop TBD methods specific for exoatmospheric targets that more fully exploit the inherent geometrical or motional characteristics of this kind of object. The approach we presented is the elliptical Hough transform (EHT) [40]; we extend this algorithm and test it with field data. Since this approach coincides with the theoretical motion model, it is expected that it will have better performance than that of the simple SHT. It must be noted that the EHT we presented differs vastly from those classical ones used in the detection of ellipses in the image processing field, although their names are somewhat similar. For the detection of ellipses in an image, the methods commonly used are the five-dimensional parameter method [41; 42], randomized Hough transform (RHT) [43; 44], and geometric symmetry method [45; 46]. These approaches cannot be directly applied to exoatmospheric applications. For instance, due to the radar line-of-sight limitation, the trajectory of an exoatmospheric target is usually only a part of an elliptical orbit, in contrast to an entire ellipse; therefore, the geometric symmetry method cannot account for this case. This study is focused on the design of a new Hough detection algorithm. The approach we presented can not only detect a weak reentry vehicle in an earlier midcourse phase but also can predict the orbit with these available detected parameters. More specifically, it has the advantage of the integration of detection, tracking, and prediction capability. Nonetheless, to limit the scope of this investigation, the algorithm should be confined to some hypotheses. One of these hypotheses is the apriori information of early warning, such that the radar can search only limited surveillance space, improve the scan data rate, and reduce the high search dimension of the parameters by a track-while-scan (TWS) mode. The main contributions of this work are as follows:  
1.