# Detection and Tracking of Weak Exoatmospheric Target with Elliptical Hough Transform
###### Abstract  
An elliptical Hough transform (EHT) algorithm is proposed in the framework of track-before-detect (TBD) for joint detection and tracking of weak exoatmospheric targets. The new approach exploits the fact that when restricted to a two-body problem, the exoatmospheric target often follows an elliptical orbit, and thus the Hough transform integrated with orbital geometry information would have better detection performance. The relationship between the original radar measurements in data space and the elliptical parameters in parameter space is explicitly derived with multiple steps of coordinate transformation. It is found that the data points mapping into the parameter space essentially represent a quartic curve. An EHT-based algorithm is then designed, and orbit planarity is also taken into account to reduce the effect of noise accumulation. The influences of primary and secondary thresholds and the signal-to-noise ratio (SNR) on the detection performance are compared by simulations. Additionally, a real radar tracking dataset from a scientific satellite on 28 May 2017 is used to investigate the efficiency of the method. By adding some imaginary clutter to the raw orbit, the results indicate that it is very effective in detecting the real satellite trajectory in a low signal-to-noise ratio (SNR) environment. The advantage of the new method lies in it can not only simultaneously detect and track weak exoatmospheric targets but also can predict the trajectory by using these available detected parameters. H 202212 January 20  
a considerably lower level. Typically, the RCS of an X-band cone-shaped warhead can be reduced to a lower bound of 0.0001 m\({}^{2}\) or even smaller [8]. When scanning a predetermined large surveillance volume, this will make the radar face a very low SNR environment. In some cases, even with the help of apriori early-warning indications (e.g., handover of the early-warning satellite), the tracking radar still cannot have the capability to find targets of interest in a certain surveillance volume. As a result, the attacker would decrease the range at which the reentry vehicles would be expected to be tracked well by surveillance radar or even lead to frequent loss of its tracks during the exoatmospheric flight. Instead of awkward working, an alternative way for the victim radar is to employ some sophisticated algorithms, and to change into a track-before-detect (TBD) [14] processing mode, such that the target's detection and tracking can be made simultaneously at a much greater surveillance range, or at least within the predetermined acquisition range. TBD approaches are quite effective algorithms for detecting weak targets in dense clutter environments in that they process multiple frames of raw data directly instead of single-frame data alone. For TBD processing, the judgment is carried out according to some accumulation metric. When the accumulation parameters are detected, the target tracks are picked up simultaneously. Since the detection is executed in the parameter space, even if the target measurements are not continuous and some points are lost due to signal decay, TBD may still work with a good performance. Therefore, TBD indeed has the advantages of providing a higher probability of detection at the same level of probability of false alarms, while circumventing the troublesome data association problem. TBD has a large family, and many algorithms can fall into this category, such as the Hough transform (HT) [15; 16; 17; 18], maximum likelihood approach (MLA) [19; 20], sequential hypothesis testing [21; 22], maximum likelihood-probabilistic data association (ML-PDA) [3; 4], [23; 24], particle filter track-before-detect (PF-TBD) [25; 26; 27; 28; 29], 3D matched filtering [30; 31], 4D-TBD [32], dynamic programming (DP) [33; 34; 35], etc. During the past several decades, many extensive studies of TBD have been published in the available literature. Generally, these techniques have some common characteristics.