Sophia Matthews, University of Maryland; Tam Nguyen, University of Maryland
https://doi.org/10.64861/ZQSP1330
Keywords: track-before-detect, optical system, SDA, modeling, photometry, astrometry
Abstract:
Track-before-detect (TBD) methods extend the sensitivity of an optical system, enabling the detection of moving objects too faint to detect in a single frame. Demonstrations of track-before-detect methods have successfully detected faint space objects, supporting Space Domain Awareness (SDA) and astronomy. In general, track-before-detect methods are implemented when target states are unknown. To make a detection, sequential images are added along multiple velocity hypotheses and the added frames are compared to a detection threshold. Typically, images are shifted along a velocity hypothesis by rounding the true pixel shift to the nearest pixel. The nearest pixel shift-and-add algorithm is computationally intensive, limiting the application of traditional track-before-detect in larger search volumes. The Fast Discrete X-Ray Transform (FaXT) is an integer pixel shift-and-add method using a divide-and-conquer algorithm; FaXT is faster than traditional track-before-detect by a factor of N, where N is the number of frames in the image stack. In this work, we analyze the performance of traditional track-before-detect and FaXT and investigate methods to improve the performance of FaXT with limited increase in runtime. _x000D_
We assess three performance metrics: photometric accuracy, astrometric accuracy, and time complexity. Photometric accuracy is the ratio of the total signal accumulated by adding frames along a velocity hypothesis. Astrometric accuracy is the accuracy of the state or track returned by the track-before-detect method. Both algorithms incur loss in photometric and astrometric accuracy because of quantization of the shifting path. The time complexity of traditional track-before-detect and FaXT are computed analytically and runtime measured empirically. _x000D_
We quantify performance of both algorithms through three investigations. The first is a deterministic analysis of the algorithms, focusing on the differences between nearest pixel shift-and-add and FaXT’s shifting algorithms. The second investigation assesses the performance of both algorithms over various signal-to-noise ratios for non-integer displacements, exploring the effects of quantizing non-integer trajectories with integer start locations and integer displacements. The third investigation is a case study evaluating the performance of nearest pixel shift-and-add and FaXT for orbits representative of real world motion._x000D_
Simulated data was used to assess the performance of both algorithms. We have developed a user-configurable SDA image simulator capable of generating unresolved images of space objects with realistic sensor models and sky background conditions. The user defines a sensor, targets, the background conditions, and the observation times; these parameters are used to generate realistic images of real world observing scenarios. _x000D_
Through our investigations, we find that while FaXT’s shifting algorithm incurs more photometric and astrometric loss than nearest pixel shift-and-addenables, FaXT enables considerably faster runtimes. With the baseline performance of FaXT and the traditional track-before-detect, we explore a least squares optimization methods to improve the photometric and astrometric accuracy of FaXT without significantly increasing runtime via refining initial FaXT detections. This method is adapted from literature to use the pixel response function of the optical system and to include higher order motion terms. We find that the refined FaXT detections are comparable to refined nearest pixel shift-and-add detection despite the greater losses associated with the initial FaXT detections._x000D_
In conclusion, we evaluate the performance of two track-before-detect methods, specifically their photometric and astrometric accuracy and time complexity. We investigate the refinement of initial TBD detections. We find that with refinement, we can meet the accuracy of traditional track-before-detect without significantly increasing the runtime of a FaXT detection pipeline. The speed of the FaXT algorithm enables large-scale blind searches for faint space objects. This work quantifies the performance difference between traditional TBD and FaXT and investigates the refinement of TBD detections, supporting SDA and astronomy. _x000D_
Date of Conference: September 15-18, 2026
Track: Space Domain Awareness