Using Co-Located Range and Doppler Radars for Initial Orbit Determination

TL;DR

The paper tackles the challenge of initial orbit determination for uncatalogued LEO debris using two short, co-located radar tracklets from the LeoLabs network. It introduces a differential-algebra (DA) framework with automatic domain splitting (ADS) to represent and propagate the resulting orbit set uncertainty, combined with three tailored IOD algorithms that exploit varying angular data availability. Through real-data test cases, the work demonstrates tracklet association, IOD solutions, and forward prediction capabilities, showing that angular measurements on both tracklets substantially reduce uncertainty. The approach offers a practical path toward improved data association and cataloging of small space objects, while also underscoring the importance of angular data quality and propagation fidelity for robust results.

Abstract

With debris larger than 1 cm in size estimated to be over one million, precise cataloging efforts are essential to ensure space operations' safety. Compounding this challenge is the oversubscribed problem, where the sheer volume of space objects surpasses ground-based observatories' observational capacity. This results in sparse, brief observations and extended intervals before image acquisition. LeoLabs' network of phased-array radars addresses this need by reliably tracking 10 cm objects and larger in low Earth orbit with 10 independent radars across six sites. While LeoLabs tracklets are extremely short, they hold much more information than typical radar observations. Furthermore, two tracklets are generally available, separated by a couple of minutes. Thus, this paper develops a tailored approach to initialize state and uncertainty from a single or pair of tracklets. Through differential algebra, the initial orbit determination provides the state space compatible with the available measurements, namely an orbit set. This practice, widely used in previous research, allows for efficient data association of different tracklets, thus enabling the addition of accurate tracks to the catalog following their independent initialization. The algorithm's efficacy is tested using real measurements, evaluating the IOD solution's accuracy and ability to predict the next passage from a single or a pair of tracklets.

Figures (8)

• Figure 1: Illustration of the two tracklets.
• Figure 2: Raw data and polynomial regression on Object 1, tracklet 2.
• Figure 3: Association analysis on tracklet 2 for the two cases.
• Figure 4: Domain and residual for Object 1, Algorithm 1.
• Figure 5: Projection of points of minimum residual at the next passage, Algorithm 1.