Thomas Dearing, CACI; Isaiah Owsley, CACI; Piyush Mehta, West Virginia University
https://doi.org/10.64861/IRTH9093
Keywords: Constrained Admissible Region, Multi-hypothesis Filtering, Radar
Abstract:
As congestion in popular orbital regimes has rapidly accelerated over the last decade, the timely detection, tracking, and prediction of space objects and debris has evolved from a compelling research topic into an urgent issue for space operational safety. One promising approach for addressing the unique complexity of this tracking problem is Multi-Hypothesis Filtering (MHF): a probabilistically coupled association and filtering scheme allowing new observation data to be softly associated with multiple objects during periods of high congestion or uncertainty. As new data is ingested by the filter, the probabilities of each soft association are estimated, ranked, and pruned until a sufficiently strong solution is identified. Historically, The MHF approach has proven particularly effective in cases of sparse or highly congested data: conditions found with increasing regularity in LEO.
However, the MHF formulation presents a unique and interesting challenge, and indeed, opportunity, when performing Initial Orbit Determination (IOD) on new unassociated observations. Specifically, complete 6 Degree of Freedom (DOF) state estimates are required to compare hypotheses against future observations. However, traditional optical and radar sensors both present unobservable degrees of freedom in measurements taken over short arcs: optical sensors lack ranging information while radars lack precise beam-steering information. In the case of optical sensors, MHF’s have historically addressed this uncertainty using a set of hypotheses to sample the uncertainty over the unobservable range/range-rate space. To restrict this unobservable range space to a bounded, finite region, a Constrained Admissible Region (CAR) is defined using bounds on feasible orbit eccentricity and semi-major axis. Mirroring the probabilistic association strategy, the produced IOD hypotheses are then scored against future observation data and gradually refined to those which continue to reliably associate with new observations. Notably, the SMA constraint of this approach has been adapted to radar observations. However, without the eccentricity constraint, the resulting CAR creates large and computationally costly hypothesis sets which render the technique unpalatable for many applications. In effect, this shortcoming limits practical MHF IOD’s to specialized radar array configurations which can directly measure or estimate both angular and angular-rate information (e.g. interferometric arrays using differential compression).
In furtherance of IARPA’s SINTRA debris detection and tracking program, this work adapts the Constrained Admissible Region (CAR) technique originally developed for angles-only optical measurements. In particular, the prevalent constraint bounds for orbital Semi-Major Axis (SMA) and eccentricity are both derived referencing the original radar measurement frame. Crucially, this approach enables the generation of highly targeted and compact IOD hypothesis sets from single radar observations, greatly expanding the family of radars which can be used to initialize MHF orbit estimates. As such, this approach particularly benefits large-scale tracking efforts where such radars are prevalent, such as debris detection in LEO. To evaluate the accuracy and numerical cost of this approach, several representative CAR examples are examined across the LEO, MEO, and GEO orbital regimes and compared with the true orbit state. This comparison yields the following key conclusions: (1) unlike in the optical case, the radar SMA CAR may be obtained analytically, (2) for cases with nominal angular error, the developed CARs for both SMA and eccentricity constraints effectively and efficiently constrain the true orbital state, and (3), the union of several CARs with different generating beam angles can (at the cost of higher computational overhead) be used to overcome large intrinsic angular error. These results form a compelling argument for the application of the radar CAR in LEO debris tracking applications.
Date of Conference: September 15-18, 2026
Track: Astrodynamics