Cameron Harris, EO Solutions; Marco Kobayashi, EO Solutions; Jeff Houchard, EO Solutions; Daron Nishimoto, EO Solutions; Jonathan Kadan, Odyssey Systems Consulting
Keywords: OTOA, Correlation, UCT, Data Association
Abstract:
In space object surveillance and identification, observation-to-orbit association (OTOA) is the process of identifying a space object by comparing its observed states with a catalog of known targets. It is possible that the observations are not consistent with the known state of any cataloged object – in this case, the object is labeled as an Uncorrelated Track, or UCT. The presence of UCTs burdens space surveillance systems to undertake additional effort to determine the object’s identity and intentions. To mitigate unnecessary UCT triage, it is important to have a robust OTOA procedure that minimizes false alarms and efficiently exploits available data. We submit this can be achieved with modern astrodynamics and estimation theory, by leveraging known covariances associated with cataloged target states.
There is literary precedent for covariance-based OTOA, as there are multiple publications on covariance-based data association for space object tracking. Current methods of OTOA for space object tracking generate hypothesis orbit states and covariances from observations. The statistical difference, known as the Mahalanobis distance, is measured between cataloged objects and the hypothesis orbit. Conveniently, the square of the Mahalanobis distance is Chi-square distributed, so the OTOA procedure elegantly becomes a sequence of Chi-square tests for each cataloged object. If the test is satisfied, then the observed space object correlates to the corresponding target in the catalog. To fit an orbit to a set of observations, some method of state estimation must be performed. The process of calculating a space object’s state from a set of measurements is known as Initial Orbit Determination (IOD).
There are notable considerations when performing IOD. First, sufficient measurements must be collected — for angles-only optical measurements, a minimum of three measurements are required for traditional IOD methods, such as Laplace, Gauss, and Gooding. Moreover, IOD of short-arcs may be inaccurate and unreliable. For this reason, current OTOA methods generate multiple hypothesis orbits from singular tracklets, which provides a greater likelihood of yielding a positive association with the true observed target.
We propose a covariance-based multi-frame OTOA method that circumvents IOD, in an effort to reduce possible failure modes. Instead of performing correlation on the orbital states, our method applies the Unscented Transform to the cataloged target covariances at each measurement epoch, transforming the target covariances to the measurement domain. Subsequently, the Mahalanobis distance can be calculated directly between the predicted position of the cataloged target and observed space object pointing angles. Any number of succeeding associated observations may be concatenated, so that a single Mahalanobis distance metric captures the statistical similarity between an observed tracklet and a cataloged target.
There are several advantages to measurement domain OTOA. First, no minimum number of observations is required for the OTOA procedure. Even a single observation may be correlated in measurement domain OTOA framework. If the observation does correlate with an object in the catalog, then the system may proceed with differential correction on the cataloged orbital state, without ever needing to perform IOD. Second, there is no concern for the orbit state inaccuracies from IOD since the OTOA is performed directly on the observed pointing angles. Empirically the measurement domain OTOA is more robust, as it is not dependent on the restrictive and often nonobvious limitations of IOD. In the event that a set of observations does not correlate with a cataloged target track, IOD will be necessary for track initiation, but this is independent of the proposed OTOA procedure.
Preliminary testing shows great promise for the proposed algorithm. The algorithm correctly correlates real angles-only observations with measurement noise and correctly correlates simulated scenes with as many as nine different space objects simultaneously present under realistic noise conditions. Regarding performance, the Python implementation of the algorithm correlates the entire NORAD catalog, consisting of nearly thirty thousand objects, in less than twenty seconds using a single processor. However, it should be acknowledged that performance may be influenced by the available compute resources and satellite propagator settings.
The measurement domain OTOA algorithm will be presented along with some sample applications to practical simulated scenes. Results will explore the impact of measurement domain OTOA on space object surveillance and orbital state estimation. Data association and state estimation results will be analyzed from the perspectives of both situational understanding and computational efficiency.
Date of Conference: September 17-20, 2024
Track: Astrodynamics