Benjamin Feuge-Miller, Applied Research Laboratories, The University of Texas at Austin; Andrew Joplin, Applied Research Laboratories, The University of Texas at Austin; Johnathan York, Applied Research Laboratories, The University of Texas at Austin
Keywords: initial orbit determination, passive radio frequency, ambiguous pseudo-range, time difference of arrival, frequency difference of arrival, daylight techniques, space domain awareness
Abstract:
Improved methods for independently detecting and monitoring spacecraft are becoming vital for Space Domain Awareness given the rapidly increasing number of active satellites in Earth orbit. Beyond simply identifying new satellites or reacquiring tracks after loss of custody, independent monitoring can mitigate cross-tagging risks and improve confidences in conjunction assessments for collision avoidance. Passive radio frequency (RF) can provide a powerful source of information for this task, as unique signals can be detected from any active and transmitting satellite by identifying periodic signatures, even if such signals are non-cooperative or their structure is not known a priori [1]. Compared to electro-optical measurements, RF signal data can be collected regardless of the illumination geometry and satellite material makeup. Furthermore, passive RF signals can be observed beyond the range of typical active radar sensors. However, many of the algorithms designed to detect and characterize unique signals from the broad RF spectrum suffer from significant ambiguities in resulting pseudo-range measurements due to the periodic nature of the signals, complicating the task of independently establishing an initial orbit estimate. Without such an estimate, external reference data would be required to run traditional precision tracking algorithms (e.g., Kalman filters) and the resulting information would no longer be independently derived. In this paper, we propose an initial orbit determination algorithm designed to exploit ambiguous RF data from arbitrary and possibly non-cooperative signals, even in the presence of transmitter biases and a complete lack of a priori information about the transmitter orbit.
The proposed algorithm begins by defining a low-dimensional coarse grid of Keplerian state vectors which is refined to a full-dimensional, higher-resolution set subject to visibility constraints using only information about the receiver positions. Proceeding in this manner improves computation tractability for reasonable runtime performance. Hypothesized reference trajectories from the higher-resolution set are then selected by evaluating pre-fit residuals with respect to the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) data from simultaneous pseudo-range and Doppler measurements of the RF signal, as such differencing mitigates transmitter clock biases. Optimization is then performed without linearization, at first using only FDOA data to improve the state estimate and then introducing the ambiguous TDOA data, a two-stage approach designed to locate the global minimum from among many local minima in a tractable manner. In avoiding linearization, the propagation model can be easily expanded to include various perturbations. To improve convergence on a wide range of orbits – spanning varied eccentricities, inclinations, and altitudes – non-linear optimization is performed by transforming the Keplerian state vector to Poincare orbital elements. The resulting initial orbit estimate is independent of prior information and merely assumes that the observed object is in Earth orbit.
We demonstrate the flexibility of this approach by simulating measurements from various IGS observation sites for a diverse set of example orbits, as may be done in a professional observation network. To validate our results, we also consider real measurement data sets from these sites, focusing on Medium Earth Orbit data as a practical illustrative example. The results from this study support the use of the presented initial orbit determination algorithm in leveraging passive radio frequency signals for the independent detection, tracking, and characterization of active spacecraft, addressing significant challenges in the use of such measurement data.
[1] S. Kozhaya, H. Kanj, and Z. M. Kassas, “Multi-constellation blind beacon estimation, Doppler tracking, and opportunistic positioning with OneWeb, Starlink, Iridium NEXT, and Orbcomm LEO satellites,” in Proceedings of IEEE/ION Position, Location and Navigation Symposium, 2023, pp. 1184–1195. doi:10.1109/PLANS53410.2023.10139969
Date of Conference: September 17-20, 2024
Track: Astrodynamics