Kullen Waggoner, Air Force Institute of Technology; David Curtis, Air Force Institute of Technology
Keywords: SSA, cislunar, Passive RF, TDOA, FDOA, Kalman Filtering
Abstract:
This paper explores and compares the use of different networks of receivers including terrestrial and space-based to conduct precision orbit determination for cislunar space situational awareness (SSA) using passive RF time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements. This research analyzes the use of existing Space Force Space Surveillance Network (SSN) ground locations as a basis for a terrestrial passive RF network and explores augmenting the terrestrial network with space-based receivers. Fundamental to SSA is the combination of some type of measurements to estimate the objects position and velocity states as well as its uncertainty covariance. This estimate enables the prediction of the future position of the object for general awareness and collision avoidance. Over the last fifty years since the dawn of the space age, the US Air Force and then the US Space Force developed a widespread network of electro-optical telescopes and radar sites to provide worldwide SSA. This information is provided in the form of two-line elements (TLE) of objects as small as a softball at LEO within orbits at altitudes of GEO and below. Within the last 10 years, planned and executed missions to regimes of space beyond the GEO belt to the moon and beyond have increased substantially. Alongside the increase in missions, a need for SSA within the cislunar regime is also rising. The moon is over ten times farther from the earth than a satellite in GEO. Expanding SSA beyond GEO into the cislunar regime presents several challenges as the volume of space and distances in this region are much greater. Electro-optical and radar measurements are somewhat limited in their effectiveness due to these large distances as well as significant solar/lunar exclusion zones. These circumstances provide an opportunity to rethink and explore less used methods of SSA such as passive RF to measure satellite locations. Potential advantages of using a TDOA and FDOA architecture is that unlike electro-optical systems, illumination and light saturation is not a factor while signal losses are much less than radar systems over long distances. This paper simulates the reception of modulated signals; transmitted from a cislunar traveling satellite and received at multiple receivers to acquire the characteristic TDOA/FDOA measurements. To simulate the performance of the TDOA/FDOA system for stochastic estimation, this research effort uses additive white gaussian noise on top of the RF TDOA/FDOA measurements. The paper uses the circularly restricted three body problem dynamics (CR3BP) to model the movement of the space objects in the cislunar and near-earth regimes. It compares stochastic batch and sequential estimation techniques including least squares estimates, Extended Kalman Filters (EKF), and Unscented Kalman Filter (UKF) in the precision state estimate/orbit determination and uncertainty calculation. Geometric dilution of precision (GDOP) for the combined TDOA/FDOA measurement and line-of-site availability are calculated for various geometries and compared to the modeled scenarios predicted accuracy showing their usefulness as a metric in evaluating potential passive RF architectures. For the scenarios simulated in this paper, cislunar objects are modelled as active satellites that will transmit intermittently in the direction of earth. The trajectories of the cislunar objects include a number of closed periodic orbits within the synodic frame around the various Lagrange points including both planar and out of plane motion. Finally, predicted estimates and covariances are modeled using the chaotic CR3BP dynamics to show predictive accuracy of different architectures for closed orbits in and around cislunar Lagrange Points. For modeling purposes, each receiver has knowledge of their own location and compares its received signals of the other nodes in the scenario.
Date of Conference: September 19-22, 2023
Track: Space-Based Assets