Analysis of TDOA/FDOA State Estimation Accuracy of Cislunar Objects for Space Situational Awareness

This paper demonstrates an innovative approach for cislunar Space Situational Awareness (SSA) by demonstrating state estimation using time difference of arrival (TDOA)/frequency difference of arrival (FDOA) from radio frequency (RF) signals transmitted by a cislunar traversing satellite. Traditional SSA methods such as electro-optical (EO) and radar have challenges that include illumination, light saturation, and signal power loss over long distances. These can be avoided with an architecture that relies on passive RF TDOA and FDOA. For this paper, RF signals are modeled as having been collected at two or more receivers and stochastic estimation techniques are applied to determine the transmitter's state estimate and covariance. To simulate the performance of the TDOA/FDOA system, this paper uses additive Gaussian white noise on the RF TDOA/FDOA measurements. The circularly restricted three body problem dynamics (CR3BP) are utilized to model the movement of the space object as it traverses cislunar space. To assess performance of this method, this paper models three two-node space-based receiver architectures and three three-node architectures and compares them to show potential advantages and disadvantages of each. All modeled receivers are in earth centered Keplerian orbits. Each receiver has knowledge of all receivers' locations and compares its collected signals with the other receivers to create the TDOA/FDOA measurements. Iterative batch least-squares estimation techniques were used for each scenario to estimate the transmitter's position and velocity as it moves in a periodic CR3BP orbit about one of the earth-moon Lagrange points. Finally, this paper analyzes how the stability of the transmitter's orbit impacts the accuracy of TDOA/FDOA state estimation.