Michael R. Thompson, Advanced Space, LLC; Matthew D. Popplewell, Advanced Space, LLC; Bradley Cheetham, Advanced Space, LLC
Keywords: cislunar, SSA, SDA, TDOA, FDOA
Abstract:
For cooperative spacecraft that transmit RF signals to the ground, using time or frequency difference of arrival (TDoA and FDoA respectively) at two or more receivers has been a common method for ground-based orbit determination for several decades. For a strong enough downlink signal, this method can work with little to no modification of spacecraft hardware. Receiving ground stations have access to very stable timing sources and can yield large baselines with stations separated by thousands of kilometers. The combination of very precise timing and large baselines can yield very precise measurements as low as single digit nanoradians for The Deep Space Networks delta-differential one-way ranging (delta-DOR) measurement type, which uses measurements of both the spacecraft and quasars to calibrate for instantaneous atmospheric conditions and provide plane-of-sky information. TDoA and FDoA can also be used with non-cooperative spacecraft, again assuming that the downlink signal is strong enough.
The reverse problem the geolocation of ground-based RF sources based on TDoA and FDoA measurements taken by multiple satellites with known orbits has also been publicly documented since the late 1980s. Another difficult problem, and one that has received significantly less attention in the literature, is the orbit determination of an RF source based on TDoA and FDoA as observed from other space platforms. This formulation can be useful for applications where the use of ground stations may not give the necessary geometric diversity for high-quality orbit determination solutions or for SDA applications where ground-based systems are stressed.
One such application where ground-based systems are stressed is SDA above the GEO belt. In recent years there has been an increased interest in the feasibility of utilizing existing systems or developing new systems to monitor resident space objects (RSOs) above the GEO belt. For this orbital regime, using space-based TDoA and FDoA observables could be useful in supplementing ground-based systems for RSOs that are emitting in RF. In general, such passive RF systems would not suffer the same exclusion constraints that plague optical systems and would have nowhere near the power requirements of active radar systems.
This study seeks to quantify whether there are observability benefits from the placement of passive RF systems on-orbit compared to other ground-based and space-based architectures. Additionally, such measurements are simulated and processed in a high-fidelity orbit determination setup for multiple simulation cases. Where possible, these studies are performed parametrically across key parameters. For example, clock stability is an important component of the accuracy of TDoA and FDoA measurements and can be a particular challenge for space-based platforms. Given this, understanding the solution accuracy across a wide range of clock stability values (or other key parameters) can provide a first order look at some of the key requirements of a system were it to be deployed in the future.
This analysis demonstrates simulated orbit determination of RSOs near the Moon given TDoA and FDoA measurements with sets of observers in MEO, GEO, and above the GEO belt. To provide points of comparison, similar ground-based observations are also simulated.
The authors hope that these analyses are useful in expanding the possible tradespace of future XDA architectures. From an optical standpoint, numerous previous studies have shown the benefits of space-based observers for avoiding exclusions suffered by ground-based systems and providing additional viewing geometries. In this study, space-based strategies are examined for passive RF systems, and their benefit is demonstrated either as a standalone system, or as part of a hybrid architecture.
Date of Conference: September 27-20, 2022
Track: Cislunar SSA