Optimizing Tracking Windows Timing for Improved Cislunar Inter-Satellite Autonomous Navigation

Abstract

With the projected expansion of the small satellite market and the rise of the lunar economy, the development of cost efficient and reliable navigation in cislunar space—defined as the region of space between Earth and Moon including the region around the surface of the Moon—has become increasingly important. However, the increase in the number of satellites strain existing communication networks in terms of availability, which exerts pressure on orbit determination quality and the financial budgets. One way to release the pressure from the existing ground station communications is through the concept of Autonomous Orbit Determination (AOD) by using inter-satellite radio two-way range between at least two satellites. The three-body problem of cislunar space-the most common region for small satellite deep space missions-makes it an ideal environment to perform AOD due to strong third body perturbations. Previous literature also has not clearly linked AOD with mission and spacecraft design related parameters, and is primarily focused on the orbit estimation aspect rather than including navigation as well.

The analysis of this work is based on a case study in which an L2 Lagrange point orbiter (LPO), called LUMIO, and an elliptical lunar orbiter (ELO), called LPF (based on the SSTL Lunar Pathfinder), perform AOD based on two-way inter-satellite ranging with a Gaussian noise level of 2.98m1σ, observed at a 300 s interval. This thesis aims to research the strategic adjustment of the timing of inter-satellite tracking sessions while optimizing for 1 year of station keeping cost for LUMIO, defined in ∆V.  Since the accuracy of the maneuvers relies on the magnitude of estimation errors from the OD process, which in turn depends on the state observability and thus relative satellite geometry during a tracking arc, solving for lowest ∆V is a complex optimization problem. Three different timing strategy categories were set up in which tracking is performed with varying levels of complexity: tracking based on constant tracking duration and interval, tracking around the perilune or apolune of the LPF satellite, and tracking based on the solution of a heuristic optimization routine that adjusts each tracking arc individually.

The overarching conclusion of this work is that improvements can be made compared to this value in each of the three strategy categories but with varying levels of ∆V. Initial observation windows were defined as a set of tracking arcs of1.0 day with a 3.0-day interval between each arc, where the predicted annual cost equated to 0.613±0.0066 1σ m/s, serving as the baseline value. The best of the constant tracking category showed an an annual ∆V of 0.375±0.0020 m/s, but this comes at the cost of large relative tracking time with a length-interval combination of 0.5-0.5 days. The best of orbit-based solutions reduce cost to an annual mean of 0.5 m/s and have relatively short tracking arcs, which makes it possible to spend more time on collecting scientific data. The Particle Swarm Optimization (PSO) algorithm shows that a reduction to 0.280±0.0134 1σ m/s can be made. All in all, from a mission design perspective, it means that it pays to adapt to a more complex tracking scheme, but employing a constant-type tracking arc timing scheme can also already yield ∆V improvements.  Advances in reducing power and fuel budgets can extend mission duration by lowering fuel consumption. Optimized tracking reduces total tracking time, requiring less power for signal transmission and freeing more power for payloads or other subsystems. This allows more time for scientific observations, increasing the mission's output.