Leveraging Sensors Fusion to Enhance One-way Lunar Navigation Signals
Authors:   Politecnico di Milano, Milan, Italy, Ceresoli Michele , Zanotti Giovanni , Lavagna Michèle 
Published: January 2024

In recent years, the Moon has been identified as a key testing ground to develop and enhance technologies for future deep-space missions, resulting in an ever-growing number of planned Moon-targeted launches from both space agencies and commercial actors. Despite having different objectives, all these users share the need to maintain accurate and reliable state estimates. In this regard, The European Space Agency (ESA) has launched the Moonlight initiative to foster the development of a dedicated Lunar Communication and Navigation System (LCNS) exploiting a small satellite constellation in lunar orbits. LCNS will deliver cost-efficient and high-performance navigation and communication services to future lunar exploration missions, enabling users simplifying their design and lowering the size, mass and power demands of the navigation payload. Additionally, the deployment of a third-party constellation may facilitate the on-board implementation of autonomous lunar navigation systems, enabling rovers, landers and spacecraft to explore the lunar environment with no need for constant human control.

At the beginning of the constellation setup, a key challenge will be the limited availability of navigation signals, due to the significantly smaller number of LCNS servicing satellites with respect to well-established Earth Global Navigation Satellite Systems (GNSS). In particular, the initial architecture will focus on maximizing the navigation performance of surface and Low Lunar Orbital (LLO) users at latitudes around the South Pole region, which is the subject of great scientific interest. Nevertheless, even for South Pole users, the LCNS constellation will still be too small to provide a continuous view of at least 4 satellites at any location, requiring the development of tailored navigation algorithms to cope with the mission requirements.

To overcome these limitations, the paper investigates strategies to mitigate the impact of these reduced-servicers-visibility windows on the estimation process by exploiting sensor fusion techniques to integrate the one-way ranging LCNS signals with a suite of well-known sensors, which might include Inertial Measurement Units (IMUs), optical cameras, altimeters and Two-Way Ranging (TWR) with the Lunar Gateway (LOP-G). The observability gain provided by each sensor is analyzed as a function of the relative servicer-user dynamics, the required pointing strategy and the measurements availability. Different inclinations of LLO are analyzed to investigate the most favorable LCNS receiver antenna pointing direction that maximizes the overall number of visible satellites throughout the simulation window. Additionally, sensors mounting location on-board the spacecraft is discussed in relationship to the LLO inclination and satellite attitude, to identify possible operational constraints that may influence the observables availability and to identify the best suited sensors clustering for a given mission profile and operational needs.

The simulation architecture consists of a high-fidelity non-Keplerian dynamics propagator, which accounts for irregular lunar gravity field and Solar Radiation Pressure (SRP) perturbations; a sensor suite to have a truthful noisy representation of the available spacecraft measurements; a dedicated sequential navigation filter. Each proposed navigation scheme underwent a Montecarlo testing campaign to comprehensively fix and tune the algorithm gains and parameters. The sensitivity of the navigation solution on the measurement noise has been assessed for each type of observable, allowing for a direct link between commercial sensor properties and the resulting navigation errors and uncertainties.

A tightly coupled approach is exploited to directly fuse the LCNS one-way ranging measurements with other sensors data, making the observables availability hold irrespective of the actual number of visible LCNS satellites. The filter is constructed to estimate both the spacecraft state and the receiver clock bias and drift, allowing to properly account for the de-synchronization of the generally low-cost user clocks with respect to the high precision atomic clocks on-board of the LCNS constellation. The outcomes show that with the sole LCNS signals and a proper pointing strategy exploitation, the navigation error swings between 10 meters, with 4 visible satellites, and 1 km when the user is above the lunar North Pole and the LCNS servicers are obstructed by the Moon. Each of the analyzed sensors further improves these statistics: for low altitude LLO users, an altimeter provides continuous discrete altitude measurements that can improve the overall error up to 60%, especially if long LCNS-unavailability windows are present. On the other hand, although TWR with LOP-G effectively offers an additional high precision observable, its availability is often synchronized with that of the LCNS satellites: being on a Southern Near Rectilinear Halo Orbit (S-NRHO), the Gateway can only provide measurements for users located above the Lunar North Pole only for a day per week.

Additionally, the performance of a variety of Runge-Kutta (RK) explicit integration schemes and dynamic approximations is tested for both Extended Kalman Filters (EKF) and Unscented Kalman Filters (UKF). A trade-off between solution accuracy and computation burden (i.e., number of required dynamic function evaluations) is performed to accommodate the needs of different spacecraft classes and available hardware. The results highlight that for filters running at 1 Hz a two-stage Heun integration method halves the CPU time required for the computations while bounding the propagation error difference with respect to Verner’s “Most Efficient” 8(7) scheme to less than 5 meters. On the other hand, at lower filter frequencies (e.g., 1/60 Hz), the same difference grows up to hundreds of meters, thus requiring a more accurate integration to properly navigate.

The paper exhaustively presents that with the proper navigation sensors, autonomous lunar navigation exploiting a dedicated Moon-centered GNSS-like infrastructure can provide accurate and reliable state estimates, paving the way to a new generation of lunar exploration missions with enhanced autonomy and reliability.

The present study has been carried out in collaboration with Telespazio.