Towards Alternative Position, Navigation and Timing Technologies supporting Autonomous Operations for Advanced Air Mobility
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Considerations for Optimal Sensor Placement for Higher Accuracy Object Localization for Urban Air Mobility
Previous research into object localization has shown that sensor placement and alignment plays an important role in achieving higher accuracy levels of the estimated location of a tracked Urban Air Mobility Vehicle. In general, a near-orthogonal intersection between the ground node observation vectors results in the highest accuracy due to a smaller overlapping uncertainty region between both. This applies to triangulation by means of ground node camera angle observations as well as trilateration by means of ground node distance measurements. However, this simple concept is not easily fulfilled with a network of a limited number of static ground nodes and a moving object to be localized. This case study performs sensitivity analyses and explores practical ways on how to achieve higher estimate accuracy levels in this context.
sensor placement↗
Considerations for Optimal Sensor Placement for Higher Accuracy Object Localization for Urban Air Mobility
Previous research into object localization has shown that sensor placement and alignment plays an important role in achieving higher accuracy levels of the estimated location of a tracked Urban Air Mobility Vehicle. In general, a near-orthogonal intersection between the ground node observation vectors results in the highest accuracy due to a smaller overlapping uncertainty region between both. This applies to triangulation by means of ground node camera angle observations as well as trilateration by means of ground node distance measurements. However, this simple concept is not easily fulfilled with a network of a limited number of static ground nodes and a moving object to be localized. This case study performs sensitivity analyses and explores practical ways on how to achieve higher estimate accuracy levels in this context.
sensor placement↗
Control of free-flying space robot manipulator systems
Control techniques for self-contained, autonomous free-flying space robots are being tested and developed. Free-flying space robots are envisioned as a key element of any successful long term presence in space. These robots must be capable of performing the assembly, maintenance, and inspection, and repair tasks that currently require astronaut extra-vehicular activity (EVA). Use of robots will provide economic savings as well as improved astronaut safety by reducing and in many cases, eliminating the need for human EVA. The focus of the work is to develop and carry out a set of research projects using laboratory models of satellite robots. These devices use air-cushion-vehicle (ACV) technology to simulate in two dimensions the drag-free, zero-g conditions of space. Current work is divided into six major projects or research areas. Fixed-base cooperative manipulation work represents our initial entry into multiple arm cooperation and high-level control with a sophisticated user interface. The floating-base cooperative manipulation project strives to transfer some of the technologies developed in the fixed-base work onto a floating base. The global control and navigation experiment seeks to demonstrate simultaneous control of the robot manipulators and the robot base position so that tasks can be accomplished while the base is undergoing a controlled motion. The multiple-vehicle cooperation project's goal is to demonstrate multiple free-floating robots working in teams to carry out tasks too difficult or complex for a single robot to perform. The Location Enhancement Arm Push-off (LEAP) activity's goal is to provide a viable alternative to expendable gas thrusters for vehicle propulsion wherein the robot uses its manipulators to throw itself from place to place. Because the successful execution of the LEAP technique requires an accurate model of the robot and payload mass properties, it was deemed an attractive testbed for adaptive control technology.
Cannon, Robert H., Jr.↗
Incremental States for Precise On-Orbit Relative Knowledge in Formation Flight
High precision and close proximity formation flight is an enabling technology for future space missions and requires an on-board relative navigation capability that is accurate to the mm-level and robust to formation parameters. Common estimation techniques linearize the entire formation about one spacecraft’s position, resulting in degraded accuracy due to linearization errors when separation distances become large. Additionally, methods which decouple absolute and relative state estimates usually require ad-hoc methods to incorporate the estimates together. This work discusses an alternative ”incremental” formulation of the relative navigation problem which is in variant to formation size, robust to coupling between absolute and relative dynamics, and can undergo similarity transformations to smoothly incorporate either absolute or relative information without numerical issues. A specific example of this architecture is presented in the context of formation navigation using Carrier-Differential Global Positioning System measurements, and is compared to a traditional leader-linearized filter. In the presence of accurate measurements, the incremental architecture is shown to reduce linearization errors and mean estimate errors by up to three orders of magnitude without the incorporation of new sensor information.
Seubert, Carl↗
Lunar Node 1 and Beyond
Lunar Node 1 (LN-1) is an S-band Navigation beacon for lunar applications that was recently designed and built at MSFC. As part of NASA's Commercial Lunar Payload Services initiative, this beacon will be delivered to the moon's surface on Intuitive Machine's NOVA-C lunar lander in November 2021. During this mission, LN-1’s goal will be to demonstrate navigation technologies that can support local surface and orbital operations around the moon, enabling autonomy which would decrease dependency on heavily utilized Earth based assets like the Deep Space Network. To do this, LN-1’s design leverages Cubesat components as well as the Multi-spacecraft Autonomous Positioning System (MAPS) algorithms, which enable the autonomous spacecraft positioning through communication-integrated navigation measurements. In addition to demonstrating the MAPS payload, the radio will also be used in standard tone-based non-coherent ranging and Doppler tracking to provide an alternate approaches and comparisons for navigation performance. LN-1 will represent a single node in a potential greater MAPS network of assets. While LN-1 awaits launch to demonstrate this initial use of one-way navigation, designs are already under way for proposed subsequent missions like LN-2 to enable expanded capability. The next steps in these missions seek to include a receive capability to allow two-way ranging support with other operational spacecraft in the lunar vicinity, and to provide some component upgrades related to the radio, power, and thermal systems that will improve the longevity of the payload in the harsh lunar environment. The LN-1 design details, status, and potential forward work with mission like LN-2 will be outlined in this presentation.
Evan John Anzalone↗
Navigation Doppler Lidar
A Doppler lidar has been developed by NASA as an alternative to radars for providing velocity and altitude data to landing vehicles. Future robotic and manned missions to planetary bodies demand precise ground-relative velocity vector and altitude data to execute complex descent maneuvers for safe, soft and pinpoint landing at a pre-designated site. This lidar sensor, referred to as Navigation Doppler Lidar (NDL), provides velocity and altitude data from over five kilometers altitude to within a few cm/sec and tens of centimeters precision, respectively. NDL technology will be demonstrated on two lunar landing missions this year that will serve as precursors for large robotic and manned landing missions to the Moon, Mars, and other solar system destinations. NDL can also benefit terrestrial aerial vehicles that cannot rely on the GPS for position and velocity data or require precision data relative to local ground.
Doppler Lidar↗
An Integrated Vision-Based System for Spacecraft Attitude and Topology Determination for Formation Flight Missions
With the space industry's increasing focus upon multi-spacecraft formation flight missions, the ability to precisely determine system topology and the orientation of member spacecraft relative to both inertial space and each other is becoming a critical design requirement. Topology determination in satellite systems has traditionally made use of GPS or ground uplink position data for low Earth orbits, or, alternatively, inter-satellite ranging between all formation pairs. While these techniques work, they are not ideal for extension to interplanetary missions or to large fleets of decentralized, mixed-function spacecraft. The Vision-Based Attitude and Formation Determination System (VBAFDS) represents a novel solution to both the navigation and topology determination problems with an integrated approach that combines a miniature star tracker with a suite of robust processing algorithms. By combining a single range measurement with vision data to resolve complete system topology, the VBAFDS design represents a simple, resource-efficient solution that is not constrained to certain Earth orbits or formation geometries. In this paper, analysis and design of the VBAFDS integrated guidance, navigation and control (GN&C) technology will be discussed, including hardware requirements, algorithm development, and simulation results in the context of potential mission applications.
Rogers, Aaron↗
Simulated Vision-based Approach and Landing System for Advanced Air Mobility
Advanced Air Mobility (AAM) aircraft require precision approach and landing systems (PALS) in several environments, such as urban, suburban, and rural. It is challenging to implement current state-of-the-art methods approved for automated approach and landing for AAM operations with challenges such as GPS degradation in urban environments and visual navigation aids like the glideslope and localizer being narrow and not allowing alternative incoming landing angles at vertiports. However, existing technology and systems, i.e., the instrument landing system (ILS) with glideslope and localizer indicators that use vision, IR, radar, or GPS methods, provide baseline perception and sensing requirements for AAM aircraft approach and landing. This paper focuses on vision-based PAL and computer vision feature correspondence methods to demonstrate a baseline navigation system while adhering to the Federal Aviation Administration requirements and regulations about heliport design (FAA AC 150/5390-2C), which is one of the closest references for vertiport requirements and regulations. The coplanar pose from orthography and scaling with iterations (COPOSIT) algorithm determines pose estimation, which feeds into an Extended Kalman filter that combines IMU with vision to create a vision-based approach and landing (VAL) sensor fusion navigation solution for GPS-denied environments. The VAL navigation solution provides promising simulation results for AAM PALS with Hough circle detection and feature correspondence, which demonstrate robustness to false positives. This paper incorporates moderately high- fidelity simulations with computer graphics rendering to show a distributed sensor network to track an AAM aircraft during approach and landing to compare with the aircraft’s onboard vision-based navigation solution.
distributed sensing↗
NASA Small Spacecraft Technology (SST) Program - Recent and Upcoming Technology Demonstrations and Development Efforts
The Small Spacecraft Technology (SST) program within NASA’s Space Technology Mission Directorate, expands the ability to execute unique missions through rapid development and demonstration of capabilities for small spacecraft applicable to exploration, science and the commercial space sector. Through targeted development and frequent in space testing, the program: • Enables execution of missions at much lower cost than previously possible • Substantially reduces the time required for development of spacecraft • Enables new mission architectures through the use of small spacecraft • Expands the reach of small spacecraft to new destinations and challenging new environments • Enables the augmentation of existing assets and future missions with supporting small spacecraft. The program achieves its objectives through: • Identification and investment in the development of new subsystem technologies to enhance or expand the capabilities of small spacecraft • Sponsorship of flight demonstrations of new technologies, capabilities and applications for small spacecraft • Promotion of the use of small spacecraft as platforms for testing and demonstrating technologies and capabilities that might have more general applications in larger-scale spacecraft and systems Technologies funded by the program that are key to advancing the utility and capability of small spacecraft were demonstrated in 2022 and 2023. Notable on-orbit demonstrations include the following. • The Cislunar Autonomous Positioning System Technology Operations and Navigation Experiment’s (CAPSTONE) navigation technology that was demonstrated for the first time in 2023 could provide autonomous onboard navigation information for future lunar missions, minimizing or eliminating human-in-the-loop mission operations. • The optical communications technology also demonstrated in 2023 by the TeraByte InfraRed Delivery (TBIRD) payload that launched on Pathfinder Technology Demonstrator-3, achieved 200 gigabit per second (Gbps) throughput on a space-to-ground optical link between a satellite in orbit and Earth, the highest data rate ever achieved by optical communications technology. • The precision laser pointing performance of NASA’s CubeSat Infrared CrossLink A (CLICK) spacecraft’s fine steering mirror control system was successfully demonstrated. This element of the laser communications system will be used to demonstrate two-way crosslink communication in low-Earth orbit by CLICK B/C anticipated to launch in late 2024. Investments in subsystem technology development through funding to university, industry, and other government partners in a number of areas will be discussed. Among others, topic areas include propulsion, autonomous swarm technology, edge computing, and thermal control. Additionally, the status of the CubeSat-alternative platform, DiskSat, strategies for accelerating the demonstration of technology payloads via the Realizing Rapid, Reduced-cost high-Risk Research (R5) project, and the status of recently completed and upcoming on-orbit demonstrations will also be presented.
Roger C Hunter↗
Localization of Ad-Hoc Lunar Constellations in Communication Failure Modes for Distributed Spacecraft Autonomy
As lunar missions increase in complexity inspired by NASA’s Artemis Program, they will require reliable and sufficient capability of the Position, Navigation, and Timing (PNT) system to support their scientific objectives. In addition, NASA's Commercial Lunar Payload Services (CLPS) program initiates the proliferation of public and private exploration partnerships using small satellites from commercial and private organizations, expanding traditionally confined low Earth orbit to be used for missions beyond geosynchronous orbit (Zucherman et al., 2022). Therefore, the Lunar PNT system is also required to provide navigation services compatible with the smaller platforms being sent by the public and private sectors, like CubeSats. However, traditional approaches to deep space missions’ navigation based on ground radio facilities have difficulties in providing sufficient support for the increasing number of users and communication at a distance from the Earth (Kaplev et al., 2022). In particular, the existing Lunar navigation technologies such as weak signal global positioning system (GPS) and deep space network (DSN) are not able to ensure operations of the upcoming small-scale Lunar missions due to their limitations in localization performance as well as capacity aspects. Another way to provide Lunar PNT service is to create a dedicated Lunar global navigation satellite system (GNSS) constellation, like GNSS systems on Earth. Space agencies like NASA, ESA, and JAXA are now developing the lunar communications relay and navigation systems (LCRNS) and Lunar navigation satellite systems (LNSS). In their systems, satellites will be deployed in moon orbits to provide the communication, positioning, navigation, and timing (CPNT) service at the lunar south pole region where the Artemis base camp will be expected (Murata et al., 2022). Meanwhile, common challenges considered in lunar PNT research arise from poor geometry of the terrestrial GNSS satellites when seen from the lunar user, highly perturbed lunar orbits, and limitations in power, size, and cost of the equipment on lunar satellites (Iiyama et al., 2023). It is also not clear if there will be enough Lunar users to support the cost and resources this would require as the Low-cost surface missions may not be able to support the large power, mass, and weight requirements that these navigation solutions entail (Niemoeller et al., 2022). As an alternative, existing Lunar science and exploration assets could be used to create a low-cost, autonomous, ad-hoc, and on-demand mission-centric Lunar PNT swarm capable of providing PNT services to these low-cost lunar missions (Hagenau et al., 2021). Introducing the non-dedicated and ad-hoc Lunar navigation constellation gives a way to provide PNT services on-demand. The non-dedicated swarm assets of Lunar constellations are designed to localize themselves with minimal interaction with Earth by adding cooperative autonomous localization to lunar missions, freeing up valuable bandwidth and ground segment resources. An autonomous localization of Lunar constellations is based on the concept of the decentralized PNT system with a distributed extended Kalman filter (DEKF) approach to state estimation for minimal onboard operating costs. In the distributed data processing algorithm, computation is broken down and assigned to each satellite, resulting in a considerably decreased computational amount while maintaining the accuracy of the orbit ephemeris and clock offsets as the result of centralized data processing (Wen et al., 2019). The DEKF requires spacecraft to perform two-way ranging operations with each other to communicate simultaneously, leveraging neighbor two-way intersatellite link (ISL) measurements such as pseudoranges to, and relative velocities between, visible satellites as sensor values (Frank et al., 2021). The Lunar autonomous PNT simulation (LAPS) demonstrated the feasibility of orbital asset localization among ad-hoc Lunar small-sat constellations based on the DEKF in Hagenau et al. (2021) and evaluated the matching algorithm proposed by Frank et al. (2021) in scheduling position estimation updates. In previous papers, all assets and measurements are assumed to be always available without consideration of the impact of intermittent and permanent communication failure. This study presents localization performance with increasing levels of network degradation for swarm assets and users to demonstrate the robustness of the decentralized Lunar PNT service in more realistic scenarios. Main issues arising from communication failure include spacecraft permanent or transient loss, antenna failures, message delays, etc. We tested four possible reasons for network degradation for 7 days in 21 satellites frozen with an altitude of 5500 km, evenly spaced around 3 circular, 40 inclination orbital planes where each spacecraft has two directional antennas. As anchor nodes with an independent estimate of their position are required in the DEKF approach, two ground nodes in each pole and one node in the gateway were implemented in the simulation. First, the most probable failure scenario involves the loss of a single spacecraft due to solar interference and technical malfunctions of the assets. Losing the availability of a single spacecraft means losing the two-way ISL measurement of the asset in the DEKF update. In order to provide the best possible quality of PNT service with limited time and resources, the distributed Lunar constellations must schedule the communication activities. The scheduler leverages mixed-integer linear programming (MILP) for the coordination and scheduling of the desired “as-needed” localization service (Niemoeller et al., 2022). We assume the scheduler has completely excluded the spacecraft information before the DEKF update in the failure scenario. When a random spacecraft has been turned off at a specific time, the robustness of the autonomous Lunar PNT system is evaluated. The simulation results give an 11.5% degradation in median position accuracy compared to the idealized performance excluding the asset loss. Second, a large number of assets may vanish due to major hardware problems or meteor strikes around the moon. A multiple spacecraft loss can degrade the localization performance very fast by losing the communication ability to do cross-plane measurements and in-plane measurements in a 3-plane constellation. When the matching-based scheduler is aware of ISL availability, we investigate a large number of in-plane and cross-plane asset vanishments both in close proximity and equally spaced throughout the orbital plane. According to the simulations, the loss of in-plane measurements gives 40.2% degradation while cross-plane measurements degrade 50.5% of asset localization performance among available assets. Therefore, it is concluded that cross-plane measurements are more important in improving the position estimation accuracy. Third, spacecraft failure information can be lost due to the internal message delay, resulting in the DEKF update scheduler to solve the matching problem with unavailable assets. The DEKF update cycle is comprised of network setup, communication, and computations where a global broadcast network and a 2-way ISL network setup take 6 minutes in total (Frank et al., 2021). Once the broadcast network successfully transmits and receives information, a random spacecraft may lose its availability right before solving the matching problem. This means the matching solution is no longer optimal, resulting in degradation in the localization performance. A numerical assessment shows the matching-based scheduler with knowing failure holds 11.5% of position accuracy degradation, whereas the scheduler without knowing failure gives 34% degraded localization performance without asset loss. Fourth, a transient loss of a single or multiple spacecraft may occur due to their antenna outages. After losing the two-way ISL availability for a few DEKF update cycles, the availability of spacecraft can easily be recovered as their states have been independently updated using measurements from anchor nodes. It is likely that the longer failure will result in worse localization performance. We have tested the transient failure of a random single asset for 30 min in the simulation, which is losing 3 update cycles in the DEKF system. From the simulation results, the position accuracy has been degraded to 4.84% which is better than the degraded localization performance of 11.5% from the permanent loss scenario among available assets. In conclusion, the autonomous Lunar PNT system based on the DEKF approach shows the ability to maintain resilience and robustness in the possible communication failure scenarios, ensuring that localization accuracy is preserved across various network degradation and outages. Future studies on investigating user localization performance near the South Pole and the broadcast network system will be continued in the following months.
Yeji Kim↗
Mineralogical, Elemental, and Tomographic Reconnaissance Investigation for CLPS (METRIC): A Payload Designed for Exploration of Terrestrial Planetary Bodies
Geological materials (indeed, all solid objects) are characterized by their crystal structure, elemental composition, and morphology. The Mineralogical, Elemental, and Tomographic Reconnaissance Investigation for CLPS (METRIC) instrument suite quantifies all three. These measurements address fundamental science questions (e.g., the origin and evolution of planetary bodies) and support the human exploration of space (e.g., the characterization of regolith for ISRU and the constraint of its geotechnical properties). METRIC comprises an X-ray Diffraction/X-ray Fluorescence instrument (XRD: mineral structure and XRF: elemental composition), an X-ray micro-Computed Tomography instrument (XCT: 3D internal micromorphology), and a hyperspectral imaging infrared spectrometer (IRS) to provide local/regional mineralogic context for these measurements. METRIC XRD/F draws heritage from the highly successful Mars Science Laboratory CheMin instrument. The METRIC XRD/F employs two separate sample cells, one optimized for XRD and one for XRF, resulting in more rapid XRD analysis (tens of minutes vs. tens of hours for CheMin) and an orders-of-magnitude improvement in XRF detection. XCT has not been deployed in space, so the METRIC XCT represents a new capability for solar system exploration. The XCT uses the same basic high-TRL components as METRIC XRD/F, decreasing its development cost for flight. The METRIC IRS is a derivative of the NASA Earth Science Technology Office funded Hyperspectral Thermal Imager instrument and utilizes the NASA Technology Transfer Program to incorporate a commercial-of-the-shelf infrared camera ruggedized for space by NASA Marshall Space Flight Center. The IRS spectral range (8–14 µm) and resolution (10.8 cm -1 ) are tailored to quantify mineralogy in rocks using their characteristic Reststrahlen bands and to characterize mineralogy of soils using the position of the Christensen Feature. The METRIC payload is currently designed for deployment to the Moon on a Commercial Lunar Payload Services (CLPS) mission, where the XRD/F and XCT would be located on a lander and the IRS would be on deployed on a companion rover to evaluate the mineralogical diversity of the landing site. A pneumatic drill designed by Honeybee Robotics would excavate regolith up to 50 cm below the lander and deliver multiple aliquots of regolith to the XRD/F and XCT. The METRIC payload could also be deployed on a rover. In this case, a sample handling system on a robotic arm could scoop regolith and/or drill rocks and deliver powder to the XRD/F and XCT located in the rover’s interior. Alternatively, METRIC instruments could be used singly or in combination on human space missions. The XRD/F and XCT could be used to characterize samples in a rover or in a science laboratory within a habitat. These data could help astronauts identify resource-enriched rocks and regolith and triage geologic samples to return samples of high interest for analysis in terrestrial laboratories. The IRS could be attached to a human-navigated rover to collect mineralogical data along a traverse and identify high-priority science samples.
E. B. Rampe↗
Investigating Low-Altitude Constellations of Ad-Hoc Lunar PNT System for Distributed Spacecraft Autonomy
In this study, we examine a low-altitude Lunar Position, Navigation, and Timing (LPNT) constellations and the localization performance of Centralized Extended Kalman Filter (CEKF) and Decentralized Extended Kalman Filter (DEKF) algorithms. The primary investigation involves a 100-node swarm operating at a 100 km altitude, in contrast to previous studies that examined a 21-node asset in a frozen-orbit at 5,500 km. The autonomous operation of large-scale swarm is based on two-way Inter-Satellite Link (ISL) measurements, which involve pseudoranges and relative velocities among swarm nodes. We perform a numerical assessment of the two filtering approaches, utilizing ‘fully sampled’ measurements from all available assets as well as ‘two ISL’ measurements where each spacecraft is restricted to only two antennas. This research includes an analysis of CEKF under 2-ISL constraints and evaluates the performance of DEKF in a 100-node swarm, which has not been explored in previous studies. In addition, we examine the impact of increasing the sampling frequency for DEKF, showing that the update cycle can be shortened from a 10-minute interval. A novel approach for ‘2-ISL limited’ DEKF will also be introduced, using a matching formulation that exhaustively enumerates all potential matches. This study provides valuable insights into large-scale distributed swarm operations, considering various filter configurations, sampling frequencies, matching strategies, and scalability of CEKF and DEKF for low-altitude LPNT applications. The Lunar PNT technology plays a key role in providing reliable and robust navigation services on the Moon's surface and the South pole, where the primary Lunar missions are planned. To support upcoming Lunar missions, including small satellites from NASA's Commercial Lunar Payload Services program, the Lunar PNT system must be adaptable to smaller platforms like CubeSats. Driven by the growing involvement of public and private exploration partnerships, the traditional low Earth orbit missions are shifting to beyond geosynchronous orbit [1]. These upcoming missions aim to foster a sustainable and innovative exploration program, in collaboration with commercial and international partners, to facilitate human expansion throughout the solar system and return new knowledge and opportunities to Earth [2]. As part of this trend, there are increasing efforts to utilize science missions in Lunar orbit to develop a non-dedicated and ad-hoc PNT network system. Two traditional approaches, the Deep Space Network (DSN) and the weak signal Global Positioning System (GPS), are established deep-space navigation technologies for missions beyond the geosynchronous orbit. Beginning in 1958, the DSN was developed to communicate with the Explorer 1 spacecraft based on the use of radiometric tracking in spacecraft navigation [3]. The DSN is capable of providing nearly unfettered coverage to spacecraft beyond low-Earth orbit (LEO), however, increased space mission volume has created concerns about future expectations of DSN usage for spacecraft navigation [4]. For cislunar mission applications, the position accuracy using DSN achieves 100 m (3σ) with at least three geometrically diverse ground stations when using radiometric tracking alone [5]. The DSN's dependence on Earth-based ground stations restricts its operational capabilities to periods of Earth visibility. This limitation, coupled with its poor localization performance, renders the DSN unsuitable for future lunar missions that demand continuous tracking and precise positioning. To satisfy the increasing requirements of DSN in Lunar applications, spacecrafts are also required to improve their onboard antenna power and efficiency of the transmission. However, there is an important aggregate cost trade between adding capabilities to every spacecraft and adding to a capacity on the ground that serves multiple spacecraft [6]. A weak GPS system can provide PNT service while the user spacecraft is bound to the Moon, leveraging a single, steerable high gain antenna with the relatively narrow beam which includes all the sources in its field of view [7]. However, the higher the altitude the receiver is above the GPS constellations, the poorer and the weaker are the relative geometry and the received signal powers, respectively, leading to a significant navigation accuracy reduction [8]. The transmitted power becomes weaker with increasing distance from the Earth as well as signals tracked from one of the side lobes of the GPS antenna pattern. As a results, the number of visible satellites and relative geometric condition of the GPS satellites at very high altitude drops dramatically and reduces the navigation solution accuracy. Therefore, the weak GPS system is also not an ideal way to provide PNT service to upcoming Lunar missions when considering its limited geometric condition and the recued navigation accuracy. Another navigation approach on the Moon is being developed, similar to the Global Navigation Satellite System (GNSS) on Earth, aiming to offer navigation service with continuous 24/7 coverage across the entire Lunar surface. For example, lunar communications relay and navigation systems (LCRNS) by NASA and Lunar navigation satellite systems (LNSS) by JAXA are designed to serve as dedicated Position, Navigation, and Timing (PNT) systems for the Moon. However, designing a dedicated LNSS and PNT service involves additional challenges, which are unique to the lunar environment, including limited payload capacity for the CubeSat platform, i.e., the size, weight, and power (SWaP) of the onboard clock, limited lunar ground monitoring stations, and limited financial investment as compared to the legacy Earth-GPS [9]. NASA’s focus on utilizing CubeSat platforms on the Moon leads to an alternative Lunar navigation platform that leverages the existing Lunar science and exploration assets. The small satellites used in Lunar missions can be used to create a low-cost, autonomous, ad-hoc, and on-demand mission-centric Lunar PNT swarm capable of providing PNT services to these low-cost lunar missions [10]. As upcoming Lunar missions will often operate at low-altitude about 30 km to 100 km for scientific observations and mapping purposes, the low-altitude orbital constellations could be employed to create an ad-hoc Lunar PNT system. However, several issues must be addressed, such as the instability of these orbits, which often require maintenance or are only suitable for short-duration missions, operating for fewer than 90 days. Additionally, at an altitude of 100 km, the satellites have a limited period during which they are above the horizon and capable of providing PNT service to users. The implementation of a non-dedicated, ad-hoc Lunar navigation constellation facilitates on-demand PNT services. A preliminary study of ad-hoc Lunar PNT system was conducted using 21 spacecraft in 5,5000 km altitude frozen orbits to test its feasibility and a basic performance of orbital asset localization among ad-hoc Lunar constellations in small satellites format [10]. These swarm assets are designed for autonomous localization with minimal Earth interaction, reducing dependency on bandwidth and ground resources. The design in [10] demonstrated the feasibility of a decentralized PNT approach, specifically employing a DEKF approach for state estimation, which helps minimize onboard operating costs. The DEKF method distributes computation across individual satellites, which lightens the computational load while maintaining accuracy in orbit ephemeris and clock offsets, similar to centralized systems [11]. In a follow-on study [12], each spacecraft was limited to 2 communications antennae, forcing the selection of measurements and scheduling spacecraft activities to perform the measurements. A matching algorithm is implemented to select the best measurements and schedule position estimation updates. The decentralized localization performance is also investigated with increasing levels of network degradation for swarm assets considering the impact of intermittent and permanent communication failure, to demonstrate the robustness and fidelity of the decentralized Lunar PNT service [13]. This study confirmed that the ad-hoc PNT constellations in frozen orbit are highly robust and resilient to communication failures. However, unlike frozen orbit swarm assets, the low-altitude satellites have a limited ground view at an altitude of 100 km, where the ad-hoc Lunar constellation consists of 98 low-altitude satellites, evenly distributed across seven circular polar orbital planes, alongside two satellites in a frozen orbit at an altitude of 5,500 km (Figure 1). Therefore, the number of satellites visible to ground users is significantly limited in low-altitude orbit constellations. As each visibility of a spacecraft remains intact for only a few ticks before it moves out of the field of view, the ground user encounters challenges in maintaining continuous navigation service, resulting in sparse availability and provision of Lunar PNT system. Consequently, service availability is primarily restricted to the Lunar South Pole region (Figure 2). Given these limitations and concerns, the localization performance of low-altitude swarm assets will be assessed in this study. We focus on the investigation of the localization performance of low-altitude swarm assets and ground users near the Lunar South Pole. The overall flow of the Lunar PNT simulation incorporates the DEKF approach of asset localization and the weighted least-squares approach in user localization (Figure 3). The autonomous Lunar PNT simulation is primarily implemented in MATLAB, where the DEKF based on the matching scheduler is implemented with Google’s OR-tools as a model builder and Gurobi optimization tool as a backend solver. The General Mission Analysis Tool (GMAT) is utilized to generate ephemeris data for swarm assets, and accounts for satellite orbital details, mass, and perturbations like solar radiation pressure and drag coefficients. Each ephemeris dataset is produced in the Moon International Celestial Reference Frame (ICRF) inertial coordinate system. For state estimation, the distributed swarm assets rely on two-way Inter-Satellite Link (ISL) measurements, which involve tracking pseudoranges and relative velocities between visible satellites and anchor nodes during each observation. Numerical evaluations of the decentralized localization process are conducted to demonstrate the feasibility of the low-altitude PNT system in providing reliable navigation services. The main approach involves using DEKF and CEKF to localize 100 satellites in low-altitude constellations, where the CEKF is implemented to serve as a baseline for comparing the performance of distributed algorithms. In both cases, we evaluate ‘fully sampled’ measurements from all available assets, and ‘two ISL’ measurements when spacecraft are constrained to have only two antennas. We test four estimation techniques: CEKF fully sampled, CEKF two ISL, DEKF fully sampled, and DEKF two ISL filters. As the DEKF update cycle is comprised of network setup, communication, and computations, a global broadcast network and 2-way ISL network setup will take from 4 to 6 minutes as maximum [12]. In this simulation, the DEKF update cycle is set to 10 minutes, including a 4-minute latency for obtaining and computing the actual measurement updates. We experiment an increased update cycle to demonstrate the feasibility and evaluate the impact on localization performance using various tuning values for measurement noise covariances (Figures 4 and 5). By comparing centralized and decentralized approaches using a matching algorithm, we analyze the influence of cross-correlation factors in the covariance matrix, assuming 100% reliability of all assets and measurements. The increased frequency and the adjustments of tuning parameters reveal distinct error patterns between the two scenarios. The localization accuracy of the swarm assets and ground users is assessed by taking the median error across 100 assets and one ground user (84.9°S, 137.5°E) over 7-day simulation period (Table 1). Since the user localization accuracy is significantly affected by the performance of the swarm assets, it is crucial to maintain high localization accuracy within the swarm. This study will continue to explore decentralized filtering for autonomous LPNT operations, with further investigation of an 'iterative' matching approach which enumerates every valid matching pair, planned for the following month.
Yeji Kim↗