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Analysis of multiple access techniques in multi-satellite and multi-spot mobile satellite systems

In this paper the analysis of mobile satellite systems adopting constellations of multi-spot satellites over non-geostationary orbits is addressed. A link design procedure is outlined, taking into account system spectrum efficiency, probability of bit error and outage probability. A semi-analytic approach to the evaluation of outage probability in the presence of fading and imperfect power control is described, and applied to single channel per carrier (SCPC) and code division multiple access (CDMA) techniques. Some results are shown for the Globalstar, Iridium and Odyssey orbital configurations.

Corazza, Giovanni E.↗

A simple model for DSS-14 outage times

A model is proposed to describe DSS-14 outage times. Discrepancy Reporting System outage data for the period from January 1986 through September 1988 are used to estimate the parameters of the model. The model provides a probability distribution for the duration of outages, which agrees well with observed data. The model depends only on a small number of parameters, and has some heuristic justification. This shows that the Discrepancy Reporting System in the Deep Space Network (DSN) can be used to estimate the probability of extended outages in spite of the discrepancy reports ending when the pass ends. The probability of an outage extending beyond the end of a pass is estimated as around 5 percent.

Rumsey, H. C.↗

Downlink Probability Density Functions for EOS-McMurdo Sound

The visibility times and communication link dynamics for the Earth Observations Satellite (EOS)-McMurdo Sound direct downlinks have been studied. The 16 day EOS periodicity may be shown with the Goddard Trajectory Determination System (GTDS) and the entire 16 day period should be simulated for representative link statistics. We desire many attributes of the downlink, however, and a faster orbital determination method is desirable. We use the method of osculating elements for speed and accuracy in simulating the EOS orbit. The accuracy of the method of osculating elements is demonstrated by closely reproducing the observed 16 day Landsat periodicity. An autocorrelation function method is used to show the correlation spike at 16 days. The entire 16 day record of passes over McMurdo Sound is then used to generate statistics for innage time, outage time, elevation angle, antenna angle rates, and propagation loss. The levation angle probability density function is compared with 1967 analytic approximation which has been used for medium to high altitude satellites. One practical result of this comparison is seen to be the rare occurrence of zenith passes. The new result is functionally different than the earlier result, with a heavy emphasis on low elevation angles. EOS is one of a large class of sun synchronous satellites which may be downlinked to McMurdo Sound. We examine delay statistics for an entire group of sun synchronous satellites ranging from 400 km to 1000 km altitude. Outage probability density function results are presented three dimensionally.

Christopher, P.↗

A solution to the problem of optimizing the fuel bias for a liquid propellant rocket by an application of the central limit theorem

A method of determining the fuel bias for a bipropellant liquid rocket that minimizes outage associated penalties on payload potential is presented. A fuel bias so derived is normally called the optimum fuel bias. The subjects discussed are: (1) probability density function of outage, (2) computer program listing, and (3) choosing the optimum fuel bias.

Viera, W. J.↗

Worldwide differential GPS for Space Shuttle landing operations

Worldwide differential Global Positioning System (WWDGPS) is viewed as an effective method of offering continuous high-quality navigation worldwide. The concept utilizes a network with as few as 33 ground stations to observe most of the error sources of GPS and provide error corrections to users on a worldwide basis. The WWDGPS real-time GPS tracking concept promises a threefold or fourfold improvement in accuracy for authorized dual-frequency users, and in addition maintains an accurate and current ionosphere model for single-frequency users. A real-time global tracking network also has the potential to reverse declarations of poor health on marginal satellites, increasing the number of satellites in the constellation and lessening the probability of GPS navigation outage. For Space Shuttle operations, the use of WWDGPS-aided P-code equipment promises performance equal to or better than other current landing guidance systems in terms of accuracy and reliability. This performance comes at significantly less cost to NASA, which will participate as a customer in a system designed as a commercial operation serving the global civil navigation community.

Loomis, Peter V. W.↗

As assessment of power system vulnerability to release of carbon fibers during commercial aviation accidents

The vulnerability of a power distribution system in Bedford and Lexington, Massachusetts to power outages as a result of exposure to carbon fibers released in a commercial aviation accident in 1993 was examined. Possible crash scenarios at Logan Airport based on current operational data and estimated carbon fiber usage levels were used to predict exposure levels and occurrence probabilities. The analysis predicts a mean time between carbon fiber induced power outages of 2300 years with an expected annual consequence of 0.7 persons losing power. In comparison to historical outage data for the system, this represents a 0.007% increase in outage rate and 0.07% increase in consequence.

Larocque, G. R.↗

Characterization of Operational Performance of Ka-Band Links in Deep Space Network

This paper presents a characterization of performance of 32-GHz Ka-band link in an operational environment. The data come from tracking of Kepler spacecraft by the NASA Deep Space Network (DSN) in the past few years. Ka-band link offers a significant signal-to-noise advantage compared to the more common X- or S-band; however, it is subject to more signal fluctuation caused by the weather. Kepler is the first mission supported by the DSN that solely rely on the higher deep space Ka-band communications link to return its high-rate science data. A well characterization of the operational performance of Kepler would benefit future Ka-band missions, especially for those operating with smaller link margin. The study examines how weather conditions at the DSN facilities (e.g., winds, clouds, rains) affect the received signal, particularly on telemetry data. It addresses questions such as how often the weather affects the link and how much degradation the link could suffer. Among the 22 Ka-band passes in 2012, heavy clouds affected one pass and two passes were impacted by high winds. The adverse weather caused at time as much as 3-dB instantaneous change in the signal to noise ratio (SNR). Estimates of degradation to the SNR as a function of wind speeds are captured based on observations. This study also quantifies the probability distribution of the variation of received signal power. With such information, future missions can better plan their link design. An optimal link design aims for just having enough margin to realize the data return with a targeted probability, with neither having too much margin that it reduces the downlink data rate nor insufficient reserve that causes frequent data outages. The study tries to provide some answers to the questions such as how much does SNR vary from one tracking pass to the next, and what is the cumulative distribution of signal fluctuation. Regarding the signal variation over many tracking passes, we found that the averaged symbol SNR (SSNR) for each pass changed by as much as 4 dB. Some variations were due to geometry such as the changing distance between spacecraft and Earth and different antenna pointing elevations. Other variations seem to be random in nature, reflecting the randomness of operational environments. Some passes were found to be quite stable, with a standard deviation of symbol SNR around 0.25 dB while others had greater variation, up to 1.4 dB. Overall, the cumulative distribution of the symbol SNR reflects that 50% of the fluctuations was less than 0.6 dB, 90% of fluctuation was within 1.6 dB and 95% within 2.2 dB. Some of the challenges in data processing, validation and modeling were captured in this paper. We observed some inconsistent measurements where operational data significantly deviate from a normal expectation. These inconsistent measurements made it hard to develop an accurate and consistent performance model, such as the degradation of signal SNR as a function of high wind. The difficulty was compounded by the fact that there were only a few Ka-band passes observed in high winds.

Pham, Timothy↗

S-band and Ku-band return service interference between TDRSS users

The Tracking Data Relay Satellite System (TDRSS) return service performance can be degraded by interference from another user when two or more spacecraft communicate with the same Tracking Data Relay Satellite (TDRS) at the same time. This paper describes the S-band and Ku-band return service self interference environment expected in the 1996 - 2010 timeframe and shows the self-interference expected for selected TDRSS users based on Communications Link Analysis and Simulation System (CLASS) Automated Conflict Resolution System (ACRS) and Interference Monitor (IM) tools. The results show: which user links are susceptible to interference from other users, the interference statistics, and whether or not interference can be avoided with appropriate interference mitigation techniques such as scheduling, cross-polarization, or Pseudo random Noise (PN) spreading. The analysis results enable Space Network (SN) managers to determine the impacts of self-interference on the TDRSS service availability. They also enable project offices to determine whether they should select return service communications parameters, such as polarization and PN spreading, to minimize the probability of being impacted by self-interference; try to schedule TDRSS support around other user spacecraft communications schedules; or accept communication outages due to self-interference.

Harrell, Linda↗

An Efficient Approach for the Reliability Analysis of Phased-Mission Systems with Dependent Failures

We consider the reliability analysis of phased-mission systems with common-cause failures in this paper. Phased-mission systems (PMS) are systems supporting missions characterized by multiple, consecutive, and nonoverlapping phases of operation. System components may be subject to different stresses as well as different reliability requirements throughout the course of the mission. As a result, component behavior and relationships may need to be modeled differently from phase to phase when performing a system-level reliability analysis. This consideration poses unique challenges to existing analysis methods. The challenges increase when common-cause failures (CCF) are incorporated in the model. CCF are multiple dependent component failures within a system that are a direct result of a shared root cause, such as sabotage, flood, earthquake, power outage, or human errors. It has been shown by many reliability studies that CCF tend to increase a system's joint failure probabilities and thus contribute significantly to the overall unreliability of systems subject to CCF.We propose a separable phase-modular approach to the reliability analysis of phased-mission systems with dependent common-cause failures as one way to meet the above challenges in an efficient and elegant manner. Our methodology is twofold: first, we separate the effects of CCF from the PMS analysis using the total probability theorem and the common-cause event space developed based on the elementary common-causes; next, we apply an efficient phase-modular approach to analyze the reliability of the PMS. The phase-modular approach employs both combinatorial binary decision diagram and Markov-chain solution methods as appropriate. We provide an example of a reliability analysis of a PMS with both static and dynamic phases as well as CCF as an illustration of our proposed approach. The example is based on information extracted from a Mars orbiter project. The reliability model for this orbiter considers the various phases of Launch, Cruise, Mars Orbit Insertion, and Orbit. Some of the CCF for the orbiter in this mission include environmental effects, such as micrometeoroids, human operator errors, and software errors.

reliability analysis↗

Electrochemical Impedance Spectroscopy of Alloys in a Simulated Space Shuttle Launch Environment

Type 304L stainless steel (304L SS) tubing is currently used in various supply lines that service the Orbiter at NASA's John F. Kennedy Space Center Launch Pads in Florida (USA). The atmosphere at the Space Shuffle launch site is very corrosive due to a combination of factors, such as the proximity of the Atlantic Ocean and the concentrated hydrochloric acid produced by the fuel combustion reaction in the solid rocket boosters. The acidic chloride environment is aggressive to most metals and causes severe pitting in many of the common stainless steel alloys such as 304L SS. Stainless steel tubing is susceptible to pitting corrosion that can cause cracking and rupture of both high-pressure gas and fluid systems. Outages in the systems where failures occur can impact the normal operation of the shuttle and launch schedules. The use of a more corrosion resistant tubing alloy for launch pad applications would greatly reduce the probability of failure, improve safety, lessen maintenance costs, and reduce downtime. A study which included ten alloys was undertaken to find a more corrosion resistant material to replace the existing 304L SS tubing. The study included atmospheric exposure at NASA's John F. Kennedy Space Center outdoor corrosion test site near the launch pads and electrochemical measurements in the laboratory which included DC techniques and electrochemical impedance spectroscopy (EIS). This paper presents the results from EIS measurements on three of the alloys: AL6XN (UN N08367), 254SMO (UNS S32l54), and 304L SS (UNS S30403). Type 304L SS was included in the study as a control. The alloys were tested in three electrolyte solutions which consisted of neutral 3.55% NaC1, 3.55% NaCl in O.1N HC1, and 3.55% NaCl in 1.ON HC1. The solutions were chosen to simulate environments that were expected to be less, similar, and more aggressive, respectively, than those present at the Space Shuttle launch pads. The results from the EIS measurements were analyzed to evaluate the corrosion susceptibility of the alloys and to predict the long-term corrosion performance of the subject materials. The results from the EIS measurements for the three alloys indicated that the higher-alloyed 254SMO and AL6XN exhibited a significantly improved resistance to corrosion than the 304L SS as the concentration of hydrochloric acid in the 3.55% NaC1 solution was increased. The polarization resistance values obtained from the EIS measurements were consistent with those from linear polarization measurements, and were indicative of the actual long-term corrosion performance of the alloys during a two-year atmospheric exposure study.

Calle, L. M.↗

An integral sunshade for optical reception antennas

Optical reception antennas (telescopes) must be capable of receiving communications even when the deep-space laser source is located within a small angle of the Sun. Direst sunlight must not be allowed to shine on the primary reflector of an optical reception antenna, because too much light would be scattered into the signal detectors. A conventional sunshade that does not obstruct the antenna aperture would have to be about five times longer than its diameter in order to receive optical communications at a solar elongation of 12 degrees without interference. Such a long sunshade could not be accommodated within the dome of any existing large-aperture astronomical facility, and providing a new dome large enough would be prohibitively expensive. It is also desirable to reduce the amount of energy a space-based large-aperture optical reception facility would expend orienting a structure with such a sizable moment of inertia. Since a large aperture optical reception antenna will probably have a hexagonally segmented primary reflector, a sunshade consisting of hexagonal tubes can be mounted in alignment with the segmentation without producing any additional geometric obstruction. An analysis of the duration and recurrence of solar-conjunction communications outages (caused when a deep-space probe near an outer planet appears to be closer to the Sun than a given minimum solar elongation), and the design equations for the integral sunshade are appended.

Kerr, E. L.↗

Integral sunshade for an optical reception antenna

Optical reception antennas (telescopes) must be capable of receiving communications even when the deep-space laser source is located within a small angle of the sun. Direct sunlight must not be allowed to shine on the primary reflector of an optical reception antenna, because too much light would be scattered into the signal detectors. A conventional sunshade that does not obstruct the antenna aperture would have to be about five times longer than its diameter in order to receive optical communications at a solar elongation of 12 degrees without interference. Such a long sunshade could not be accommodated within the dome of any existing large-aperture astronomical facility, and providing a new dome large enough would be prohibitively expensive. It is also desirable to reduce the amount of energy a space-based large-aperture optical reception facility would expend orienting a structure with such a sizable moment of inertia. Since a large aperture optical reception antenna will probably have a hexagonally segmented primary reflector, a sunshade consisting of hexagonal tubes can be mounted in alignment with the segmentation without producing any additional geometric obstruction. An analysis of the duration and recurrence of solar-conjunction communications outages (caused when a deep-space probe near an outer planet appears to be closer to the sun than a given minimum solar elongation), and the design equations for the integral sunshade are appended.

Kerr, Edwin L.↗

ACTS Propagation Measurements in Maryland and Virginia

Rapid growth in new satellite services incorporating very small aperture terminals (VSAT) and ultra small aperture terminals (USAT) is expected in the coming years. Small size terminals allow for widespread use of satellite services in small business and domestic applications. Due to congestion of lower frequency bands such as C and Ku, most of these services will use Ka-band (2/20 GHz) frequencies. Propagation impairments produced by the troposphere is a limiting factor for the effective use of the 20/30 GHz band and the use of smaller Earth terminals makes it difficult to provide sufficient link margins for propagation related outages. In this context, reliable prediction of propagation impairments for low margin systems becomes important. Due to the complexity of propagation phenomena propagation modeling is mainly attempted on an empirical basis. As such, the availability of reliable measured data that extend to probability levels well in excess of the traditional limit of 1 percent is of great importance in the development, validation, and refinement of propagation models. The beacon payload on the Advanced Communications Technology Satellite (ACTS) together with the propagation measurement terminals developed under the NASA ACTS propagation program provide an excellent opportunity to collect such data on a long-term basis. This paper presents the results of ACTS propagation measurements conducted in the Washington, DC metropolitan area by COMSAT Laboratories.

Dissanayake, Asoka↗

Availability of positioning and receiver autonomous integrity monitoring for the global positioning system

Receiver-autonomous integrity monitoring (RAIM) of GPS data is examined by means of a simulation of the availability of a RAIM system that can provide both a GPS coverage model and a Markov reliability model. State probabilities of GPS failure scenarios are assigned with the Markov model with a maximum of 6 simultaneous satellite failures. The parametric analysis of the failures on GPS RAIM availability includes the maximum allowable value of the horizontal dilution of precision (HDOP), the mean time to repair, and the efficacy of incorporating altimeter measurements. When the HDOP requirement is relaxed the number of RAIM outages is minimized, and poor satellite geometry can lead to a large HDOP. The use of an altimeter can also reduce outages, and RAIM availability increases with optimistic values for the mean time to repair.

Kline, Paul A.↗

Landslide Likelihood Prediction using Machine Learning Algorithms

The supply of electricity via power plants is criticalto the operation of many critical infrastructure systems in mod-ern society. Natural hazards can disrupt the power supply, causepower outages that can halt economic growth, and impede emer-gency response until power is restored. The proposed work aimsto predict the landslides likelihood in these critical infrastructurelocations in the Northeastern USA using integrated databases ofexplanatory variables and machine learning algorithms. First,data related to landslides are obtained and merged, includingtopographic, soil moisture, and precipitation-related data. Fiveregression algorithms, namely: Random Forest, Extreme Gradi-ent Boosting (XGBoost), K-Nearest Neighbor regression (KNN),Linear Support Vector Regressor (SVR), and Linear regression,are utilized to predict the landslide probability and evaluatedon the dataset. The accuracy of the models is assessed by usingstatistical metrics such as mean absolute error (MAE), meansquared error (MSE), and root mean squared error (RMSE).The study results show that Random Forest outperformed othermodels with the mutual information feature selection method.It achieved an MSE of 0.0011 with mutual information-basedfeature selection and an MSE of 0.00157 without feature selection.KNN regressor outperformed the other models with an MSEof 0.00139 with correlation-based information selection. Theproposed landslide identification model with Random Forestalgorithm shows outstanding robustness and great potential intackling the landslide likelihood prediction by employing MLalgorithms.

Vasundhara Acharya↗

High Reliability Requires More than Providing Spares

It is sometimes optimistically hoped that a space life support system can be kept working throughout a long duration mission by repairing failed components, as long as sufficient spares are flown. It is usually assumed that the components have constant known failure rates. Then the needed numbers of spares can be computed to have any particular probability that all failed components can be replaced by available spares. This approach can provide high reliability if its favorable assumptions, including constant known failure rates, are satisfied. Other favorable assumptions are that the failures are statistically independent, repair will be successful without causing further failures, and all failures are due to internal component failures. These assumptions are not usually justified. The failure rates may be estimates that are inadequately verified because of insufficient testing. Failure rates may change due to materials substitutions, manufacturing changes, redesigns to fix failures, and new failures caused by redesigns. Failures that are not statistically independent may result from one common cause, such as a design or manufacturing error or a cascade of cause and effect, possibly caused by an external event such as a power outage. Repair may be unsuccessful or cause damage. Many failures occur at component interfaces or at the overall systems level, not within isolated components. Other failures causes are completely external to the system, due to assembly, maintenance, and operational errors or to unexpected environmental challenges. Replacement with sufficient spares can compensate for expected internal component failures but may not be able to cope with unpredictable design and manufacturing flaws, human errors, and environmental impacts. Reliability estimates based on providing sufficient spares to compensate for expected failures may be far too high. They are essentially upper bounds on reliability that might be approached if many frequent but often unconsidered failure causes can be eliminated.

spares↗

Optimization of Second Fault Detection Thresholds to Maximize Mission POS

In order to support manned spaceflight safety requirements, the Space Launch System (SLS) has defined program-level requirements for key systems to ensure successful operation under single fault conditions. To accommodate this with regards to Navigation, the SLS utilizes an internally redundant Inertial Navigation System (INS) with built-in capability to detect, isolate, and recover from first failure conditions and still maintain adherence to performance requirements. The unit utilizes multiple hardware- and software-level techniques to enable detection, isolation, and recovery from these events in terms of its built-in Fault Detection, Isolation, and Recovery (FDIR) algorithms. Successful operation is defined in terms of sufficient navigation accuracy at insertion while operating under worst case single sensor outages (gyroscope and accelerometer faults at launch). In addition to first fault detection and recovery, the SLS program has also levied requirements relating to the capability of the INS to detect a second fault, tracking any unacceptable uncertainty in knowledge of the vehicle's state. This detection functionality is required in order to feed abort analysis and ensure crew safety. Increases in navigation state error and sensor faults can drive the vehicle outside of its operational as-designed environments and outside of its performance envelope causing loss of mission, or worse, loss of crew. The criteria for operation under second faults allows for a larger set of achievable missions in terms of potential fault conditions, due to the INS operating at the edge of its capability. As this performance is defined and controlled at the vehicle level, it allows for the use of system level margins to increase probability of mission success on the operational edges of the design space. Due to the implications of the vehicle response to abort conditions (such as a potentially failed INS), it is important to consider a wide range of failure scenarios in terms of both magnitude and time. As such, the Navigation team is taking advantage of the INS's capability to schedule and change fault detection thresholds in flight. These values are optimized along a nominal trajectory in order to maximize probability of mission success, and reducing the probability of false positives (defined as when the INS would report a second fault condition resulting in loss of mission, but the vehicle would still meet insertion requirements within system-level margins). This paper will describe an optimization approach using Genetic Algorithms to tune the threshold parameters to maximize vehicle resilience to second fault events as a function of potential fault magnitude and time of fault over an ascent mission profile. The analysis approach, and performance assessment of the results will be presented to demonstrate the applicability of this process to second fault detection to maximize mission probability of success.

Anzalone, Evan↗

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↗