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All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Uncertainties in estimates of the risks of late effects from space radiation

Methods used to project risks in low-Earth orbit are of questionable merit for exploration missions because of the limited radiobiology data and knowledge of galactic cosmic ray (GCR) heavy ions, which causes estimates of the risk of late effects to be highly uncertain. Risk projections involve a product of many biological and physical factors, each of which has a differential range of uncertainty due to lack of data and knowledge. Using the linear-additivity model for radiation risks, we use Monte-Carlo sampling from subjective uncertainty distributions in each factor to obtain an estimate of the overall uncertainty in risk projections. The resulting methodology is applied to several human space exploration mission scenarios including a deep space outpost and Mars missions of duration of 360, 660, and 1000 days. The major results are the quantification of the uncertainties in current risk estimates, the identification of factors that dominate risk projection uncertainties, and the development of a method to quantify candidate approaches to reduce uncertainties or mitigate risks. The large uncertainties in GCR risk projections lead to probability distributions of risk that mask any potential risk reduction using the "optimization" of shielding materials or configurations. In contrast, the design of shielding optimization approaches for solar particle events and trapped protons can be made at this time and promising technologies can be shown to have merit using our approach. The methods used also make it possible to express risk management objectives in terms of quantitative metrics, e.g., the number of days in space without exceeding a given risk level within well-defined confidence limits. Published by Elsevier Ltd on behalf of COSPAR.

Non-NASA Center↗
NASA NTRS2008

LiGa(OTf)(sub 4) as an Electrolyte Salt for Li-Ion Cells

Lithium tetrakis(trifluoromethane sulfo - nato)gallate [abbreviated "LiGa(OTf)4" (wherein "OTf" signifies trifluoro - methanesulfonate)] has been found to be promising as an electrolyte salt for incorporation into both liquid and polymer electrolytes in both rechargeable and non-rechargeable lithium-ion electrochemical cells. This and other ingredients have been investigated in continuing research oriented toward im proving the performances of rechargeable lithium-ion electrochemical cells, especially at low temperatures. This research at earlier stages, and the underlying physical and chemical principles, were reported in numerous previous NASA Tech Briefs articles. As described in more detail in those articles, lithiumion cells most commonly contain nonaqueous electrolyte solutions consisting of lithium hexafluorophosphate (LiPF6) dissolved in mixtures of cyclic and linear alkyl carbonates, including ethylene carbonate (EC), propylene carbonate (PC), dimethyl carbonate (DMC), diethyl carbonate (DEC), and ethyl methyl carbonate (EMC). Although such LiPF6-based electrolyte solutions are generally highly ionically conductive and electrochemically stable, as needed for good cell performance, there is interest in identifying alternate lithium electrolyte salts that, relative to LiPF6, are more resilient at high temperature and are less expensive. Experiments have been performed on LiGa(OTf)4 as well as on several other candidate lithium salts in pursuit of this interest. As part of these experiments, LiGa(OTf)4 was synthesized by the reaction of Ga(OTf)3 with an equimolar portion of LiOTf in a solvent consisting of anhydrous acetonitrile. Evaporation of the solvent yielded LiGa(OTf)4 as a colorless crystalline solid. The LiGa(OTf)4 and the other salts were incorporated into solutions with PC and DMC. The resulting electrolyte solutions exhibited reasonably high ionic conductivities over a relatively wide temperature range down to 40 C (see figure). In cyclic voltammetry measurements, LiGa(OTf)4 and the other salts exhibited acceptably high electrochemical stability over the relatively wide potential window of 0 to 5 V versus Li+/Li. 13C nuclear-magneticresonance measurements yielded results that suggested that in comparison with the other candidate salts, LiGa(OTf)4 exhibits less ion pairing. Planned further development will include optimization of the salt and solvent contents of such electrolyte solutions and incorporation of LiGa(OTf)4 into gel and solid-state polymer electrolytes. Of the salts, LiGa(OTf)4 is expected to be especially desirable for incorporation into lithium polymer electrolytes, wherein decreased ion pairing is advantageous and the large delocalized anions can exert a plasticizing effect.

Reddy, V. Prakash↗
NASA NTRS2006

Exploring the Production of NOx by Lightning and Its Impact on Tropospheric Ozone

Our quantitative understanding of free tropospheric (FT) chemistry is quite poor. State-of-the-art regional air quality models (e.g., US EPA's CMAQ) perform very poorly in simulating FT chemistry, with Uniform ozone around 70 ppb throughout the FT in summer, while ozonesonde data show much higher levels of ozone and much spatial-temporal structure. Such models completely neglect lightning-NOx (LNOx) emissions (the most significant source of NOx in the FT), and also contain large uncertainties in the specifications of intercontinental transport, stratosphere-troposphere exchange (STE) and PBLFT exchange (PFTE). Global air chemistry models include LNOx, but in very crude fashion, with the frequency and distribution of lightning being based on modeled cloud parameters (hence large uncertainty), lightning energetics being assumed to be constant for all flashes (literature value, while in reality there is at least a two-orders of magnitude variability from flash-to-flash), and the production of NOx in the surrounding heated air, per Joule of heating, being assumed to be constant also (literature value, while in fact it is a non-linear function of the dissipated heat and local air density, p). This situation is commonly blamed on paucity of pertinent observational data, but for the USA, there is now a wealth of surface- and satellite-based data of lightning available to permit much improved observation-based estimation of LNOx emissions. In the FT, such NOx has a long residence time, and also the ozone production efficiency from NOx there is considerably higher than in the PBL. It is, therefore, of critical importance in FT chemistry. This paper will describe the approach and data products of an ongoing NSSTC project aimed at a much-improved quantification of not only LNOx production on the scale of continental USA based on local and regional lightning observations, but also of intercontinental transport, STE and PFTE, all in upgraded simulations of tropospheric transport and chemistry. In our approach for LNOx, (a) we utilize continuous observed lightning information from the NLDN ground network and from satellite imagers (OTD and LIS) to quantify lightning frequency and distribution at the spatial-temporal scales of models such as CMAQ; (b) we develop new methodologies to quantify flash-specific lightning energy dissipation as heat (epsilon) using data from the research-grade lightning measurement facility at NASA-KSC, and to parameterize epsilon based on regional lightning monitoring data (ground- and satellite-based); and, (c) we develop a new parameterization of NOx production as a function of epsilon and rho. Based on such observation-based information, we are working to develop a gridded, episodic LNOx emissions inventory for the USA for use in models like CMAQ. We are also developing approaches for global(MOZART)- regional(CMAQ) chemistry coupling to improve intercontinental transport and STE. Finally, we are developing new methodologies for assimilation of satellite-observed (GOES) clouds into meteorological modeling (MM5), to improve PFTE and to optimize co-location of cloud convection and observed lightning. We will incorporate these improvements in CMAQ simulations over the USA to better understand FT processes and chemistry, and its impact on ground-level ozone.

Gillani, Noor↗
NASA NTRS1993

Dynamics and control of coherent structures in the turbulent wall layer: An overview

We expand the velocity field in the vicinity of the wall in empirical eigenfunctions obtained from experiment. Truncating our system and using Galerkin projection, we obtain a closed set of non-linear ordinary differential equations with ten degrees of freedom. We find a rich dynamical behavior, including in particular a heteroclinic attracting orbit giving rise to intermittency. The intermittent jump from one attracting point to the other resembles in many respects the bursts observed in experiments. Specifically, the time between jumps and the duration of the jumps, is approximately that observed in a burst; the jump begins with the formation of a narrowed and intensified updraft, like the ejection phase of a burst, and is followed by a gentle, diffuse downdraft like the sweep phase of a burst. The magnitude of the Reynolds stress spike produced during a burst is limited by our truncation. The behavior is quite robust, much of it being due to the symmetries present (Aubry's group has examined dimensions up to 128 with persistence of the global behavior). We have examined eigenvalues and coefficients obtained from experiment, and from exact simulation, which differ in magnitude. Similar behavior is obtained in both cases; in the latter case, the heteroclinic orbits connect limit cycles instead of fixed points, corresponding to cross-stream waving of the streamwise rolls. The bifurcation diagram remains structurally similar, but somewhat distorted. The role of the pressure term is made clear - it triggers the intermittent jumps, which otherwise would occur at longer and longer intervals, as the system trajectory is attracted closer and closer to the heteroclinic cycle. The pressure term results in the jumps occurring at essentially random times, and the magnitude of the signal determines the average timing. Stretching of the wall region shows that the model is consistent with observations of polymer drag reduction. Change of the third order coefficients, corresponding to acceleration or deceleration of the mean flow, changes the heteroclinic cycles from attracting to repelling, increasing or decreasing the stability, in agreement with observations. The existence of fixed points is an artifact introduced by the projection; however, a decoupled model still displays the rich dynamics. Numerous assumptions made in Aubry et al. (1988) can now be proved exactly. Feeding back eigenfuncitons with the proper phase can delay the bursting, (the heteroclinic jump to the other fixed point), decreasing the drag. It is also possible to speed up the bursting, increasing mixing to control separation. Our approach is optimal for short time tracking in control.

Berkooz, Gal↗
NASA NTRS1995

Cloud Ozone Dust Imager (CODI): Investigation and Technical Plan - Volume 1

The Cloud Ozone Dust Imager (CODI) is proposed to investigate the current climatic balance of the Mars atmosphere, with particular emphasis on the important but poorly understood roles which dust and water ice aerosols play in this balance. The large atmospheric heating (20-50 K) resulting from global dust storms around Mars perihelion is well recognized. However, groundbased observations of Mars atmospheric temperatures, water vapor, and clouds since the Viking missions have identified a much colder, cloudier atmosphere around Mars aphelion that may prove as important as global dust storms in determining the interannual and long-term behavior of the Mars climate. The key climate issues CODI is designed to investigate are: 1) the degree to which non-linear interactions between atmospheric dust heating, water vapor saturation, and cloud nucleation influence the seasonal and interannual variability of the Mars atmosphere, and 2) whether the strong orbital forcing of atmospheric dust loading, temperatures and water vapor saturation determines the long-term balance of Mars water, as reflected in the north-south hemispheric asymmetries of atmospheric water vapor and polar water ice abundances. The CODI experiment will measure the daily, seasonal and (potentially) interannual variability of atmospheric dust and cloud opacities, and the key physical properties of these aerosols which determine their role in the climate cycles of Mars. CODI is a small (1.2 kg), fixed pointing camera, in which four wide-angle (+/- 70 deg) lenses illuminate fixed filters and CCD arrays. Simultaneous sky/surface imaging of Mars is obtained at an angular resolution of 0.28 deg/pixel for wavelengths of 255, 336, 502, and 673 nm (similar to Hubble Space Telescope filters). These wavelengths serve to measure atmospheric ozone (255 and 336 nm), discriminate ice and dust aerosols (336 and 673 nm), and construct color images (336, 502, and 673 nm). The CODI images are detected on four 512 x 512 pixel arrays, as partitioned on two 1024 x 1024 CCD's operated in frame transfer mode. The center of the CODI field-of-view is canted 40 deg from the zenith direction to obtain sky brightness measurements and a 20 deg surface field-of-view. Daily image observations will be conducted when the Sun is greater than or equal to 5 deg outside the edge of the CODI field-of-view, and twilight and nighttime imaging will obtained on a weekly basis. The 673 nm channel includes a polarizer wheel to obtain sky/surface polarimetry. A dust cover protects the entire lens assemblies of all four CODI channels. This opaque dust cover, which is normally opened for CODI imaging, includes a small fixed mirror and transparent window positioned above the 673 nm lens, to redirect the 673 nm field-of-view to the surface for descent imaging. Fixed pointing, internal data buffering, low operating power (2-4 W for less than or equal to 30 seconds), selective data transmission, and simple operational characteristics of the CODI experiment place minimum resource and operational demands on the Mars Surveyor 1998 lander. The CODI science goals are optimized for, but not restricted to, a low-latitude landing site (20 deg S-30 deg N). The primary CODI measurement objectives are the opacities, wave forms, particle properties (size, shape, and alignment), and heights of clouds; the opacities, particle properties, and vertical distribution of dust; and the opacity and vertical distribution of ozone. The variability of cloud, ozone, and dust opacities will be determined on diurnal, daily, and seasonal timescales. Wind velocities will be determined from cloud motions and wave characteristics; and the temporal variability of atmospheric water vapor, with limited altitude information, will be inferred from the CODI ozone observations. Secondary measurement objectives include limited descent imaging capability, surface uv-visible photometry and polarimetry, photochemistry, and meteorite infall rates.

Clancy, R. Todd↗
NASA NTRS2004

The Role of Ontologies in Schema-based Program Synthesis

Program synthesis is the process of automatically deriving executable code from (non-executable) high-level specifications. It is more flexible and powerful than conventional code generation techniques that simply translate algorithmic specifications into lower-level code or only create code skeletons from structural specifications (such as UML class diagrams). Key to building a successful synthesis system is specializing to an appropriate application domain. The AUTOBAYES and AUTOFILTER systems, under development at NASA Ames, operate in the two domains of data analysis and state estimation, respectively. The central concept of both systems is the schema, a representation of reusable computational knowledge. This can take various forms, including high-level algorithm templates, code optimizations, datatype refinements, or architectural information. A schema also contains applicability conditions that are used to determine when it can be applied safely. These conditions can refer to the initial specification, to intermediate results, or to elements of the partially-instantiated code. Schema-based synthesis uses AI technology to recursively apply schemas to gradually refine a specification into executable code. This process proceeds in two main phases. A front-end gradually transforms the problem specification into a program represented in an abstract intermediate code. A backend then compiles this further down into a concrete target programming language of choice. A core engine applies schemas on the initial problem specification, then uses the output of those schemas as the input for other schemas, until the full implementation is generated. Since there might be different schemas that implement different solutions to the same problem this process can generate an entire solution tree. AUTOBAYES and AUTOFILTER have reached the level of maturity where they enable users to solve interesting application problems, e.g., the analysis of Hubble Space Telescope images. They are large (in total around 100kLoC Prolog), knowledge intensive systems that employ complex symbolic reasoning to generate a wide range of non-trivial programs for complex application do- mains. Their schemas can have complex interactions, which make it hard to change them in isolation or even understand what an existing schema actually does. Adding more capabilities by increasing the number of schemas will only worsen this situation, ultimately leading to the entropy death of the synthesis system. The root came of this problem is that the domain knowledge is scattered throughout the entire system and only represented implicitly in the schema implementations. In our current work, we are addressing this problem by making explicit the knowledge from Merent parts of the synthesis system. Here; we discuss how Gruber's definition of an ontology as an explicit specification of a conceptualization matches our efforts in identifying and explicating the domain-specific concepts. We outline the dual role ontologies play in schema-based synthesis and argue that they address different audiences and serve different purposes. Their first role is descriptive: they serve as explicit documentation, and help to understand the internal structure of the system. Their second role is prescriptive: they provide the formal basis against which the other parts of the system (e.g., schemas) can be checked. Their final role is referential: ontologies also provide semantically meaningful "hooks" which allow schemas and tools to access the internal state of the program derivation process (e.g., fragments of the generated code) in domain-specific rather than language-specific terms, and thus to modify it in a controlled fashion. For discussion purposes we use AUTOLINEAR, a small synthesis system we are currently experimenting with, which can generate code for solving a system of linear equations, Az = b.

Bures, Tomas↗
NASA NTRS1992

Experimental tests of a superposition hypothesis to explain the relationship between the vestibuloocular reflex and smooth pursuit during horizontal combined eye-head tracking in humans

1. We used a modeling approach to test the hypothesis that, in humans, the smooth pursuit (SP) system provides the primary signal for cancelling the vestibuloocular reflex (VOR) during combined eye-head tracking (CEHT) of a target moving smoothly in the horizontal plane. Separate models for SP and the VOR were developed. The optimal values of parameters of the two models were calculated using measured responses of four subjects to trials of SP and the visually enhanced VOR. After optimal parameter values were specified, each model generated waveforms that accurately reflected the subjects' responses to SP and vestibular stimuli. The models were then combined into a CEHT model wherein the final eye movement command signal was generated as the linear summation of the signals from the SP and VOR pathways. 2. The SP-VOR superposition hypothesis was tested using two types of CEHT stimuli, both of which involved passive rotation of subjects in a vestibular chair. The first stimulus consisted of a "chair brake" or sudden stop of the subject's head during CEHT; the visual target continued to move. The second stimulus consisted of a sudden change from the visually enhanced VOR to CEHT ("delayed target onset" paradigm); as the vestibular chair rotated past the angular position of the stationary visual stimulus, the latter started to move in synchrony with the chair. Data collected during experiments that employed these stimuli were compared quantitatively with predictions made by the CEHT model. 3. During CEHT, when the chair was suddenly and unexpectedly stopped, the eye promptly began to move in the orbit to track the moving target. Initially, gaze velocity did not completely match target velocity, however; this finally occurred approximately 100 ms after the brake onset. The model did predict the prompt onset of eye-in-orbit motion after the brake, but it did not predict that gaze velocity would initially be only approximately 70% of target velocity. One possible explanation for this discrepancy is that VOR gain can be dynamically modulated and, during sustained CEHT, it may assume a lower value. Consequently, during CEHT, a smaller-amplitude SP signal would be needed to cancel the lower-gain VOR. This reduction of the SP signal could account for the attenuated tracking response observed immediately after the brake. We found evidence for the dynamic modulation of VOR gain by noting differences in responses to the onset and offset of head rotation in trials of the visually enhanced VOR.(ABSTRACT TRUNCATED AT 400 WORDS).

Non-NASA Center↗
NASA NTRS2015

Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation

When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating each component weight during the nonlinear propagation stage an approximation of the true pdf can be successfully reconstructed. Particle filtering (PF) methods have gained popularity recently for solving nonlinear estimation problems due to their straightforward approach and the processing capabilities mentioned above. The basic concept behind PF is to represent any pdf as a set of random samples. As the number of samples increases, they will theoretically converge to the exact, equivalent representation of the desired pdf. When the estimated qth moment is needed, the samples are used for its construction allowing further analysis of the pdf characteristics. However, filter performance deteriorates as the dimension of the state vector increases. To overcome this problem Ref. [5] applies a marginalization technique for PF methods, decreasing complexity of the system to one linear and another nonlinear state estimation problem. The marginalization theory was originally developed by Rao and Blackwell independently. According to Ref. [6] it improves any given estimator under every convex loss function. The improvement comes from calculating a conditional expected value, often involving integrating out a supportive statistic. In other words, Rao-Blackwellization allows for smaller but separate computations to be carried out while reaching the main objective of the estimator. In the case of improving an estimator's variance, any supporting statistic can be removed and its variance determined. Next, any other information that dependents on the supporting statistic is found along with its respective variance. A new approach is developed here by utilizing the strengths of the adaptive Gaussian sum propagation in Ref. [2] and a marginalization approach used for PF methods found in Ref. [7]. In the following sections a modified filtering approach is presented based on a special state-space model within nonlinear systems to reduce the dimensionality of the optimization problem in Ref. [2]. First, the adaptive Gaussian sum propagation is explained and then the new marginalized adaptive Gaussian sum propagation is derived. Finally, an example simulation is presented.

state estimation↗
NASA NTRSDate not supplied

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↗