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NASA NTRS2004

On-the-Fly Mapping for Calibrating Directional Antennas

An improved method of calibrating a large directional radio antenna of the type used in deep-space communication and radio astronomy has been developed. This method involves a raster-scanning-and-measurement technique denoted on-the-fly (OTF) mapping, applied in consideration of the results of a systematic analysis of the entire measurement procedure. Phenomena to which particular attention was paid in the analysis include (1) the noise characteristics of a total-power radiometer (TPR) that is used in the measurements and (2) tropospherically induced radiometer fluctuations. The method also involves the use of recently developed techniques for acquisition and reduction of data. In comparison with prior methods used to calibrate such antennas, this method yields an order-of-magnitude improvement in the precision of determinations of antenna aperture efficiency, and improvement by a factor of five or more in the precision of determination of pointing error and beam width. Prerequisite to a meaningful description of the present method is some background information concerning three aspects of the problem of calibrating an antenna of the type in question: In OTF mapping measurements in which a TPR is used, the desired data are the peak temperature corresponding to a radio source, the pointing offset when the antenna is commanded to point toward the source, and the shape of the main lobe of the antenna beam, all as functions of the antenna beam elevation and azimuth angles. These data enable one to calculate the (1) antenna aperture efficiency by comparing the measured peak temperature with that expected for a 100-percent-efficient antenna, (2) the mechanical pointing error resulting from small misalignments of various parts of the antenna structure, and (3) misalignments of the antenna subreflector and other mirrors. For practical reasons having to do with obtaining adequate angular resolution and all-sky coverage, it is necessary to perform azimuth and elevation scans fairly rapidly. Many natural radio sources used in calibrating antennas are only approximately pointlike: some sources subtend angles greater than the beam width of a given antenna. In such a case, the antenna partially resolves the source structure and does not collect all of the radiation emitted by the source. This makes it necessary to estimate how much of the total known radiation from the source would actually be collected by the antenna if it were 100-percent efficient. The resulting estimate, leading to a source-size correction factor, introduces another degree of uncertainty to the measurements. OTF mapping can remove this uncertainty

Rochblatt, David↗

NASA NTRSDate not supplied

Quantifying Leak Rates and Vacuum Impact on Granular Soil Column Pneumatic Seal

Introduction: All In-Situ Resource Utilization (ISRU) regolith reactor systems that aim to extract gases or vapors must maintain a seal along the flow path of the regolith from the inlet hopper to where extracted gases or vapors are generated. Using a column of regolith at the inlet has been proposed as an alternative to systems using series of mechanical valves to reduce mass and complexity. Preliminary investigations into the use of regolith itself as a barrier to escaping fluids have been conducted, which this research seeks to expand upon. Different vertical regolith simulant plug diameters and heights were tested under vacuum with dry nitrogen to observe leak rates and approximate steady state pressure gradient equilibria. The effect of absolute ambient pressure was also studied by repeating tests at incremental pressures ranging from 10e-5 Torr up to 1 atm to corroborate ambient bench tests from previous work. The impact of regolith dynamics was addressed to emulate continuous-feed regolith reaction processes by measuring leak rates through continuously draining simulant columns. OB-1 lunar highlands regolith simulant was used. Experimental Setup: Regolith simulant columns were constructed using a motorized butterfly valve separating upper acrylic tubes of various diameters from a larger, lower aluminum pipe plenum (See Figure 1). The butterfly valve was cracked open such that gas could freely pass through whereas regolith would bridge and stay suspended as a cohesive plug above in the acrylic portion. These assemblies were loaded into a vacuum chamber, and a compressed dry nitrogen line was routed into the lower plenum. Pressure transducers measured the absolute pressure of the lower plenum, which was compared to absolute chamber pressure to monitor the pressure gradient across the regolith simulant. A precision mass flow controller enabled fine control of plenum pressure. The plenum pressure was quasi-statically increased to set points informed by previous work [1] before shutting off the gas supply to allow the now pressurized gas volume to dissipate through the simulant into the chamber in what was referred to as a ‘leak test.’ In a separate set of tests, the pressure was allowed to quasi-statically build until visual disturbances in the soil were observed via remote camera feeds. Initial leak rate tests were repeated on the disturbed soil to observe changes in leak rates between initial as-poured and post-bubbling soil conditions. This test schedule was applied to simulant columns of three different diameters (approximately 2, 4, and 6 inches) as well as two different heights (around 8 and 16 inches) and was repeated at least three times for each configuration. Plenums were also pressurized while the butterfly valves were opened slightly further to facilitate slow, controlled, constant flowrate draining of the simulant to observe the impact that continuous-feed systems might have on leak rate through the regolith column. Finally, the regolith columns were reset and refilled and static leak rate tests were repeated approximately every decade in ambient pressure from 10e-5 Torr up to ambient conditions to observe the impact of transitioning out of the molecular flow regime on regolith column seal performance. Analysis: Trends with respect to each factor examined were constructed and reported alongside commentary on the most likely responsible physical phenomena. Confidence intervals were applied to the predictive findings of the data by quantifying instrumentation error and accounting for probabilistic impacts of curve fitting the generic exponential function onto pressure decay data. The leak rate is assumed directly proportional to the exponential term coefficient, while the steady-state static pressure gradient is assumed to be the asymptotic limit of each curve fit. Finally, a generic model developed by Ogino et al. [2] and later tuned for ambient testing was re-tuned using vacuum data to estimate leak rates on the lunar surface. Results: Pressure decay rates decreased up to 27-fold under vacuum when compared to ambient pressure, as shown in Figure 2. Simulant column diameter was found to exponentially correlate to both regolith column leak rate and steady-state equilibrium pressure delta. Height was found to be linearly related to leak rate –doubling the regolith column height consistently yielded around a 40% reduction in leak rate. Dynamic regolith draining was found to slightly increase leak rate, although to a lower degree than expected. Conclusion: Because of the transition into molecular gas flow through regolith, vacuum testing is required to properly estimate performance. Regolith columns should be designed as narrow as possible to avoid bridging and minimize leak rate, and as tall as is feasible to both further reduce leak rate and to help prevent bubbling, which has been shown to degrade the quality of the regolith seal. Disrupted soil was found to exhibit higher leak rates than pristine, as-poured soil, indicating the need to consider the impact of recovery from depressurization events. Regolith columns appear equally feasible for both dosed and continuous-feed reactors.

ISRU↗

NASA NTRSDate not supplied

Evaluating GXS Impact in the Context of International Coordination

The proposed NOAA/NASA Geostationary eXtended Observations (GeoXO) program plans to include a hyperspectral infrared (IR) sounder on its central satellite. Expected to launch in the mid-2030s, the GeoXO Sounder (GXS) will join international counterparts in a geostationary orbit. Ahead of launch, the NASA Global Modeling and Assimilation Office (GMAO) assessed the potential effectiveness of GXS both as a single GEO IR sounder and as part of a global ring of such instruments, including those already being built by international agencies. Using an observing system simulation experiment (OSSE) framework, GXS was assessed from a global numerical weather prediction (NWP) perspective. The ability of GXS, both alone and as part of a global ring of GEO sounders, to improve weather prediction of thermodynamic variables was evaluated globally and regionally. Compared to a control, GXS dominated regional analysis and forecast improvements, and contributed significantly to global increases in forecast skill. However, more sustained global improvements on the order of 4 days rely on international partnerships. Using the FSOI metric over CONUS, the GXS observations provide the strongest radiance impact on the moist energy error norm reduction. Additionally, GXS shows the capability to improve hurricane forecast track errors, resulting in improved forecast warnings. Overall, the persistent atmospheric profile information from GXS over much of the western hemisphere provide an opportunity to improve the representation of weather systems and their forecasts.

Erica McGrath-Spangler↗

NASA NTRSDate not supplied

Evaluating GXS Impact in the Context of International Coordination

Erica McGrath-Spangler↗

NASA NTRS1986

Landsat D Thematic Mapper image dimensionality reduction and geometric correction accuracy

To characterize and quantify the performance of the Landsat thematic mapper (TM), techniques for dimensionality reduction by linear transformation have been studied and evaluated and the accuracy of the correction of geometric errors in TM images analyzed. Theoretical evaluations and comparisons for existing methods for the design of linear transformation for dimensionality reduction are presented. These methods include the discrete Karhunen Loeve (KL) expansion, Multiple Discriminant Analysis (MDA), Thematic Mapper (TM)-Tasseled Cap Linear Transformation and Singular Value Decomposition (SVD). A unified approach to these design problems is presented in which each method involves optimizing an objective function with respect to the linear transformation matrix. From these studies, four modified methods are proposed. They are referred to as the Space Variant Linear Transformation, the KL Transform-MDA hybrid method, and the First and Second Version of the Weighted MDA method. The modifications involve the assignment of weights to classes to achieve improvements in the class conditional probability of error for classes with high weights. Experimental evaluations of the existing and proposed methods have been performed using the six reflective bands of the TM data. It is shown that in terms of probability of classification error and the percentage of the cumulative eigenvalues, the six reflective bands of the TM data require only a three dimensional feature space. It is shown experimentally as well that for the proposed methods, the classes with high weights have improvements in class conditional probability of error estimates as expected.

Ford, G. E.↗

NASA NTRS1985

Least squares collocation applied to local gravimetric solutions from satellite gravity gradiometry data

An autonomous spaceborne gravity gradiometer mission is being considered as a post Geopotential Research Mission project. The introduction of satellite diometry data to geodesy is expected to improve solid earth gravity models. The possibility of utilizing gradiometer data for the determination of pertinent gravimetric quantities on a local basis is explored. The analytical technique of least squares collocation is investigated for its usefulness in local solutions of this type. It is assumed, in the error analysis, that the vertical gravity gradient component of the gradient tensor is used as the raw data signal from which the corresponding reference gradients are removed to create the centered observations required in the collocation solution. The reference gradients are computed from a high degree and order geopotential model. The solution can be made in terms of mean or point gravity anomalies, height anomalies, or other useful gravimetric quantities depending on the choice of covariance types. Selected for this study were 30 x 30 foot mean gravity and height anomalies. Existing software and new software are utilized to implement the collocation technique. It was determined that satellite gradiometry data at an altitude of 200 km can be used successfully for the determination of 30 x 30 foot mean gravity anomalies to an accuracy of 9.2 mgal from this algorithm. It is shown that the resulting accuracy estimates are sensitive to gravity model coefficient uncertainties, data reduction assumptions and satellite mission parameters.

Robbins, J. W.↗

NASA NTRSDate not supplied

Validation of Remotely Sensed and Modeled Soil Moisture at Forested and Unforested Sites

Soil moisture is an important driver for forest ecosystems, influencing fire occurrence and extent, insect and pathogen impacts, and tree growth, which creates a need for regular, globally extensive soil moisture information that only satellite-based sensors or models can achieve. However, the reliability of soil moisture measurements in forests is not well understood due to a lack of suitable validation sites (especially relative to unforested ecosystems) and interference caused by high vegetation water content on remotely sensed measurements; although recent studies have started to address this gap [1], [2], [3], [4]. Here we validate the performance of multiyear remotely sensed (SMAP/Sentinel), remotely sensed data assimilation modelled (SMAP-L4), and modelled (NLDAS) surface and root zone (0-1 m) soil moisture datasets with data from in-situ sensors at 39 National Ecological Observatory Network (NEON) sites throughout the contiguous US. Due to differences in spatial resolution, NEON soil moisture (~0.2 km measurement zone) correlations were expected to be stronger with the SMAP/Sentinel product (3 km resolution) than with coarser resolution SMAP-L4 (9 km resolution) or NLDAS products (13 km resolution). However, given the sensitivity of satellite measurements to vegetation water content we expected a deterioration in the correlations based on remotely sensed measurements (SMAP/Sentinel and SMAP-L4) as aboveground biomass increased, whereas the model-based data (NLDAS) was expected to be largely insensitive to vegetation type. We recognize that the SMAP/Sentinel product was developed for unforested regions, therefore our application is outside its primary use case. Soil moisture is measured at up to 8 depths in five soil plots spaced up to 40 m apart at each NEON terrestrial site. Correlation parameters were calculated for the three remotely sensed and modelled data products relative to in-situ measurement following Entekhabi et al. [5]. The datasets comprised 94 (SMAP-L4), 28 (SMAP/Sentinel), and 106 (NLDAS) sites-years for surface soils and 13 (SMAP-L4) and 14 (NLDAS) site-years for the root zone. At unforested sites, the performance of the three remotely sensed and modelled data products was similar for surface soils (Table 1). For example, unbiased RMSD (ubRMSD), which SMAP uses as its primary performance metric [6], ranged from 0.05 to 0.06 m3 m-3 (Table 1), indicating the ability of all three products to track changes in soil moisture over time. The performance of the three products deteriorated at forested sites, however, while the difference in performance was modest for SMAP-L4 and NLDAS, the deterioration in SMAP/Sentinel performance was substantial. For instance, SMAP/Sentinel ubRMSD increased from 0.06 to 0.11 m3 m-3 and absolute mean difference (Abs MD; which includes measurement bias and spatial representativeness errors) increased from 0.06 to 0.16 m3 m-3, indicating both a reduction in ability to track temporal changes and absolute amounts of soil moisture in forest ecosystems. SMAP-L4 and NLDAS had lower unbiased RMSD for root zone (0-1 m) than surface soils at both forested and unforested sites (Tables 1 and 2; SMAP/Sentinel does not produce a root zone measurement). However, in most cases the correlation coefficient (r) was lower for the root zone than surface soils, suggesting the lower unbiased RMSD may be attributed to greater temporal stability of soil moisture in the root zone rather than improved data product performance. Mean difference and absolute mean difference, which encompass measurement bias and spatial representativeness errors, were greater for root zone than surface soils at unforested sites for both data products, but the opposite was generally true at forested sites. As with surface soils, there was relatively little change in the performance of SMAP-L4 and NLDAS between the unforested and forested sites. In summary, all three data products were able to adequately represent soil moisture at unforested sites, at least when aggregating across sites. However, while the performance of all three products deteriorated at forested sites, SMAP-L4 and NLDAS maintained sufficient performance to remain suitable for some use cases (ubRMSD <0.06 m3 m-3 and RMSD <0.13 m3 m-3). In contrast, the relatively poorer performance of the SMAP/Sentinel product at forested sites seems insufficient for most use cases (ubRMSD >0.1 m3 m-3 and RMSD >0.2 m3 m-3). We attribute the large reduction in the performance of the SMAP/Sentinel product in forests to its use of C-band wavelengths, which are particularly sensitive to vegetation interference, and apparently outweighed any gains provided by its higher spatial resolution. A combined SMAP/NISAR soil moisture product may provide improved performance relative to SMAP/Sentinel due to NISAR’s use of L-band wavelengths, which are less sensitive to vegetation (NISAR is scheduled for launch in early 2024).

Edward Ayres↗

NASA NTRS2012

Comparison of Predictive Modeling Methods of Aircraft Landing Speed

Expected increases in air traffic demand have stimulated the development of air traffic control tools intended to assist the air traffic controller in accurately and precisely spacing aircraft landing at congested airports. Such tools will require an accurate landing-speed prediction to increase throughput while decreasing necessary controller interventions for avoiding separation violations. There are many practical challenges to developing an accurate landing-speed model that has acceptable prediction errors. This paper discusses the development of a near-term implementation, using readily available information, to estimate/model final approach speed from the top of the descent phase of flight to the landing runway. As a first approach, all variables found to contribute directly to the landing-speed prediction model are used to build a multi-regression technique of the response surface equation (RSE). Data obtained from operations of a major airlines for a passenger transport aircraft type to the Dallas/Fort Worth International Airport are used to predict the landing speed. The approach was promising because it decreased the standard deviation of the landing-speed error prediction by at least 18% from the standard deviation of the baseline error, depending on the gust condition at the airport. However, when the number of variables is reduced to the most likely obtainable at other major airports, the RSE model shows little improvement over the existing methods. Consequently, a neural network that relies on a nonlinear regression technique is utilized as an alternative modeling approach. For the reduced number of variables cases, the standard deviation of the neural network models errors represent over 5% reduction compared to the RSE model errors, and at least 10% reduction over the baseline predicted landing-speed error standard deviation. Overall, the constructed models predict the landing-speed more accurately and precisely than the current state-of-the-art.

Diallo, Ousmane H.↗

NASA NTRS2021

Physics-Based SNOWPACK Model Improves Representation of Near-Surface Antarctic Snow and Firn Density

Estimates of snow and firn density are required for satellite-altimetry-based retrievals of ice sheet mass balance that rely on volume-to-mass conversions. Therefore, biases and errors in presently used density models confound assessments of ice sheet mass balance and by extension ice sheet contribution to sea level rise. Despite this importance, most contemporary firn densification models rely on simplified semi-empirical methods, which are partially reflected by significant modeled density errors when compared to observations. In this study, we present a new drifting-snow compaction scheme that we have implemented into SNOWPACK, a physics-based land surface snow model. We show that our new scheme improves existing versions of SNOWPACK by increasing simulated near-surface (defined as the top 10 m) density to be more in line with observations (near-surface bias reduction from −44.9 to −5.4 kg m−3). Furthermore, we demonstrate high-quality simulation of near-surface Antarctic snow and firn density at 122 observed density profiles across the Antarctic ice sheet, as indicated by reduced model biases throughout most of the near-surface firn column when compared to two semi-empirical firn densification models (SNOWPACK mean bias=−9.7 kg m−3, IMAU-FDM mean bias=−32.5 kg m−3, GSFC-FDM mean bias=15.5 kg m−3). Notably, our analysis is restricted to the near surface where firn density is most variable due to accumulation and compaction variability driven by synoptic weather and seasonal climate variability. Additionally, the GSFC-FDM exhibits lower mean density bias from 7–10 m (SNOWPACK bias=−22.5 kg m−3, GSFC-FDM bias=10.6 kg m−3) and throughout the entire near surface at high-accumulation sites (SNOWPACK bias=−31.4 kg m−3, GSFC-FDM bias=−4.7 kg m−3). However, we found that the performance of SNOWPACK did not degrade when applied to sites that were not included in the calibration of semi-empirical models. This suggests that SNOWPACK may possibly better represent firn properties in locations without extensive observations and under future climate scenarios, when firn properties are expected to diverge from their present state.

Eric Keenan↗

NASA NTRS2009

Astrometry With the Hubble Space Telescope: Trigonometric Parallaxes of Planetary Nebula Nuclei NGC 6853, NGC 7293, ABELL 31, and DeHt 5

We present absolute parallaxes and relative proper motions for the central stars of the planetary nebulae NGC 6853 (The Dumbbell), NGC 7293 (The Helix), Abell 31, and DeHt 5. This paper details our reduction and analysis using DeHt 5 as an example. We obtain these planetary nebula nuclei (PNNi) parallaxes with astrometric data from Fine Guidance Sensors FGS 1r and FGS 3, white-light interferometers on the Hubble Space Telescope. Proper motions, spectral classifications and VJHKT2M and DDO51 photometry of the stars comprising the astrometric reference frames provide spectrophotometric estimates of reference star absolute parallaxes. Introducing these into our model as observations with error, we determine absolute parallaxes for each PNN. Weighted averaging with previous independent parallax measurements yields an average parallax precision, sigma (sub pi)/ pi = 5%. Derived distances are: d(sub NGC6853) = 405(exp +28 sub -25) pc, d(sub NGC7293) = 216(exp +14 sub -12) pc, d(sub Abell31) = 621(exp +91 sub -70) pc, and d(sub DeHt5) = 345(exp +19 sub -17) pc. These PNNi distances are all smaller than previously derived from spectroscopic analyses of the central stars. To obtain absolute magnitudes from these distances requires estimates of interstellar extinction. We average extinction measurements culled from the literature, from reddening based on PNNi intrinsic colors derived from model SEDs, and an assumption that each PNN experiences the same rate of extinction as a function of distance as do the reference stars nearest (in angular separation) to each central star. We also apply Lutz-Kelker bias corrections. The absolute magnitudes and effective temperatures permit estimates of PNNi radii through both the Stefan-Boltzmann relation and Eddington fluxes. Comparing absolute magnitudes with post-AGB models provides mass estimates. Masses cluster around 0.57 solar Mass, close to the peak of the white dwarf mass distribution. Adding a few more PNNi with well-determined distances and masses, we compare all the PNNi with cooler white dwarfs of similar mass, and confirm, as expected, that PNNi have larger radii than white dwarfs that have reached their final cooling tracks.

STARS↗

NASA NTRS2024

Development of a Data Fusion Methodology for Lineload Aerodynamic Databases for a Launch Vehicle during Liftoff and Transition

The need for databases for the distributed loading on launch vehicles during the early portion of flight necessitates the use of expensive computational flows in regimes where wake effects dominate. While also being expensive, this is a regime that computational tools tend to historically have problems simulating accurately. To help tackle this problem, a method of data fusion to combine computational results to wind tunnel derived force and moment data is developed. Using this method, significant reduction in computational costs and increases in confidence of the final product is possible and has been used to generate several databases for the Space Launch System (SLS) at NASA. While the full details of database generation are not part of this work, the crucial method at its core is developed here. Two SLS geometries are used throughout the work to demonstrate the techniques. These are two of the larger geometries and represent both planned crewed missions to the Moon as well as potential cargo missions to deep space. The method uses principal component analysis (PCA) to generate a reduced ordered model (ROM) to help fill in the full parameter space. Other similar techniques are explored, but were not found to have a significant result on the predictions of the ROM. Because the full number of components are kept to generate the model, this lack of difference is expected. This method is then extended to ensure that predicted surfaces match trusted force and moment data derived from wind tunnel testing. This extension is done by setting up a constrained optimization problem in order to minimize the deviation from the surface resolved computational data while still integrating to the desired values. When generating the constrained optimization problem, a weighting factor to balance these competing needs is introduced. The work compares previously introduced weighting terms from similar work to the proposed terms and shows that the previously used terms do not have as desirable behavior in this flow regime. This method is then expanded by developing a technique to incorporate uncertainty quantification into the developed data fusion methodology. This expansion takes a two pronged approach. One examines transferring the uncertainties in the force and moment database and characterizes how those adjustments change the predicted lineloads. The second looks at model form error and looks how rebuilding the model using slightly different data changes the predictions. These two terms are then combined in order to create an uncertainty model that takes both effects into account. The limitations of the proposed methods is then discussed as well as possible techniques to address these shortcomings.

Launch Vehicles↗

NASA NTRSDate not supplied

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↗