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Quantifying Uncertainties in Nighttime Light Retrievals From Suomi-NPP and NOAA-20 VIIRS Day/Night Band Data

Satellite observations of nighttime lights (NTL) from Suomi-NPP and NOAA-20 VIIRS Day/Night Band data have been widely used to estimate human activities. Long-term changes such as urban development and abrupt short-term changes such as power outages have been monitored from temporal NTL acquired by satellites. While high temporal NTL variation has been found across NTL data of varying temporal scale (e.g., daily, monthly, and annual composites), the sources of measurement error and uncertainty are poorly understood. This paper quantifies the sources of VIIRS-derived NTL uncertainty due to view-illumination geometry, surface Bidirectional Reflectance Distribution Function (BRDF)/albedo, and the effects of snow cover, lunar irradiance, aerosol loading, cloud mask, vegetation, geometry, and ephemeral artifacts (e.g., the Aurora Borealis). Based on this current assessment of NASA Black Marble retrievals (VNP46, Collection V001), we found that angular and atmospheric effects dominate retrieval uncertainty. Errors introduced by upstream data inputs (e.g., a coarser nighttime snow cover flag and misclassification errors in the existing VIIRS nighttime cloud mask) were also found to impact retrieval quality. Despite these challenges, a consistent daily NTL time series record can be routinely generated from top-of-atmosphere VNP46 radiances. Key recommendations include: (1) the use of lunar-BRDF adjusted and atmospherically corrected NTL (i.e., as identified as high-quality retrievals in the VNP46 QA fields), (2) development and improvement to the VIIRS snow cover and cloud masks algorithms to accurately reflect NTL retrieval conditions, (3) characterizing seasonal variations in NTL due to vegetation and snow, (4) reducing geometric effects due to the spatial mismatch of gridded pixel and observation footprint, (5) employing angularly-consistent NTL observations from multiple VIIRS instruments (i.e., Suomi-NPP and NOAA-20) to reduce pixel-based uncertainties and address persistent data gaps, and (6) being mindful of surface-reflected radiance from aurora events at mid-to-high latitudes.

Zhuosen Wang↗

Multisectoral Climate Impact Hotspots in a Warming World

The impacts of global climate change on different aspects of humanity's diverse life-support systems are complex and often difficult to predict. To facilitate policy decisions on mitigation and adaptation strategies, it is necessary to understand, quantify, and synthesize these climate-change impacts, taking into account their uncertainties. Crucial to these decisions is an understanding of how impacts in different sectors overlap, as overlapping impacts increase exposure, lead to interactions of impacts, and are likely to raise adaptation pressure. As a first step we develop herein a framework to study coinciding impacts and identify regional exposure hotspots. This framework can then be used as a starting point for regional case studies on vulnerability and multifaceted adaptation strategies. We consider impacts related to water, agriculture, ecosystems, and malaria at different levels of global warming. Multisectoral overlap starts to be seen robustly at a mean global warming of 3 degC above the 1980-2010 mean, with 11% of the world population subject to severe impacts in at least two of the four impact sectors at 4 degC. Despite these general conclusions, we find that uncertainty arising from the impact models is considerable, and larger than that from the climate models. In a low probability-high impact worst-case assessment, almost the whole inhabited world is at risk for multisectoral pressures. Hence, there is a pressing need for an increased research effort to develop a more comprehensive understanding of impacts, as well as for the development of policy measures under existing uncertainty.

policies↗

J-85 jet engine noise measured in the ONERA S1 wind tunnel and extrapolated to far field

Noise from a J-85 turbojet with a conical, convergent nozzle was measured in simulated flight in the ONERA S1 Wind Tunnel. Data are presented for several flight speeds up to 130 m/sec and for radiation angles of 40 to 160 degrees relative to the upstream direction. The jet was operated with subsonic and sonic exhaust speeds. A moving microphone on a 2 m sideline was used to survey the radiated sound field in the acoustically treated, closed test section. The data were extrapolated to a 122 m sideline by means of a multiple-sideline source-location method, which was used to identify the acoustic source regions, directivity patterns, and near field effects. The source-location method is described along with its advantages and disadvantages. Results indicate that the effects of simulated flight on J-85 noise are significant. At the maximum forward speed of 130 m/sec, the peak overall sound levels in the aft quadrant were attentuated approximately 10 dB relative to sound levels of the engine operated statically. As expected, the simulated flight and static data tended to merge in the forward quadrant as the radiation angle approached 40 degrees. There is evidence that internal engine or shock noise was important in the forward quadrant. The data are compared with published predictions for flight effects on pure jet noise and internal engine noise. A new empirical prediction is presented that relates the variation of internally generated engine noise or broadband shock noise to forward speed. Measured near field noise extrapolated to far field agrees reasonably well with data from similar engines tested statically outdoors, in flyover, in a wind tunnel, and on the Bertin Aerotrain. Anomalies in the results for the forward quadrant and for angles above 140 degrees are discussed. The multiple-sideline method proved to be cumbersome in this application, and it did not resolve all of the uncertainties associated with measurements of jet noise close to the jet. The simulation was complicated by wind-tunnel background noise and the propagation of low frequency sound around the circuit.

Soderman, Paul T.↗

Estimating Sonic Boom Metrics Across a Community Using a Kalman Filter

As part of the Quesst mission, NASA will fly the X‑59 aircraft over selected communities to evaluate community responses to low-intensity sonic booms. The purpose of these community tests is to determine the dose-response relationship between the noise exposure metrics and the community response. The independent variables for the dose-response relationship are the noise exposure metrics experienced by survey respondents within the community. Two sources of noise exposure metrics are available in each community: measurements at sparse locations throughout the community, and calculations from propagation models across the community. Both the measurements and calculations are subject to uncertainty. A Kalman filter is proposed to combine the measured and calculated noise exposure metrics to obtain the best estimate of the true noise exposure metrics across the community. The noise exposure metrics estimated by the Kalman filter have lower uncertainty than either the measured or calculated noise exposure metrics alone. Simulations demonstrate that the Kalman filter produces a more accurate estimate of the true noise exposure metrics than other noise estimation methods.

Sonic boom↗

Progress toward double-differential cross-section measurements of single charged-pion production in charged current muon neutrino interactions on argon with SBND

Resonant neutrino–nucleus processes constitute a significant portion of neutrino interactions in the few-GeV energy region. Charged-current interactions with a muon and one single charged pion in the final state (CC1$\pi$) are primarily sensitive to resonant processes, while also receiving contributions from non-resonant processes and being strongly affected by nuclear effects and final-state interactions. A precise understanding of this channel is essential for improving neutrino interaction models and reducing systematic uncertainties in oscillation measurements. The Short-Baseline Near Detector (SBND) at Fermilab has collected the largest neutrino–argon dataset to date, providing an excellent opportunity to study CC1$\pi$ interactions on argon. This analysis aims to improve existing single-differential cross-section measurements by reporting results in a variety of kinematic variables and to perform the first double-differential CC1$\pi$ cross-section measurement on argon, using novel techniques for pion energy reconstruction.

Pelegrina-Gutiérrez, Luis [Granada U.] (ORCID:0000↗

Pulsed Airborne Lidar Measurements of Atmospheric CO2 Column Absorption and Line Shapes from 3-13 km Altitudes

We have developed a pulsed lidar technique for measuring the tropospheric CO2 concentrations as a candidate for NASA's planned ASCENDS space mission. Our technique uses two pulsed laser transmitters allowing simultaneous measurement of a CO2 absorption line in the 1570 nm band, O2 extinction in the Oxygen A-band and surface height and backscatter. The lidar measures the energy and time of flight of the laser echoes reflected from the atmosphere and surface. The lasers are rapidly and precisely stepped in wavelength across the CO2 line and an O2 line region during the measurement. The direct detection receiver uses a telescope and photon counting detectors, and measures the background light and energies of the laser echoes from the surface along with scattering from any aerosols in the path. The gas extinction and column densities for the CO2 and O2 gases are estimated from the ratio of the on- and off- line signals via the DIAL technique. Time gating is used to isolate the laser echo signals from the surface, and to reject laser photons scattered in the atmosphere. The time of flight of the laser pulses are also used to estimate the height of the scattering surface and to identify cases of mixed cloud and ground scattering. We have developed an airborne lidar to demonstrate the CO2 measurement from the NASA Glenn Lear-25 aircraft. The airborne lidar steps the pulsed laser's wavelength across the selected CO2 line with 20 steps per scan. The line scan rate is 450 Hz, the laser pulse widths are 1 usec, and laser pulse energy is 24 uJ. The time resolved laser backscatter is collected by a 20 cm telescope, detected by a photomultiplier and is recorded by a photon counting system. We made initial airborne measurements on flights during fall 2008. Laser backscatter and absorption measurements were made over a variety of land and water surfaces and through thin clouds. The atmospheric CO2 column measurements using the 1572.33 nm CO2 lines. Two flights were made above the US Department of Energy's (DOE) SGP ARM site at altitudes from 3-8 km. These flights were coordinated with DOE investigators who flew an in-situ CO2 sensor on a Cessna aircraft under the path. The increasing CO2 line absorptions with altitudes were evident and comparison with in-situ measurements showed agreements to 6 ppm. In spring 2009 we improved the aircraft's nadir window and during July and August we made 9 additional 2 hour long flights and measured the atmospheric CO2 absorption and line shapes using the 1572.33 nm CO2 line. Measurements were made at stepped altitudes from 3-13 km over a variety of surface types in Nebraska, Illinois, the SGP ARM site, and near and over the Chesapeake Bay in North Carolina and eastern Virginia. Strong laser signals and clear CO2 line shapes were observed at all altitudes, and some measurements were made through thin clouds. The flights over the ARM site were underflown with in-situ measurements made from the DOE Cessna. Analysis shows that the average signal levels follow predicted values, the altimetry measurements had an uncertainty of about 4 m, and that the average optical line depths follow the number density calculated from in-situ sensor readings. The Oklahoma and east coast flights were coordinated with a LaRC/ITT CO2 lidar on the LaRC UC-12 aircraft, a LaRC in-situ CO2 sensor, and the Oklahoma flights also included a JPL CO2 lidar on a Twin Otter aircraft. More details of the flights, measurements, analysis and scaling to space will be described in the presentation.

Abshire, James↗

Infrared Imagery of Shuttle (IRIS). Task 2

An opto-electronic breadboard of 10 channels of the IR temperature measuring system was produced as well as a scaled up portion of the tracking system reticle in order to verify Task 1 assumptions. The breadboards and the tests performed on them are described and both raw and reduced data are presented. Tests show that the electronics portion of the imaging system will provide a dc to 10,000 Hz bandwidth that is flat and contributes no more than 0.4% of full-scale uncertainty to the measurement. Conventional packaging is adequate for the transresistance amplifier design. Measurement errors expected from all sources tested are discussed.

Chocol, C. J.↗

Using real-time nuclear activation detectors for measuring neutron yields from D(D, T)n reactions on the national ignition facility (NIF)

The National Ignition Facility (NIF) has 48 Real-Time Nuclear Activation Detectors distributed around the target chamber capable of measuring deuterium-triton reaction neutron yields with high precision. Here, in this work, we extend this functionality to deuterium–deuterium (DD) reaction neutrons using a nuclear reaction that occurs in the detector’s scintillator material. The corresponding decay of the activated material has a very short half-life of 5 s, which necessitates rapid data collection immediately following an experiment. In this regime, dead time can be very high (>50%) adding significant uncertainty to the measurement. To combat this, we have developed a dead time model that can self-consistently describe the measured data. Initial results show reasonable agreement (within 20%) with DD neutron yields from neutron time-of-flight spectrometers.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Testing Seam Concepts for Advanced Multilayer Insulation

Multilayer insulation (MLI) is considered the state of the art insulation for cryogenic propellant tanks in the space environment. MLI traditionally consists of multiple layers of metalized films separated by low conductivity spacers. In order to better understand some of the details within MLI design and construction, GRC has been investigating the heat loads caused by multiple types of seams. To date testing has been completed with 20 layer and 50 layer blankets. Although a truly seamless blanket is not practical, a blanket lay-up where each individual layer was overlapped and tapped together was used as a baseline for the other seams tests. Other seams concepts tested included: an overlap where the complete blanket was overlapped on top of itself; a butt joint were the blankets were just trimmed and butted up against each other, and a staggered butt joint where the seam in the out layers is offset from the seam in the inner layers. Measured performance is based on a preliminary analysis of rod calibration tests conducted prior to the start of seams testing. Baseline performance for the 50 layer blanket showed a measured heat load of 0.46 Watts with a degradation to about 0.47 Watts in the seamed blankets. Baseline performance for the 20 layer blanket showed a measured heat load of 0.57 Watts. Heat loads for the seamed tests are still begin analyzed. So far analysis work has suggested the need for corrections due to heat loads from both the heater leads and the instrumentation wires. A careful re-examination of the calibration test results with these factors accounted for is also underway. This presentation will discuss the theory of seams in MLI, our test results to date, and the uncertainties in our measurements.

multilayer insulation↗

Optical Strain Measurement of an Inflated Cylinder using Photogrammetry with Application to Scientific Balloons

A study is presented using photogrammetry to measure the biaxial strain in an inflated cylinder. Two cylinders constructed from polyethylene and each approximately 222 mm in diameter and 930 mm in length were studied. The first had a 0.038 mm wall thickness while the second had a 0.02 mm wall thickness. The cylinders were inflated to a maximum pressure of 1379 Pa. The strain was determined from data collected from 60 retro-reflective targets arranged in a 12 x 5 grid. The uncertainty of the measurement system was determined to be 0.08, 0.04 and 0.06 mm in the x, y, and z directions respectively. The hoop and meridional strains determined from displacement data were compared to values obtained from a finite element analysis of a related proxy problem. The predicted hoop strains showed good agreement over the entire range of pressures while the meridional strains showed good agreement at the lower pressures.

Blandino, Joseph R.↗

Constraints on the Spacetime Variation of the Fine-structure Constant Using DESI Emission-line Galaxies

We present strong constraints on the spacetime variation of the fine-structure constant α using the Dark Energy Spectroscopic Instrument (DESI). In this pilot work, we utilize ∼110,000 galaxies with strong and narrow [O III ] λλ4959, 5007 emission lines to measure the relative variation Δα/α in space and time. The [O III ] doublet is arguably the best choice for this purpose owing to its wide wavelength separation between the two lines and its strong emission in many galaxies. Our galaxy sample spans a redshift range of 0 < z < 0.95, covering half of all cosmic time. We divide the sample into subsamples in 10 redshift bins (Δz = 0.1), and calculate Δα/α for the individual subsamples. The uncertainties of the measured Δα/α are roughly between 2 × 10 −6 and 2 × 10 −5 . We find an apparent α variation with redshift at a level of Δα/α = (2–3) × 10 −5 . This is highly likely to be caused by systematics associated with wavelength calibration, since such small systematics can be caused by a wavelength distortion of 0.002–0.003 Å, which is beyond the accuracy that the current DESI data can achieve. We refine the wavelength calibration using sky lines for a small fraction of the galaxies, but this does not change our main results. We further probe the spatial variation of α in small redshift ranges, and do not find obvious, large-scale structures in the spatial distribution of Δα/α. As DESI is ongoing, we will include more galaxies, and by improving the wavelength calibration, we expect to obtain a better constraint that is comparable to the strongest current constraint.

79 ASTRONOMY AND ASTROPHYSICS↗

Using Gaia Data 2 to Constrain Local Dark Matter Density and Thin Dark Disk

We use stellar kinematics from the latest Gaia data release (DR2) to measure the local dark matter (DM) density ρDM in a heliocentric cylinder of radius R = 150 pc and half-height z = 200 pc. We also explore the prospect of using our analysis to estimate the DM density in local substructure by setting constraints on the surface density and scale height of a thin dark disk aligned with the baryonic disk and formed due to dissipative dark matter self-interactions. Performing the statistical analysis within a Bayesian framework for three types of tracers, we obtain ρDM = 0.016 ± 0.010 Mꙩ/p c 3 for A stars; early G stars give a similar result, while F stars yield a significantly higher value. For a thin dark disk, A stars set the strongest constraint: excluding surface densities (5–12) Mꙩ/pc 2 for scale heights below 100 pc with 95% confidence. The upper bound of this constraint implies . 1% of the Milky Way DM mass is present in a dissipative dark sector. Comparing our results with those derived using Tycho-Gaia Astrometric Solution (TGAS) data, we find that the uncertainty in our measurements of the local DM content is dominated by systematic errors that arise from assumptions of our dynamical analysis in the low z region. Furthermore, there will only be a marginal reduction in these uncertainties with more data in the Gaia era. We comment on the robustness of our method and discuss potential improvements for future work.

dark matter theory↗

Multiplicity dependence of ϒ production at forward rapidity in pp collisions at $\sqrt{s}$ = 13 TeV

The measurement of ϒ(1S), ϒ(2S), and ϒ(3S) yields as a function of the charged-particle multiplicity density, d N ch /d η , using the ALICE experiment at the LHC, is reported in pp collisions at √s = 13 TeV. The Υ meson yields are measured at forward rapidity (2.5 < y < 4) in the dimuon decay channel, whereas the charged-particle multiplicity is defined at central rapidity (| η | <1). Both quantities are divided by their average value in minimum bias events to compute the self-normalized quantities. The increase of the self-normalized ϒ(1S), ϒ(2S), and ϒ(3S) yields is found to be compatible with a linear scaling with the self-normalized d N ch /d η , within the uncertainties. The self-normalized yield ratios of excited-to-ground ϒ states are compatible with unity within uncertainties. Similarly, the measured double ratio of the self-normalized ϒ(1S) to the self-normalized J/ ψ yields, both measured at forward rapidity, is compatible with unity for self-normalized charged-particle multiplicities beyond one. The measurements are compared with theoretical predictions incorporating initial or final state effects.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The 55Fe X-ray Energy Response of Mercury Cadmium Telluride Near-Infrared Detector Arrays

A technique involving Fe-55 X-rays provides a straightforward method to measure the response of a detector. The detector's response can lead directly to a calculation of the conversion gain (e(-) ADU(-1) ), as well as aid detector design and performance studies. We calibrate the Fe-15 X-ray energy response and pair production energy of HgCdTe using 8 HST WFC3 1.7 micron flight grade detectors. The results show that each Ka X-ray generates 2273 +/- 137 electrons, which corresponds to a pair-production energy of 2.61 +/- 0.16 eV. The uncertainties are dominated by our knowledge of the conversion gain. In future studies, we plan to eliminate this uncertainty by directly measuring conversion gain at very low light levels.

Fox, Ori↗

Attitude stability of LDEF: Refinement of results from the silver pinhole camera

A measurement was previously described of the angular offset and attitude stability of the LDEF spacecraft using a simple pinhole camera device in the UAH experiment A0114. This device uses a silver surface to record the impact zone of atmospheric atomic oxygen passing through a small pinhole on the front surface of the satellite. The shape and size of this zone are well defined if the satellite velocity and gas temperature are known. The circular symmetry of the zone would be distorted by oscillation of the LDEF about its stable attitude, or by the effect of the co-rotation of the Earth's atmosphere for cases of satellites in nonequatorial orbits. The observed ellipticity of 1.05 with the major axis in the yaw direction is equivalent to an oscillation of + or - 0.2 deg about the stable attitude. The uncertainty in that measurement was estimated at about 0.1 deg. A refined analysis based on summing distributions of flux versus incidence angle for a large number of orbital positions, and including a co-rotating atmosphere, indicates that the combined distributions produce a result consistent with the measured exposed spot. It is suggested that, within the precision of the measurements, no actual oscillation of the LDEF is required to produce the results. Thus, the LDEF may have maintained a stable attitude to better than 0.1 deg, even under conditions of maximum aerodynamic perturbation when the silver oxygen record was made. This error is some two orders of magnitude lower than the predicted uncertainty in yaw oscillation and may indicate that the predict methodologies are too conservative.

Peters, P. N.↗

Conceptual Designs for Irradiation Creep Testing of SiC in HFIR

Understanding irradiation creep of nuclear fuel cladding is important to properly size the initial fuel-cladding gap and understand when pellet-cladding contact is expected to occur due to a combination of fuel swelling and cladding creep-down. Irradiation creep also plays a role in relaxing stresses that develop in-pile. Silicon carbide fiber–reinforced silicon carbide matrix (SiC/SiC) composites are the leading long-term accident-tolerant fuel cladding concept for light-water reactors (LWRs). Although some limited data are available regarding irradiation creep of the individual constituents (fibers, matrix), data regarding irradiation creep of SiC/SiC composites are currently insufficient. Additional data regarding irradiation creep compliance and the rupture lifetime (combination of creep and slow crack growth) are needed to understand material limitations. This work describes the design and development of two irradiation vehicles that are being pursued for testing SiC/SiC concepts in the High Flux Isotope Reactor (HFIR). The first is a passive experiment, referred to as the PRECISE experiment, that leverages the constant coolant pressure of HFIR to compress a metallic bellows and provide a well-characterized load to drive creep in a SiC/SiC dog bone specimen. The total creep strain would be quantified post-irradiation by measuring dimensional changes of the specimen length as well as local dimensional changes within the gauge region. Non-stressed specimens would also be irradiated under the same conditions to provide an indication of dimensional changes due to radiation-induced swelling in the absence of creep. A second, more complex experiment, referred to as the INSITE experiment, is being designed in parallel that would use pneumatics to pressurize a metal bellows and linear variable differential transformers (LVDTs) to measure the specimen displacement in situ during irradiation. Such an experiment would provide significantly more data regarding the evolution of the creep compliance as a function of dose and applied stress within a single experiment but would require significantly more development time and cost to execute. The primary concern with the INSITE experiment is the accuracy, reliability, and expected lifetime of the LVDTs during irradiation at elevated temperatures. Efforts are being made to adjust the experiment design and operating procedure to limit LVDT temperatures and mitigate or otherwise compensate for uncertainties due to factors such as temperature fluctuations, creep in the surrounding structural materials, and drift of the LVDTs. This work describes the experiment designs, thermal and structural analysis that were performed to ensure that the desired temperature and stress conditions can be achieved, some initial sensitivity analyses to predict the evolution of the radiation-induced specimen displacements, and potential sources of uncertainty in the measurements. Out-of-pile testing is being performed in parallel to confirm that the test trains achieve the expected stress states in the specimens and do not result in prohibitive stress concentrators (e.g., in the grip regions) that might risk pre-mature failure. The PRECISE experiments are proceeding toward fabrication and assembly with HFIR insertion planned during fiscal year 2026. The INSITE experiment is progressing toward out-of-pile demonstrations, which will provide more conclusive evidence regarding the feasibility of executing these tests in HFIR or whether alternative displacement monitoring techniques may need to be considered.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Revised ion temperatures for Voyager plasma measurements in the Io plasma torus

A calculation error in previous computations of ion temperatures in the Io plasma torus of the Jovian magnetosphere from Voyager plasma-science-experiment measurements is reported, and its effects on subsequently published studies are evaluated. It is found that the temperatures reported by Bagenal et al. (1980) and Bagenal and Sullivan (1981) for Jupiter and by Bridge et al. (1981) for Saturn are half the correct values, with major effects on ionic-species scale heights, plasma-density maps, and flux-tube content estimations. The temperatures given by Bridge et al. (1979) and McNutt et al. (1981) are not affected by the error. A corrected isodensity contour map is presented, and uncertainties in the measurement of ion temperatures are discussed.

Bagenal, F.↗

Use of nonlinear identification in robust attitude and attitude rate estimation for SAMPEX

A method is described for obtaining optimal attitude estimation/identification algorithms for spacecraft lacking attitude rate measurement devices (rate gyros), and then demonstrated using actual flight data from the Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX) spacecraft. SAMPEX does not have on-board rate sensing, and relies on sun sensors and a three-axis magnetometer for attitude determination. The absence of rate data normally reduces both the total amount of data available and the sampling density (in time) by a substantial fraction. In addition, attitude data is occasionally unavailable (for example, during sun occultation). As a result, the sensitivity of the estimates to model uncertainty and to measurement noise increases. In order to maintain accuracy in the attitude estimates, there is an increased need for accurate models of the rotational dynamics. The Minimum Model Error(MME)/Least Square Correlation(LSC) algorithm accurately identifies an improved model for SAMPEX to be used during periods of complete data loss or extreme noise. The model correction is determined by estimating only one orbit(the identification pass) just prior to the assumed data loss(the prediction pass). The MME estimator correctly predicted the states during the identification phase, but more importantly determines the necessary model correction trajectory, d(t). The LSC algorithm is then used to find this trajectory's functional form, H(x(t)). The results show significant improvement of the new corrected model's attitude estimates as compared to the original uncorrected model's estimates. The possible functional form of the correction term is limited at this point in the study to functions strictly of the estimated states. The results, however, strongly suggest that functions based on the relative position of the satellite may also be possible candidates for future consideration.

Mook, D. Joseph↗