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NASA NTRS1992

Estimation of effective aerodynamic roughness with altimeter measurements

A new method is presented for estimating the aerodynamic roughness length of heterogeneous land surfaces and complex landscapes using elevation measurements performed with an airborne laser altimeter and the Seasat radar altimeter. Land surface structure is characterized at increasing length scales by considering three basic landscape elements: (1) partial to complete canopies of herbaceous vegetation; (2) sparse obstacles (e.g., shrubs and trees); and (3) local relief. Measured parameters of land surface geometry are combined to obtain an effective aerodynamic roughness length which parameterizes the total atmosphere-land surface stress.

Menenti, M.↗

NASA NTRS2006

Dilution of Precision-Based Lunar Navigation Assessment for Dynamic Position Fixing

The NASA Vision for Space Exploration is focused on the return of astronauts to the Moon. While navigation systems have already been proven in the Apollo missions to the moon, the current exploration campaign will involve more extensive and extended missions requiring new concepts for lunar navigation. In contrast to Apollo missions, which were limited to the near-side equatorial region of the moon, missions under the Exploration Systems Initiative will require navigation on the moon's limb and far-side. As these regions have poor Earth visibility, a navigation system comprised solely of Earth-based tracking stations will not provide adequate navigation solutions in these areas. In this paper, a Dilution of Precision (DoP) based analysis of the performance of a network of Moon orbiting satellites is provided. The analysis extends previous analysis of a Lunar Network (LN) of navigation satellites by providing an assessment of the capability associated with a variety of assumptions. These assumptions are with regard to the navigation receiver and satellite visibility. The assessment is accomplished by making appropriately formed estimates of DoP. Different adaptations of DoP (i.e. GDoP, PDoP, etc.) are associated with a different set of assumptions regarding augmentations to the navigation receiver or transceiver. A significant innovation described in this paper is the "Generalized" Dilution of Precision. In the same sense that the various versions of DoP can be represented as a functional of the observability grammian, Generalized DoP is defined as a functional of the sum of observability grammians associated with a batch of radiometric measurements. Generalized DoP extends the DoP concept to cases in which radiometric range and range-rate measurements are integrated over time to develop an estimate of user position (referred to here as a 'dynamic' solution.) Generalized DoP allows for the inclusion of cases in which the receiver location is underdetermined when assessed in the usual 'kinematic' sense. The Generalized DoP concept is thereby a method to assess the navigation capability associated with constellations with sparse coverage. This alleviates the burden of performing a full "covariance analysis" for each point on the surface of the Moon.

Sands, Obed S.↗

NASA NTRS2006

Dilution of precision-based lunar navigation assessment for dynamic position fixing

The NASA vision of exploration is focused on the return of astronauts to the Moon [1]. While navigation systems have already been proven in the Apollo missions to the moon, the current exploration campaign will involve more extensive and extended missions requiring new concepts for lunar navigation. In contrast to Apollo missions, which were limited to the near-side equatorial region of the moon, missions under the Exploration Systems Initiative will require navigation on the moon’s limb and far-side. As these regions have poor Earth visibility, a navigation system comprised solely of Earth-based tracking stations will not provide adequate navigation solutions in these areas. In this paper, a Dilution of Precision (DoP) based analysis of the performance of a network of Moon orbiting satellites is provided. The analysis extends previous analysis of a Lunar Network (LN) of navigation satellites by providing an assessment of the capability associated with a variety of assumptions regarding the navigation receiver and satellite visibility. The assessment is accomplished by making appropriately formed estimates of DoP, with different adaptations of DoP (i.e. GDoP, PDoP, etc.) being associated with a different set of assumptions regarding augmentations to the navigation receiver or transceiver A significant innovation described in this paper is the “Generalized” Dilution of Precision. In the same sense that the various versions of DoP can be represented as a functional of the observability grammian, Generalized DoP is defined as a functional of the sum of observability grammians associated with a batch of radiometric measurements. Generalized DoP extends the DoP concept to cases in which radiometric range and range-rate measurements are integrated over time to develop an estimate of user position (referred to here as a ‘dynamic’ solution.) Generalized DoP allows for the inclusion of cases in which the receiver location is underdetermined when assessed in the usual ‘kinematic’ sense. The Generalized DoP concept is thereby a method to assess the navigation capability associated with constellations with sparse coverage without the burden of performing a full “covariance analysis” for each point on the surface of the Moon.

Berry, Kevin↗

NASA NTRS2011

Object-based Mapping of the Circumpolar Taiga-Tundra Ecotone with MODIS Tree Cover

The circumpolar taiga-tundra ecotone was delineated using an image segmentation based mapping approach with multi-annual MODIS Vegetation Continuous Fields (VCF) tree cover data. Circumpolar tree canopy cover (TCC) throughout the ecotone was derived by averaging MODIS VCF data from 2000 - 2005 and adjusting the averaged values using linear equations relating MODIS TCC to Quickbird-derived tree cover estimates. The adjustment helped mitigate VCF's overestimation of tree cover in lightly forested regions. An image segmentation grouped pixels representing similar tree cover into polygonal features (objects) that form the map of the transition zone. Eachfeature represents an area much larger than the 500m MODIS pixel to characterize thepatterns of sparse forest patches on a regional scale. Comparisons of the adjusted average tree cover data were made with (1) two existing tree line definitions aggregated for each 1deg longitudinal interval in North America and Eurasia and (2) Landsat-derived Canadianproportion of forest cover for Canada. The adjusted TCC from MODIS VCF shows, on average, greater than 12% TCC for all but one regional zone at the intersection with independently delineated tree lines. Adjusted values track closely with Canadian proportion of forest cover data in areas of low tree cover. Those polygons near the boreal/tundra interface with either (1) mean adjusted TCC values between 5-20% , or (2) mean adjusted TCC values <5% but with a standard deviation > 5% were used to identify the ecotone.

Ransom, Kenneth J.↗

NASA NTRS2016

Uncertainty and Sensitivity Analysis of Afterbody Radiative Heating Predictions for Earth Entry

The objective of this work was to perform sensitivity analysis and uncertainty quantification for afterbody radiative heating predictions of Stardust capsule during Earth entry at peak afterbody radiation conditions. The radiation environment in the afterbody region poses significant challenges for accurate uncertainty quantification and sensitivity analysis due to the complexity of the flow physics, computational cost, and large number of un-certain variables. In this study, first a sparse collocation non-intrusive polynomial chaos approach along with global non-linear sensitivity analysis was used to identify the most significant uncertain variables and reduce the dimensions of the stochastic problem. Then, a total order stochastic expansion was constructed over only the important parameters for an efficient and accurate estimate of the uncertainty in radiation. Based on previous work, 388 uncertain parameters were considered in the radiation model, which came from the thermodynamics, flow field chemistry, and radiation modeling. The sensitivity analysis showed that only four of these variables contributed significantly to afterbody radiation uncertainty, accounting for almost 95% of the uncertainty. These included the electronic- impact excitation rate for N between level 2 and level 5 and rates of three chemical reactions in uencing N, N(+), O, and O(+) number densities in the flow field.

West, Thomas K., IV↗

NASA NTRSDate not supplied

Forecasting with the GEOS-CF System and Other NASA Resources to Support Air Quality Management

Air quality (AQ) is a major and growing concern for public health around the world. Economic development, population growth, and climate change are all expected to exacerbate already poor AQ in many regions. Furthermore, AQ is often only sparsely monitored with reference-grade in-situ instruments. NASA resources and products have the potential to help in addressing this AQ data gap. The GEOS-CF (Goddard Earth Observing System – Composition Forecasting) global atmospheric composition modeling system is run each day at a global scale to provide recent estimates and five-day forecasts at hourly temporal resolution of atmospheric constituents relevant to AQ. NASA satellite missions (along with those of other space agencies) provide remotely-sensed estimates of atmospheric composition relevant to AQ. This paper gives a brief overview of these capabilities, and outlines the efforts underway to combine model forecasts, satellite retrievals, and surface-based measurements to provide more comprehensive and accurate estimates and forecasts of local AQ which will be broadly applicable and accessible globally.

GEOS-CF↗

NASA NTRS2024

Forecasting with the GESO-CF System and Other NASA Resources to Support Air Quality Management

Air quality (AQ) is a major and growing concern for public health around the world. Economic development, population growth, and climate change are all expected to exacerbate already poor AQ in many regions. Further-more, AQ is often only sparsely monitored with reference-grade in-situ instruments. NASA resources and products have the potential to help in addressing this AQ data gap. The GEOS-CF (Goddard Earth Observing System –Composition Forecasting) global atmospheric composition modeling system is run each day at a global scale to provide recent estimates and five-day forecasts at hourly temporal resolution of atmospheric constituents relevant to AQ. NASA satellite missions (along with those of other space agencies) provide remotely-sensed estimates of atmospheric composition relevant to AQ. This paper gives a brief over-view of these capabilities, and outlines the efforts underway to combine model forecasts, satellite retrievals, and surface-based measurements to provide more comprehensive and accurate estimates and forecasts of local AQ which will be broadly applicable and accessible globally.

Forecasting↗

NASA NTRS1984

Efficient spares matrix multiplication scheme for the CYBER 203

This work has been directed toward the development of an efficient algorithm for performing this computation on the CYBER-203. The desire to provide software which gives the user the choice between the often conflicting goals of minimizing central processing (CPU) time or storage requirements has led to a diagonal-based algorithm in which one of three types of storage is selected for each diagonal. For each storage type, an initialization sub-routine estimates the CPU and storage requirements based upon results from previously performed numerical experimentation. These requirements are adjusted by weights provided by the user which reflect the relative importance the user places on the resources. The three storage types employed were chosen to be efficient on the CYBER-203 for diagonals which are sparse, moderately sparse, or dense; however, for many densities, no diagonal type is most efficient with respect to both resource requirements. The user-supplied weights dictate the choice.

Lambiotte, J. J., Jr.↗

NASA NTRSDate not supplied

Efficient Parametric Uncertainty Analysis of an Earth Entry Vehicle Concept Using Least Angle Regression

The objective of this work was to outline and apply an efficient and accurate parametric un-certainty propagation approach to the analysis of convective heating on an Earth entry vehicle concept. The described approach was based on Least Angle Regression used to solve a sparse and underdetermined linear system in the point-collocation non-intrusive polynomial chaos surrogate method. This approach involved an iterative process to computing the non-zero terms of the underlying polynomial chaos model using only enough samples to converge uncertainty interval predictions and Sobol index values based global nonlinear sensitivity estimates. The Earth entry vehicle was analyzed at three points along a representative trajectory for a Mars return mission. 329 sources of uncertainty were identified in the computational fluid dynamics model used to predict the forebody convective heating. These included uncertainty in flow field chemical rates, collision integrals, heats of formation, surface finite rate char model reaction rates, wall roughness height, and the turbulent Schmidt number. Results from this study showed that convective heating uncertainty as high as 50% of the nominal was predicted with only about 50 evaluations of the computational model. This was far fewer than would be required for a sampling-based approach or a full basis polynomial chaos model, which would have required over 50,000 samples. Additionally, results showed that over 90% of the total convective heating uncertainty was due to uncertainty in the N2catalytic rate on the surface, while the remainder of the uncertainty was attributed to the turbulent Schmidt number and the wall roughness uncertainties.

Thomas K West IV↗

NASA NTRS2018

Random Variables with Moment-Matching Staircase Density Functions

This paper proposes a family of random variables for uncertainty modeling. The variables of interest have a bounded support set, and prescribed values for the first four moments. We present the feasibility conditions for the existence of any of such variables, and propose a class of variables that conforms to such constraints. This class is called staircase because the density of its members is a piecewise constant function. Convex optimization is used to calculate their distributions according to several optimality criteria, including maximal entropy and maximal log-likelihood. The flexibility and efficiency of staircases enable modeling phenomena having a possibly skewed and/or multimodal response at a low computational cost. Furthermore, we provide a means to account for the uncertainty in the distribution caused by estimating staircases from data. These ideas are illustrated by generating empirical staircase predictor models. We consider the case in which the predictor matches the sample moments exactly (a setting applicable to large datasets), as well as the case in which the predictor accounts for the sampling error in such moments (a setting applicable to sparse datasets). A predictor model for the dynamics of an aeroelastic airfoil subject to flutter instability is used as an example. The resulting predictor not only describes the system's response accurately, but also enables carrying out a risk analysis for safe flight.

Luis G. Crespo↗

NASA NTRSDate not supplied

Lessons from Earth Bioaerosol Sampling for Venus Habitability & Biosignature Science

Venus’s clouds are often discussed as a potential habitat. Several high-priority science goals – cloud aerosol composition, internal radiative flux, and aerosol residence time and circulation models – will improve our understanding of Venus in an astrobiology context. Lessons from Earth’s aerobiosphere can inform these requirements and interpretation of results. A stable Venus aerobiosphere would need microorganisms to reproduce faster than they settle out due to gravity. This is a joint constraint of the potential nutrients and energy influx, bioenergetic costs such as desiccation and radiation damage, and aerosol dynamics. Though life cycles involving S- and Fe-based redox metabolism have been proposed, at an optimistic estimate of 75% H2SO4, Venus aerosol water activity (aw) is still ~0.02, far below the observed microbial growth limit of ~0.6. Long-term desiccation with brief spurts of repair, growth and reproduction in response to transient water influx (perhaps volcanism) is the most likely model for Earth-like life on Venus – a ‘desert bloom’ scenario. In Earth’s troposphere, clouds can carry 103 – 105 cells/mL, some metabolically active. A better analogue may be Earth’s stratospheric sulfate aerosol layer: supercooled sulfuric acid aerosols (acid weight fraction 0.6 – 0.85, 0.1 – 1 µm diameter, 0.1 – 1 cm-3) with little water activity, long residence times, high UV radiation, and only sporadic influx from surface particle sources. Viable cells isolated from this region are rare (~102 cells/m3), though ‘hot spots’ at tropospheric mixing occur. Cells are primarily in inactive forms such as spores, and it is unclear if any are associated with sulfate aerosols or simply co-located. Given the heterogeneities in Venus clouds and the model of a sparse, largely dormant ecosystem, a single transect on descent would most likely pass through a low-water, inactive region, missing potential signs of habitability or biosignatures. Even a passive aerial platform (balloon) may end up following a single air mass over its lifetime. A better strategy for Venus would target an aerial region with some upwelling from surface sources, and take multiple transects separated in time and space. Earth’s stratospheric bioaerosol population could provide a starting point for estimating the required lower volume and detection limits.

Earth↗

NASA NTRS2014

Evaluating an Automated Approach for Monitoring Forest Disturbances in the Pacific Northwest from Logging, Fire and Insect Outbreaks with Landsat Time Series Data

Forests are the largest aboveground sink for atmospheric carbon (C), and understanding how they change through time is critical to reduce our C-cycle uncertainties. We investigated a strong decline in Normalized Difference Vegetation Index (NDVI) from 1982 to 1991 in Pacific Northwest forests, observed with the National Ocean and Atmospheric Administration's (NOAA) series of Advanced Very High Resolution Radiometers (AVHRRs). To understand the causal factors of this decline, we evaluated an automated classification method developed for Landsat time series stacks (LTSS) to map forest change. This method included: (1) multiple disturbance index thresholds; and (2) a spectral trajectory-based image analysis with multiple confidence thresholds. We produced 48 maps and verified their accuracy with air photos, monitoring trends in burn severity data and insect aerial detection survey data. Area-based accuracy estimates for change in forest cover resulted in producer's and user's accuracies of 0.21 +/- 0.06 to 0.38 +/- 0.05 for insect disturbance, 0.23 +/- 0.07 to 1 +/- 0 for burned area and 0.74 +/- 0.03 to 0.76 +/- 0.03 for logging. We believe that accuracy was low for insect disturbance because air photo reference data were temporally sparse, hence missing some outbreaks, and the annual anniversary time step is not dense enough to track defoliation and progressive stand mortality. Producer's and user's accuracy for burned area was low due to the temporally abrupt nature of fire and harvest with a similar response of spectral indices between the disturbance index and normalized burn ratio. We conclude that the spectral trajectory approach also captures multi-year stress that could be caused by climate, acid deposition, pathogens, partial harvest, thinning, etc. Our study focused on understanding the transferability of previously successful methods to new ecosystems and found that this automated method does not perform with the same accuracy in Pacific Northwest forests. Using a robust accuracy assessment, we demonstrate the difficulty of transferring change attribution methods to other ecosystems, which has implications for the development of automated detection/attribution approaches. Widespread disturbance was found within AVHRR-negative anomalies, but identifying causal factors in LTSS with adequate mapping accuracy for fire and insects proved to be elusive. Our results provide a background framework for future studies to improve methods for the accuracy assessment of automated LTSS classifications.

Landsat↗

NASA NTRS1988

Navigation with noncoherent data - A demonstration for VEGA Venus flyby phase

Deep Space navigation with noncoherent (one-way) data types is demonstrated for the VEGA Venus flyby phase under extreme conditions. Estimates and statistics are computed using one-way Doppler and wideband Very Long Baseline Interferometry (VLBI) data. The behavior of the onboard oscillator is modeled for both spacecraft to obtain useful orbit determination results. Even with this limitation, it is demonstrated that one-way data solutions are comparable with the solutions using both Soviet sparse coherent (two-way) and wideband VLBI data. During the useful life time of VEGA balloons, the two solutions differ by a maximum of 4.7 km in position and 7.6 cm/sec in velocity for VEGA 1 and by a maximum of 8 km and 42 cm/sec for VEGA 2.

Bhat, Ramachandra S.↗

NASA NTRS2006

Thermal Band Atmospheric Correction Using Atmospheric Profiles Derived from Global Positioning System Radio Occultation and the Atmospheric Infrared Sounder

This Rapid Prototyping Capability study explores the potential to use atmospheric profiles derived from GPS (Global Positioning System) radio occultation measurements and by AIRS (Atmospheric Infrared Sounder) onboard the Aqua satellite to improve surface temperature retrieval from remotely sensed thermal imagery. This study demonstrates an example of a cross-cutting decision support technology whereby NASA data or models are shown to improve a wide number of observation systems or models. The ability to use one data source to improve others will be critical to the GEOSS (Global Earth Observation System of Systems) where a large number of potentially useful systems will require auxiliary datasets as input for decision support. Atmospheric correction of thermal imagery decouples TOA radiance and separates surface emission from atmospheric emission and absorption. Surface temperature can then be estimated from the surface emission with knowledge of its emissivity. Traditionally, radiosonde sounders or atmospheric models based on radiosonde sounders, such as the NOAA (National Oceanic & Atmospheric Administration) ARL (Air Resources Laboratory) READY (Real-time Environmental Application and Display sYstem), provide the atmospheric profiles required to perform atmospheric correction. Unfortunately, these types of data are too spatially sparse and too infrequently taken. The advent of high accuracy, global coverage, atmospheric data using GPS radio occultation and AIRS may provide a new avenue for filling data input gaps. In this study, AIRS and GPS radio occultation derived atmospheric profiles from the German Aerospace Center CHAMP (CHAllenging Minisatellite Payload), the Argentinean Commission on Space Activities SAC-C (Satellite de Aplicaciones Cientificas-C), and the pair of NASA GRACE (Gravity Recovery and Climate Experiment) satellites are used as input data in atmospheric radiative transport modeling based on the MODTRAN (MODerate resolution atmospheric TRANsmittance) radiative transport software to separate out the atmospheric component of measured top of atmosphere radiance. Simulated water bodies across a variety of MODTRAN model atmospheres including desert, mid-latitude, tropical and sub-artic conditions provide test bed conditions. Atmospherically corrected radiance and surface temperature results were compared to those obtained using traditional radiosonde balloon data and models. In general, differences between the different techniques were less than 2 percent indicating the potential value satellite derived atmospheric profiles have to atmospherically correct thermal imagery.

Pagnutti, Mary↗

NASA NTRS2016

Assessing Woody Vegetation Trends in Sahelian Drylands Using MODIS Based Seasonal Metrics

Woody plants play a major role for the resilience of drylands and in peoples' livelihoods. However, due to their scattered distribution, quantifying and monitoring woody cover over space and time is challenging. We develop a phenology driven model and train/validate MODIS (MCD43A4, 500m) derived metrics with 178 ground observations from Niger, Senegal and Mali to estimate woody cover trends from 2000 to 2014 over the entire Sahel. The annual woody cover estimation at 500 m scale is fairly accurate with an RMSE of 4.3 (woody cover %) and r(exp 2) = 0.74. Over the 15 year period we observed an average increase of 1.7 (+/- 5.0) woody cover (%) with large spatial differences: No clear change can be observed in densely populated areas (0.2 +/- 4.2), whereas a positive change is seen in sparsely populated areas (2.1 +/- 5.2). Woody cover is generally stable in cropland areas (0.9 +/- 4.6), reflecting the protective management of parkland trees by the farmers. Positive changes are observed in savannas (2.5 +/- 5.4) and woodland areas (3.9 +/- 7.3). The major pattern of woody cover change reveals strong increases in the sparsely populated Sahel zones of eastern Senegal, western Mali and central Chad, but a decreasing trend is observed in the densely populated western parts of Senegal, northern Nigeria, Sudan and southwestern Niger. This decrease is often local and limited to woodlands, being an indication of ongoing expansion of cultivated areas and selective logging.We show that an overall positive trend is found in areas of low anthropogenic pressure demonstrating the potential of these ecosystems to provide services such as carbon storage, if not over-utilized. Taken together, our results provide an unprecedented synthesis of woody cover dynamics in theSahel, and point to land use and human population density as important drivers, however only partially and locally offsetting a general post-drought increase.

Brandt, Martin↗

NASA NTRS2004

Testing the PV-Theta Mapping Technique in a 3-D CTM Model Simulation

Mapping lower stratospheric ozone into potential vorticity (PV)- potential temperature (Theta) coordinates is a common technique employed to analyze sparse data sets. Ozone transformed into a flow-following dynamical coordinate system is insensitive to meteorological variations. Therefore data from a wide range of times/locations can be compared, so long as the measurements were made in the same airmass (as defined by PV). Moreover, once a relationship between ozone and PV/Theta is established, a full 3D ozone field can be estimated from this relationship and the 3D analyzed PV field. However, ozone data mapped in this fashion can be hampered by noisy PV fields, or "mis-matches" in the resolution and/or exact location of the ozone and PV measurements. In this study, we investigate the PV-ozone relationship using output from a recent 50-year run of the Goddard 3D chemical transport model (CTM). Model constituents are transported using off-line dynamics from the finite volume general circulation model (FVGCM). By using the internally consistent model PV and ozone fields, we minimize noise due to mis-matching and resolution issues. We calculate correlations between model ozone and PV throughout the stratosphere, and test the sensitivity of the technique to initial data resolution. To do this we degrade the model data to that of various satellite instruments, then compare the mapped fields derived from the sub-sampled data to the full resolution model data. With these studies we can determine appropriate limits for the PV-theta mapping technique in latitude, altitude, and as a function of original data resolution.

Frith, Stacey M.↗

NASA NTRS1990

The Design-To-Cost Manifold

Design-to-cost is a popular technique for controlling costs. Although qualitative techniques exist for implementing design to cost, quantitative methods are sparse. In the launch vehicle and spacecraft engineering process, the question whether to minimize mass is usually an issue. The lack of quantification in this issue leads to arguments on both sides. This paper presents a mathematical technique which both quantifies the design-to-cost process and the mass/complexity issue. Parametric cost analysis generates and applies mathematical formulas called cost estimating relationships. In their most common forms, they are continuous and differentiable. This property permits the application of the mathematics of differentiable manifolds. Although the terminology sounds formidable, the application of the techniques requires only a knowledge of linear algebra and ordinary differential equations, common subjects in undergraduate scientific and engineering curricula. When the cost c is expressed as a differentiable function of n system metrics, setting the cost c to be a constant generates an n-1 dimensional subspace of the space of system metrics such that any set of metric values in that space satisfies the constant design-to-cost criterion. This space is a differentiable manifold upon which all mathematical properties of a differentiable manifold may be applied. One important property is that an easily implemented system of ordinary differential equations exists which permits optimization of any function of the system metrics, mass for example, over the design-to-cost manifold. A dual set of equations defines the directions of maximum and minimum cost change. A simplified approximation of the PRICE H(TM) production-production cost is used to generate this set of differential equations over [mass, complexity] space. The equations are solved in closed form to obtain the one dimensional design-to-cost trade and design-for-cost spaces. Preliminary results indicate that cost is relatively insensitive to changes in mass and that the reduction of complexity, both in the manufacturing process and of the spacecraft, is dominant in reducing cost.

Dean, Edwin B.↗

NASA NTRS1978

Recursive estimator for OSO-8 attitude

Modifications and enhancements that have been made to the Recursive Estimation Attitude Program (REAP) are discussed. Continuous attitudes for OSO-8 to + or - 0.05 degree accuracy are determined from Sun and star slit sensors mounted on the spinning portion of the spacecraft. The bulk of the attitude production is performed by a Weighted Least Squares (WLS) batch processor, but REAP is used for problem passes such as those involving gas jet maneuvers, sparse star fields, or star sensor saturation by high energy particles in the South Atlantic Anomaly.

Headrick, R. D.↗