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NASA NTRSDate not supplied

A New Statistical Estimate of the Radar Coverage of the Low Earth Orbit Debris Environment

For over three decades, the NASA Orbital Debris Program Office (ODPO) has used the Goldstone Orbital Debris Radar, Haystack Ultrawideband Satellite Imaging Radar (HUSIR), and Haystack Auxiliary (HAX) radar assets to collect data on the low Earth orbit (LEO) debris environment. Each radar, with its unique beamwidth, altitude and inclination coverage, and limiting size threshold, operates in a beam park mode to statistically sample the orbital debris population in LEO. Provided that these assets are shared with other users, the orbital debris data collection is not continuous; rather, intermittent data collects are acquired and sent to the NASA ODPO. To understand the sampling process conducted by each radar over time and any related observational biases, a Statistical Confirmation of Radar Uniformity or Bias (SCRUB) code has been implemented to model the coverage of these assets for informing future operations, as well as usage of the data collected from these ground-based sensors. For this analysis, Right Ascension of the Ascending Node (RAAN) is used as a metric to measure statistical coverage. A complete survey of the LEO environment is understood to be measurements that sufficiently sample all values of RAAN for each altitude-inclination pair visible from the radar asset. Regions of incompleteness or statistical bias can help inform future observation campaigns. The SCRUB tool evaluates the coverage of the LEO environment, not by examining individual objects that may pass through a sensor’s field of view (FOV), but by determining which orbit planes pass through the FOV. Once a pointing geometry for a radar site, observation time, and range extent are configured by the user, SCRUB computes the inclinations and altitudes that are visible by the sensor. For each inclination-altitude pair, there is a distinct pair of possible RAAN values, corresponding to the ascending and descending orbit passing through that point in the sensor cone. Repeating this process for all points in the beam, and for multiple time periods during an observation window, creates a matrix of all inclination-altitude-RAAN combinations that are visible during a sensor run. This process can then be repeated for all observations within a year (for an annual survey), propagating all the RAAN values to a common epoch, typically the start of a calendar year, and combining the observations to assemble a full estimate of the RAAN coverage of the LEO environment. This RAAN coverage can then be analyzed for uniformity of sampling, within a certain inclination-altitude pair, or between larger regions of the space environment. This paper provides a general overview of the radar assets utilized by ODPO, typical analysis data products assuming circular orbits, and a discussion of the algorithms that feed between modeling and measurement operations. Following the description of the algorithm, estimates of coverage using HUSIR radar data collected from multiple years are developed and compared.

Chris L Ostrom↗
NASA NTRS1977

Optimal spatial sampling techniques for ground truth data in microwave remote sensing of soil moisture

The paper examines optimal sampling techniques for obtaining accurate spatial averages of soil moisture, at various depths and for cell sizes in the range 2.5-40 acres, with a minimum number of samples. Both simple random sampling and stratified sampling procedures are used to reach a set of recommended sample sizes for each depth and for each cell size. Major conclusions from statistical sampling test results are that (1) the number of samples required decreases with increasing depth; (2) when the total number of samples cannot be prespecified or the moisture in only one single layer is of interest, then a simple random sample procedure should be used which is based on the observed mean and SD for data from a single field; (3) when the total number of samples can be prespecified and the objective is to measure the soil moisture profile with depth, then stratified random sampling based on optimal allocation should be used; and (4) decreasing the sensor resolution cell size leads to fairly large decreases in samples sizes with stratified sampling procedures, whereas only a moderate decrease is obtained in simple random sampling procedures.

Rao, R. G. S.↗
NASA NTRS1977

Remote sensing-aided systems for snow qualification, evapotranspiration estimation, and their application in hydrologic models

The design of general remote sensing-aided methodologies was studied to provide the estimates of several important inputs to water yield forecast models. These input parameters are snow area extent, snow water content, and evapotranspiration. The study area is Feather River Watershed (780,000 hectares), Northern California. The general approach involved a stepwise sequence of identification of the required information, sample design, measurement/estimation, and evaluation of results. All the relevent and available information types needed in the estimation process are being defined. These include Landsat, meteorological satellite, and aircraft imagery, topographic and geologic data, ground truth data, and climatic data from ground stations. A cost-effective multistage sampling approach was employed in quantification of all the required parameters. The physical and statistical models for both snow quantification and evapotranspiration estimation was developed. These models use the information obtained by aerial and ground data through appropriate statistical sampling design.

Korram, S.↗
NASA NTRS2002

Evolution of Galaxies and the Star Formation Rate in the Infrared

A central goal of extragalactic observational astronomy is to understand how normal galaxies evolve with redshift, and particularly when galaxies formed their stars. While optical and rest-frame UV (ultraviolet) observations have begun to address these issues, the interpretation of such data is particularly challenging because of the sensitivity to dust obscureness (at optical and UV wavelengths). The absorbed light is re-radiated at IR (infrared) wavelengths, hence the optimal indicators of the star formation rate (SFR) is at a rest-frame of (lambda) (is approximately equal to) 60 microns. The SIRTF (space infrared telescope facility) mission will revolutionize the study of the global evolution of the SFR by providing mass-selected, complete samples of galaxies and fares estimators of the SFR. This research program is to study the SFR using statistical samples of galaxies in the local universe, at intermediate redshifts, and set the stage for continuing studies up to z = 5.

Pahre, Michael, A.↗
NASA NTRS2021

New giant planet beyond the snow line for an extended MOA exoplanet microlens sample

Characterizing a planet detected by microlensing is hard if the planetary signal is weak or the lens-source relative trajectory is far from caustics. However, statistical analyses of planet demography must include those planets to accurately determine occurrence rates. As part of a systematic modelling effort in the context of a >10-yr retrospective analysis of MOA’s survey observations to build an extended MOA statistical sample, we analyse the light curve of the planetary microlensing event MOA-2014-BLG-472. This event provides weak constraints on the physical parameters of the lens, as a result of a planetary anomaly occurring at low magnification in the light curve. We use a Bayesian analysis to estimate the properties of the planet, based on a refined Galactic model and the assumption that all Milky Way’s stars have an equal planet-hosting probability. We find that a lens consisting of a 1.9(+2.2,−1.2)M(J) giant planet orbiting a 0.31(+0.36,−0.19)Mꙩ host at a projected separation of 0.75±0.24au is consistent with the observations and is most likely, based on the Galactic priors. The lens most probably lies in the Galactic bulge, at 7.2(+0.6,−1.7)kpc from Earth. The accurate measurement of the measured planet-to-host star mass ratio will be included in the next statistical analysis of cold planet demography detected by microlensing.

Clément Ranc↗
NASA NTRS2015

Optimization of Microphone Locations for Acoustic Liner Impedance Eduction

Two impedance eduction methods are explored for use with data acquired in the NASA Langley Grazing Flow Impedance Tube. The first is an indirect method based on the convected Helmholtz equation, and the second is a direct method based on the Kumaresan and Tufts algorithm. Synthesized no-flow data, with random jitter to represent measurement error, are used to evaluate a number of possible microphone locations. Statistical approaches are used to evaluate the suitability of each set of microphone locations. Given the computational resources required, small sample statistics are employed for the indirect method. Since the direct method is much less computationally intensive, a Monte Carlo approach is employed to gather its statistics. A comparison of results achieved with full and reduced sets of microphone locations is used to determine which sets of microphone locations are acceptable. For the indirect method, each array that includes microphones in all three regions (upstream and downstream hard wall sections, and liner test section) provides acceptable results, even when as few as eight microphones are employed. The best arrays employ microphones well away from the leading and trailing edges of the liner. The direct method is constrained to use microphones opposite the liner. Although a number of arrays are acceptable, the optimum set employs 14 microphones positioned well away from the leading and trailing edges of the liner. The selected sets of microphone locations are also evaluated with data measured for ceramic tubular and perforate-over-honeycomb liners at three flow conditions (Mach 0.0, 0.3, and 0.5). They compare favorably with results attained using all 53 microphone locations. Although different optimum microphone locations are selected for the two impedance eduction methods, there is significant overlap. Thus, the union of these two microphone arrays is preferred, as it supports usage of both methods. This array contains 3 microphones in the upstream hard wall section, 14 microphones opposite the liner, and 3 microphones in the downstream hard wall section.

Jones, M. G.↗
NASA NTRS2013

Orbital Debris: Past, Present, and Future

In the early days of spaceflight, the gBig Sky h theory was the near universally accepted paradigm for dealing with collisions of orbiting objects. This theory was also used during the early years of the aviation industry. Just as it did in aviation, the gBig Sky h theory breaks down as more and more objects accumulate in the environment. Fortunately, by the late 1970 fs some visionaries in NASA and the US Department of Defense (DoD) realized that trends in the orbital environment would inevitably lead to increased risks to operational spacecraft from collisions with other orbiting objects. The NASA Orbital Debris Program was established at and has been conducted at Johnson Space Center since 1979. At the start of 1979, fewer than 5000 objects were being tracked by the US Space Surveillance Network and very few attempts had been made to sample the environment for smaller sizes. Today, the number of tracked objects has quadrupled. Ground ]based and in situ measurements have statistically sampled the LEO environment over most sizes and mitigation guidelines and requirements are common among most space faring nations. NASA has been a leader, not only in defining the debris environment, but in promoting awareness of the issues in the US and internationally, and in providing leadership in developing policies to address the issue. This paper will discuss in broad terms the evolution of the NASA debris program from its beginnings to its present broad range of debris related research. The paper will discuss in some detail current research topics and will attempt to predict future research trends.

Stansbery, Gene↗
NASA NTRS1998

Implementation and Testing of Turbulence Models for the F18-HARV Simulation

This report presents three methods of implementing the Dryden power spectral density model for atmospheric turbulence. Included are the equations which define the three methods and computer source code written in Advanced Continuous Simulation Language to implement the equations. Time-history plots and sample statistics of simulated turbulence results from executing the code in a test program are also presented. Power spectral densities were computed for sample sequences of turbulence and are plotted for comparison with the Dryden spectra. The three model implementations were installed in a nonlinear six-degree-of-freedom simulation of the High Alpha Research Vehicle airplane. Aircraft simulation responses to turbulence generated with the three implementations are presented as plots.

Yeager, Jessie C.↗
NASA NTRS1991

CRN5EXP: Expert system for statistical quality control

The purpose of the Expert System CRN5EXP is to assist in checking the quality of the coils at two very important mills: Hot Rolling and Cold Rolling in a steel plant. The system interprets the statistical quality control charts, diagnoses and predicts the quality of the steel. Measurements of process control variables are recorded in a database and sample statistics such as the mean and the range are computed and plotted on a control chart. The chart is analyzed through patterns using the C Language Integrated Production System (CLIPS) and a forward chaining technique to reach a conclusion about the causes of defects and to take management measures for the improvement of the quality control techniques. The Expert System combines the certainty factors associated with the process control variables to predict the quality of the steel. The paper presents the approach to extract data from the database, the reason to combine certainty factors, the architecture and the use of the Expert System. However, the interpretation of control charts patterns requires the human expert's knowledge and lends to Expert Systems rules.

Hentea, Mariana↗
NASA NTRS2000

Analysis of the Diurnal Cycle of Precipitation and its Relation to Cloud Radiative Forcing using TRMM Products

By incorporating the Tropical Rain Measuring Mission (TRMM) satellite orbital information into the geodesic version of the Colorado State University General Circulation Model (CSU GCM), we are able to fly a satellite in the GCM, and sample the simulated atmosphere in the same way as the TRMM sensors sample the real atmosphere. The TRMM sampling statistics of precipitation and radiative fluxes at annual, intraseasonal, monthly-mean and composited diurnal time scales are evaluated by comparing the satellite-sampled against fully-sampled simulated atmospheres. This information provides a valuable guidance for efficient usage of TRMM data and future satellite mission planning.

Randall, David A.↗
NASA NTRS1986

Statistics of the geomagnetic secular variation for the past 5Ma

A new statistical model is proposed for the geomagnetic secular variation over the past 5Ma. Unlike previous models, the model makes use of statistical characteristics of the present day geomagnetic field. The spatial power spectrum of the non-dipole field is consistent with a white source near the core-mantle boundary with Gaussian distribution. After a suitable scaling, the spherical harmonic coefficients may be regarded as statistical samples from a single giant Gaussian process; this is the model of the non-dipole field. The model can be combined with an arbitrary statistical description of the dipole and probability density functions and cumulative distribution functions can be computed for declination and inclination that would be observed at any site on Earth's surface. Global paleomagnetic data spanning the past 5Ma are used to constrain the statistics of the dipole part of the field. A simple model is found to be consistent with the available data. An advantage of specifying the model in terms of the spherical harmonic coefficients is that it is a complete statistical description of the geomagnetic field, enabling us to test specific properties for a general description. Both intensity and directional data distributions may be tested to see if they satisfy the expected model distributions.

Constable, C. G.↗
NASA NTRS1988

Statistics of the geomagnetic secular variation for the past 5 m.y

A new statistical model is proposed for the geomagnetic secular variation over the past 5Ma. Unlike previous models, the model makes use of statistical characteristics of the present day geomagnetic field. The spatial power spectrum of the non-dipole field is consistent with a white source near the core-mantle boundary with Gaussian distribution. After a suitable scaling, the spherical harmonic coefficients may be regarded as statistical samples from a single giant Gaussian process; this is the model of the non-dipole field. The model can be combined with an arbitrary statistical description of the dipole and probability density functions and cumulative distribution functions can be computed for declination and inclination that would be observed at any site on Earth's surface. Global paleomagnetic data spanning the past 5Ma are used to constrain the statistics of the dipole part of the field. A simple model is found to be consistent with the available data. An advantage of specifying the model in terms of the spherical harmonic coefficients is that it is a complete statistical description of the geomagnetic field, enabling us to test specific properties for a general description. Both intensity and directional data distributions may be tested to see if they satisfy the expected model distributions.

Constable, C. G.↗
NASA NTRS2001

Flying the TRMM Satellite in a GCM

By incorporating the Tropical Rainfall Measurement Mission (TRMM) satellite orbital information into the Colorado State University General Circulation Model (CSU GCM), we are able to 'fly' a satellite in the GCM, and sample the simulated atmosphere in the same way as the TRMM sensors sample the real atmosphere. The TRMM-sampled statistics for precipitation and radiative fluxes at annual, intraseasonal, monthly-mean and seasonal-mean diurnal time scales are evaluated by comparing the satellite-sampled against fully-sampled simulated atmospheres. The sampling rates of the TRMM sensors are significantly affected by the sensors' swath widths. The TRMM Microwave Imager (TMI) and the Visible Infrared Scanner (VIRS) sample each 2.25 x 2.25 degree grid box in the Tropics and subtropics about once per day, but at a different local time every day, while the Precipitation Radar (PR) and the Clouds and the Earth's Radiant Energy System (CERES) sensor visit each grid box about once every three days and twice per day, respectively. Besides inadequate samplings resulting from sensors' swath widths, there is a large, systematic diurnal undersampling associated with TRMM's orbital geometry for grid boxes away from the Equator. When only one month of TRMM data are used, this diurnal undersampling can lead to more daytime samples relative to nighttime samples in one hemisphere, and more nighttime samples relative to daytime samples in the other hemisphere. The resulting sampling biases (3-6 W m(exp-2)) are very pronounced in outgoing longwave radiation (OLR) over the subtropical land masses. The sampling errors in OLR monthly- and seasonal-means are less than 8 W m(exp-2) (5%) for each 2.25 x 2.25 degree grid box. The OLR monthly- and seasonal-means are not sensitive to diurnal undersamplings associated with the TRMM orbits and sensors' swath widths. However, this is not the case for total precipitation. Diurnal undersampling could produce errors as large as 20% in the Tropics and 40% in the subtropics, for the zonally averaged monthly-mean rain rates. The TRMM orbits sample each 2.25 x 2.25 degree grid box in the Tropics and subtropics 1-6 times for each hour of the day within a single season. The seasonal-mean diurnal cycles of precipitation and OLR are not well sampled for any one grid box. By either accumulating the satellite data for a long enough period, or averaging the data over a large area with a relatively uniform diurnal signal, the diurnal cycles of precipitation and OLR can be satisfactorily sampled. The effects TRMM sampling errors on the inferred tropical-mean hydrologic cycle and radiative fluxes are also evaluated. There are strong spurious oscillations associated with TRMM's orbital geometry, with periods of 23 days and 3-4 months, in tropical-mean daily and monthly precipitation. While the relative fluctuations of the sampled-OLR are negligible, the relative fluctuations of the sampled precipitation have magnitudes similar to those of the observed climate variability. Caution must therefore be used when applying TRMM observations of tropical-mean precipitation to interpret climate variations at intraseasonal and interannual scales.

Lin, Xin↗
NASA NTRS2001

Use of TRMM Data to Test an Improved Parameterization of Stratiform Precipitation

By incorporating the TRMM satellite orbital information into the most recent geodesic version of the Colorado State University General Circulation Model (CSU GCM), we are able to fly a satellite in the GCM, and sample the simulated atmosphere in the same way as the TRMM sensors sample the real atmosphere. The TRMM sampling statistics of precipitation and radiative fluxes at annual, intra-seasonal, monthly-mean and composited diurnal time scales are evaluated by comparing the satellite-sampled against fully-sampled simulated atmospheres. This information provides a valuable guidance for efficient usage of TRMM data and future satellite mission planning. We have also evaluated the effects of TRMM sampling errors on the inferred tropical-mean hydrologic cycle and radiative fluxes. We have found that there are strong spurious oscillations associated with the TRMM orbital geometry, with periods of 23 days and 3-4 months, in tropical-mean daily and monthly precipitation. Caution must therefore be used when applying TRMM observations of tropical-mean precipitation to interpret climate variations at intraseasonal and interannual scales.

Randall, David A.↗
NASA NTRSDate not supplied

NASA’s Orbital Debris Optical Program: ES-MCAT Nearing Full Operational Capability (FOC)

The NASA JAO/ES-MCAT (Eugene Stansbery Meter Class Autonomous Telescope) Facility is nearing Full Operational Capability, or FOC. ES-MCAT is now fully capable of autonomously running all observations, including: (a) monitoring weather and closing when conditions are not safe, as well as halting observations when conditions are not suitable (e.g. too cloudy) for operations, (b) start-up/shut-down nightly tasking, (c) collecting calibration data and survey or TLE-tracked data, and (d) processing all collected data, including on-chip photometry and astrometry calibrations using the GAIA star catalogue. The processed data are then further analyzed at NASA Johnson Space Center to correlate detections with known objects in the Space Surveillance Network (SSN) catalogue. MCAT can collect data of specific objects with known orbits or can search for objects with orbits similar to those of spacecraft or rocket bodies that have recently broken up. However, the primary goal for ES-MCAT is to survey the geosynchronous (GEO) belt to provide a statistical sample of the GEO debris environment for both engineering models for spacecraft designers and long-term environment evolutionary purposes. The approach for sweeping the sky to statistically survey GEO has been investigated and updated from past surveys taken by NASA and will be reported, herein referred to as the Candy Cane method. ES-MCAT’s optical performance and the limiting magnitude for the full optical system will be discussed. An analysis used to determine which filter to use for GEO surveys (SDSS r′) includes combining the reflectivity of the primary and secondary mirrors, transmission of the field corrector and CCD window, and the quantum efficiency of the CCD detector, resulting in throughput of the full optical path. This throughput is then combined with the expected typical transparency of the atmosphere at ES-MCAT’s altitude/location for the Sloan Digital Sky Survey (SDSS) g′r′i′z′ and Johnson/Kron-Cousins BVRI filters to yield expected relative throughput.

S. M. Lederer↗
NASA NTRS1981

Users manual for the US baseline corn and soybean segment classification procedure

A user's manual for the classification component of the FY-81 U.S. Corn and Soybean Pilot Experiment in the Foreign Commodity Production Forecasting Project of AgRISTARS is presented. This experiment is one of several major experiments in AgRISTARS designed to measure and advance the remote sensing technologies for cropland inventory. The classification procedure discussed is designed to produce segment proportion estimates for corn and soybeans in the U.S. Corn Belt (Iowa, Indiana, and Illinois) using LANDSAT data. The estimates are produced by an integrated Analyst/Machine procedure. The Analyst selects acquisitions, participates in stratification, and assigns crop labels to selected samples. In concert with the Analyst, the machine digitally preprocesses LANDSAT data to remove external effects, stratifies the data into field like units and into spectrally similar groups, statistically samples the data for Analyst labeling, and combines the labeled samples into a final estimate.

Horvath, R.↗
NASA NTRS1997

Design of Neural Networks for Fast Convergence and Accuracy: Dynamics and Control

A procedure for the design and training of artificial neural networks, used for rapid and efficient controls and dynamics design and analysis for flexible space systems, has been developed. Artificial neural networks are employed, such that once properly trained, they provide a means of evaluating the impact of design changes rapidly. Specifically, two-layer feedforward neural networks are designed to approximate the functional relationship between the component/spacecraft design changes and measures of its performance or nonlinear dynamics of the system/components. A training algorithm, based on statistical sampling theory, is presented, which guarantees that the trained networks provide a designer-specified degree of accuracy in mapping the functional relationship. Within each iteration of this statistical-based algorithm, a sequential design algorithm is used for the design and training of the feedforward network to provide rapid convergence to the network goals. Here, at each sequence a new network is trained to minimize the error of previous network. The proposed method should work for applications wherein an arbitrary large source of training data can be generated. Two numerical examples are performed on a spacecraft application in order to demonstrate the feasibility of the proposed approach.

Maghami, Peiman G.↗
NASA NTRS1998

Design of Neural Networks for Fast Convergence and Accuracy

A novel procedure for the design and training of artificial neural networks, used for rapid and efficient controls and dynamics design and analysis for flexible space systems, has been developed. Artificial neural networks are employed to provide a means of evaluating the impact of design changes rapidly. Specifically, two-layer feedforward neural networks are designed to approximate the functional relationship between the component spacecraft design changes and measures of its performance. A training algorithm, based on statistical sampling theory, is presented, which guarantees that the trained networks provide a designer-specified degree of accuracy in mapping the functional relationship. Within each iteration of this statistical-based algorithm, a sequential design algorithm is used for the design and training of the feedforward network to provide rapid convergence to the network goals. Here, at each sequence a new network is trained to minimize the error of previous network. The design algorithm attempts to avoid the local minima phenomenon that hampers the traditional network training. A numerical example is performed on a spacecraft application in order to demonstrate the feasibility of the proposed approach.

Maghami, Peiman G.↗