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NASA NTRS2002

On the Singularity in the Estimation of the Quaternion-of-Rotation

It has been claimed in the archival literature that the covariance matrix of a Kalman filter, which is designed to estimate the quaternion-of-rotation, is necessarily rank, deficient because the normality constraint of the quaternion produces dependence between the quaternion elements. In reality, though, this phenomenon does not occur. The covariance matrix is not singular, and the filter is well behaved. Several simple examples are presented th at demonstrate the regularity of the covariance matrix. First, a Kalman filter is designed to estimate variables subject to a functional relationship. Then the particular problem of quaternion estimation is analyzed. It is shown that the discrepancy stems from the fact that the functional relationship exists between the elements of the quaternion but not between its estimate elements.

Bar-Itzhack, Itzhack Y.↗

NASA NTRS2002

Comparison of Two Methods for Estimating the Sampling-Related Uncertainty of Satellite Rainfall Averages Based on a Large Radar Data Set

The uncertainty of rainfall estimated from averages of discrete samples collected by a satellite is assessed using a multi-year radar data set covering a large portion of the United States. The sampling-related uncertainty of rainfall estimates is evaluated for all combinations of 100 km, 200 km, and 500 km space domains, 1 day, 5 day, and 30 day rainfall accumulations, and regular sampling time intervals of 1 h, 3 h, 6 h, 8 h, and 12 h. These extensive analyses are combined to characterize the sampling uncertainty as a function of space and time domain, sampling frequency, and rainfall characteristics by means of a simple scaling law. Moreover, it is shown that both parametric and non-parametric statistical techniques of estimating the sampling uncertainty produce comparable results. Sampling uncertainty estimates, however, do depend on the choice of technique for obtaining them. They can also vary considerably from case to case, reflecting the great variability of natural rainfall, and should therefore be expressed in probabilistic terms. Rainfall calibration errors are shown to affect comparison of results obtained by studies based on data from different climate regions and/or observation platforms.

Lau, William K. M.↗

NASA NTRS2003

The MAP Spacecraft Angular State Estimation After Sensor Failure

This work describes two algorithms for computing the angular rate and attitude in case of a gyro and a Star Tracker failure in the Microwave Anisotropy Probe (MAP) satellite, which was placed in the L2 parking point from where it collects data to determine the origin of the universe. The nature of the problem is described, two algorithms are suggested, an observability study is carried out and real MAP data are used to determine the merit of the algorithms. It is shown that one of the algorithms yields a good estimate of the rates but not of the attitude whereas the other algorithm yields a good estimate of the rate as well as two of the three attitude angles. The estimation of the third angle depends on the initial state estimate. There is a contradiction between this result and the outcome of the observability analysis. An explanation of this contradiction is given in the paper. Although this work treats a particular spacecraft, the conclusions have a far reaching consequence.

Bar-Itzhack, Itzhack Y.↗

NASA NTRS2002

Optimal Strategies for Validating TRMM Rainfall Estimates with Rain-Gauge Data

In spite of all their problems, rain gauges measure rainfall in such a direct way when compared with other methods of estimating rainfall that comparing their totals to satellite estimates remains an essential tool in the validation of satellite products. Some disagreement between averages of satellite data and rain-gauge data is expected because of the very different sampling patterns of the two systems--the satellite provides only occasional snapshots of large areas, whereas rain gauges provide continuous measurements over very small areas. A quantitative estimate of the expected level of disagreement due to the differences in sampling is needed in order for comparisons of the two kinds of averages to be informative. As part of an earlier effort to determine the sampling error of satellite averages, a space-time model for rainfall statistics was developed. Sets of parameter values for the model have been obtained for which the model statistics are found to agree quite well with those of radar data taken over the Atlantic during GATE and the western Pacific during TOGA COARE. Although the model was intended to represent the statistics of relatively large scale fluctuations of rain, it is surprisingly consistent with the very different scales on which rain gauges observe. Implications for maximizing the benefit in comparisons of rain gauge averages and TRMM estimates are derived using the model predictions.

Bell, Thomas L.↗

NASA NTRS2003

The Effect of Sensor Failure on the Attitude and Rate Estimation of MAP Spacecraft

Bar-Itzhack, Itzhack Y.↗

NASA NTRS2003

Ocean Primary Production Estimates from Terra MODIS and Their Dependency on Satellite Chlorophyll Alpha Algorithms

Simplistic models relating global satellite ocean color, temperature, and light to ocean net primary production (ONPP) are sensitive to the accuracy and limitations of the satellite estimate of chlorophyll and other input fields, as well as the primary productivity model. The standard MODIS ONPP product uses the new semi-analytic chlorophyll algorithm as its input for two ONPP indexes. The three primary MODIS chlorophyll Q estimates from MODIS, as well as the SeaWiFS 4 chlorophyll product, were used to assess global and regional performance in estimating ONPP for the full mission, but concentrating on 2001. The two standard ONPP algorithms were examined with 8-day and 39 kilometer resolution to quantify chlorophyll algorithm dependency of ONPP. Ancillary data (MLD from FNMOC, MODIS SSTD1, and PAR from the GSFC DAO) were identical. The standard MODIS ONPP estimates for annual production in 2001 was 59 and 58 GT C for the two ONPP algorithms. Differences in ONPP using alternate chlorophylls were on the order of 10% for global annual ONPP, but ranged to 100% regionally. On all scales the differences in ONPP were smaller between MODIS and SeaWiFS than between ONPP models, or among chlorophyll algorithms within MODIS. Largest regional ONPP differences were found in the Southern Ocean (SO). In the SO, application of the semi-analytic chlorophyll resulted in not only a magnitude difference in ONPP (2x), but also a temporal shift in the time of maximum production compared to empirical algorithms when summed over standard oceanic areas. The resulting increase in global ONPP (6-7 GT) is supported by better performance of the semi-analytic chlorophyll in the SO and other high chlorophyll regions. The differences are significant in terms of understanding regional differences and dynamics of ocean carbon transformations.

Essias, Wayne E.↗

NASA NTRS2002

Software for Estimating Costs of Testing Rocket Engines

A high-level parametric mathematical model for estimating the costs of testing rocket engines and components at Stennis Space Center has been implemented as a Microsoft Excel program that generates multiple spreadsheets. The model and the program are both denoted, simply, the Cost Estimating Model (CEM). The inputs to the CEM are the parameters that describe particular tests, including test types (component or engine test), numbers and duration of tests, thrust levels, and other parameters. The CEM estimates anticipated total project costs for a specific test. Estimates are broken down into testing categories based on a work-breakdown structure and a cost-element structure. A notable historical assumption incorporated into the CEM is that total labor times depend mainly on thrust levels. As a result of a recent modification of the CEM to increase the accuracy of predicted labor times, the dependence of labor time on thrust level is now embodied in third- and fourth-order polynomials.

Hines, Merion M.↗

NASA NTRS2004

Software for Estimating Costs of Testing Rocket Engines

Hines, Merlon M.↗

NASA NTRS2003

Use of MODIS-Derived Fire Radiative Energy to Estimate Smoke Aerosol Emissions over Different Ecosystems

Biomass burning is the main source of smoke aerosols and certain trace gases in the atmosphere. However, estimates of the rates of biomass consumption and emission of aerosols and trace gases from fires have not attained adequate reliability thus far. Traditional methods for deriving emission rates employ the use of emission factors e(sub x), (in g of species x per kg of biomass burned), which are difficult to measure from satellites. In this era of environmental monitoring from space, fire characterization was not a major consideration in the design of the early satellite-borne remote sensing instruments, such as AVHRR. Therefore, although they are able to provide fire location information, they were not adequately sensitive to variations in fire strength or size, because their thermal bands used for fire detection saturated at the lower end of fire radiative temperature range. As such, hitherto, satellite-based emission estimates employ proxy techniques using satellite derived fire pixel counts (which do not express the fire strength or rate of biomass consumption) or burned areas (which can only be obtained after the fire is over). The MODIS sensor, recently launched into orbit aboard EOS Terra (1999) and Aqua (2002) satellites, have a much higher saturation level and can, not only detect the fire locations 4 times daily, but also measures the at-satellite fire radiative energy (which is a measure of the fire strength) based on its 4 micron channel temperature. Also, MODIS measures the optical thickness of smoke and other aerosols. Preliminary analysis shows appreciable correlation between the MODIS-derived rates of emission of fire radiative energy and smoke over different regions across the globe. These relationships hold great promise for deriving emission coefficients, which can be used for estimating smoke aerosol emissions from MODIS active fire products. This procedure has the potential to provide more accurate emission estimates in near real-time, providing opportunities for various disaster management applications such as alerts, evacuation and, smoke dispersion forecasting.

Ichoku, Charles↗

NASA NTRS2001

A semi-automatic method for left ventricle volume estimate: an in vivo validation study

This study aims to the validation of the left ventricular (LV) volume estimates obtained by processing volumetric data utilizing a segmentation model based on level set technique. The validation has been performed by comparing real-time volumetric echo data (RT3DE) and magnetic resonance (MRI) data. A validation protocol has been defined. The validation protocol was applied to twenty-four estimates (range 61-467 ml) obtained from normal and pathologic subjects, which underwent both RT3DE and MRI. A statistical analysis was performed on each estimate and on clinical parameters as stroke volume (SV) and ejection fraction (EF). Assuming MRI estimates (x) as a reference, an excellent correlation was found with volume measured by utilizing the segmentation procedure (y) (y=0.89x + 13.78, r=0.98). The mean error on SV was 8 ml and the mean error on EF was 2%. This study demonstrated that the segmentation technique is reliably applicable on human hearts in clinical practice.

NASA Discipline Cardiopulmonary↗

NASA NTRS1992

Fractionation of carbon isotopes by phytoplankton and estimates of ancient CO2 levels

Reports of the 13C content of marine particulate organic carbon are compiled and on the basis of GEOSECS data and temperatures, concentrations, and isotopic compositions of dissolved CO2 in the waters in which the related phytoplankton grew are estimated. In this way, the fractionation of carbon isotopes during photosynthetic fixation of CO2 is found to be significantly correlated with concentrations of dissolved CO2. Because ancient carbon isotopic fractionations have been determined from analyses of sedimentary porphyrins [Popp et al., 1989], the relationship between isotopic fractionation and concentrations of dissolved CO2 developed here can be employed to estimate concentrations of CO2 dissolved in ancient oceans and, in turn, partial pressures of CO2 in ancient atmospheres. The calculations take into account the temperature dependence of chemical and isotopic equilibria in the dissolved-inorganic-carbon system and of air-sea equilibria. Paleoenvironmental temperatures for each sample are estimated from reconstructions of paleogeography, latitudinal temperature gradients, and secular changes in low-latitude sea surface temperature. It is estimated that atmospheric partial pressures of CO2 were over 1000 micro atm 160 - 100 Ma ago, then declined to values near 300 micro atm during the next 100 Ma. Analysis of a high-resolution record of carbon isotopic fractionation at the Cenomanian-Turonian boundary suggests that the partial pressure of CO2 in the atmosphere was drawn down from values near 840 micro atm to values near 700 micro atm during the anoxic event.

NASA Discipline Exobiology↗

NASA NTRS2004

Volume and Mass Estimation of Three-Phase High Power Transformers for Space Applications

Spacecraft historically have had sub-1kW(sub e), electrical requirements for GN&C, science, and communications: Galileo at 600W(sub e), and Cassini at 900W(sub e), for example. Because most missions have had the same order of magnitude power requirements, the Power Distribution Systems (PDS) use existing, space-qualified technology and are DC. As science payload and mission duration requirements increase, however, the required electrical power increases. Subsequently, this requires a change from a passive energy conversion (solar arrays and batteries) to dynamic (alternator, solar dynamic, etc.), because dynamic conversion has higher thermal and conversion efficiencies, has higher power densities, and scales more readily to higher power levels. Furthermore, increased power requirements and physical distribution lengths are best served with high-voltage, multi-phase AC to maintain distribution efficiency and minimize voltage drops. The generated AC-voltage must be stepped-up (or down) to interface with various subsystems or electrical hardware. Part of the trade-space design for AC distribution systems is volume and mass estimation of high-power transformers. The volume and mass are functions of the power rating, operating frequency, the ambient and allowable temperature rise, the types and amount of heat transfer available, the core material and shape, the required flux density in a core, the maximum current density, etc. McLyman has tabulated the performance of a number of transformers cores and derived a "cookbook" methodology to determine the volume of transformers, whereas Schawrze had derived an empirical method to estimate the mass of single-phase transformers. Based on the work of McLyman and Schwarze, it is the intent herein to derive an empirical solution to the volume and mass estimation of three-phase, laminated EI-core power transformers, having radiated and conducted heat transfer mechanisms available. Estimation of the mounting hardware, connectors, etc. is not included.

Kimnach, Greg L.↗

NASA NTRS1997

Human heading estimation during visually simulated curvilinear motion

Recent studies have suggested that humans cannot estimate their direction of forward translation (heading) from the resulting retinal motion (flow field) alone when rotation rates are higher than approximately 1 deg/sec. It has been argued that either oculomotor or static depth cues are necessary to disambiguate the rotational and translational components of the flow field and, thus, to support accurate heading estimation. We have re-examined this issue using visually simulated motion along a curved path towards a layout of random points as the stimulus. Our data show that, in this curvilinear motion paradigm, five of six observers could estimate their heading relatively accurately and precisely (error and uncertainty < approximately 4 deg), even for rotation rates as high as 16 deg/sec, without the benefit of either oculomotor or static depth cues signaling rotation rate. Such performance is inconsistent with models of human self-motion estimation that require rotation information from sources other than the flow field to cancel the rotational flow.

NASA Center ARC↗

NASA NTRS2004

Subduction in an Eddy-Resolving State Estimate of the Northeast Atlantic Ocean

Are eddies an important contributor to subduction in the eastern subtropical gyre? Here, an adjoint model is used to combine a regional, eddy-resolving numerical model with observations to produce a state estimate of the ocean circulation. The estimate is a synthesis of a variety of in- situ observations from the Subduction Experiment, TOPEX/POSEIDON altimetry, and the MTI General Circulation Model. The adjoint method is successful because the Northeast Atlantic Ocean is only weakly nonlinear. The state estimate provides a physically-interpretable, eddy-resolving information source to diagnose subduction. Estimates of eddy subduction for the eastern subtropical gyre of the North Atlantic are larger than previously calculated from parameterizations in coarse-resolution models. Furthermore, eddy subduction rates have typical magnitudes of 15% of the total subduction rate. Eddies contribute as much as 1 Sverdrup to water-mass transformation, and hence subduction, in the North Equatorial Current and the Azores Current. The findings of this thesis imply that the inability to resolve or accurately parameterize eddy subduction in climate models would lead to an accumulation of error in the structure of the main thermocline, even in the relatively-quiescent eastern subtropical gyre.

WATER MASS TRANSFORMATIONS↗

NASA NTRS2005

Near-Infrared (0.67-4.7 microns) Optical Constants Estimated for Montmorillonite

Various models of the reflectance from particulate surfaces are used for interpretation of remote sensing data of solar system objects. These models rely upon the real (n) and imaginary (k) refractive indices of the materials. Such values are limited for commonly encountered silicates at visual and near-infrared wavelengths (lambda, 0.4-5 microns). Availability of optical constants for candidate materials allows more thorough modeling of the observations obtained by Earth-based telescopes and spacecraft. Two approaches for determining the absorption coefficient (alpha=2pik/lambda) from reflectance measurements of particulates have been described; one relies upon Kubelka-Munk theory and the other Hapke theory. Both have been applied to estimate alpha and k for various materials. Neither enables determination of the wavelength dependence of n, n=f(lambda). Thus, a mechanism providing this ability is desirable. Using Hapke-theory to estimate k from reflectance measurements requires two additional quantities be known or assumed: 1) n=f(lambda) and 2) d, the sample particle diameter. Typically n is assumed constant (c) or modestly varying with lambda; referred to here as n(sub 0). Assuming n(sub 0), at each lambda an estimate of k is used to calculate the reflectance and is iteratively adjusted until the difference between the model and measured reflectance is minimized. The estimated k's (k(sub 1)) are the final results, and this concludes the typical analysis.

Roush, T. L.↗

NASA NTRS2005

A Broadband Microwave Radiometer Technique at X-band for Rain and Drop Size Distribution Estimation

Radiometric brightess temperatures below about 12 GHz provide accurate estimates of path attenuation through precipitation and cloud water. Multiple brightness temperature measurements at X-band frequencies can be used to estimate rainfall rate and parameters of the drop size distribution once correction for cloud water attenuation is made. Employing a stratiform storm model, calculations of the brightness temperatures at 9.5, 10 and 12 GHz are used to simulate estimates of path-averaged median mass diameter, number concentration and rainfall rate. The results indicate that reasonably accurate estimates of rainfall rate and information on the drop size distribution can be derived over ocean under low to moderate wind speed conditions.

Meneghini, R.↗

NASA NTRS2005

Near-infrared (0.67-4.7 micron) Optical Constants Estimated for Montmorillonite

Various models of the reflectance from particulate surfaces are used for interpretation of remote sensing data of solar system objects. These models rely upon the real (n) and imaginary (k) refractive indices of the materials. Such values are limited for commonly encountered silicates at visual and near-infrared wavelengths (lambda, 0.4-5 micron). Availability of optical constants for candidate materials allows more thorough modeling of the observations obtained by Earth-based telescopes and spacecraft. Two approaches for determining the absorption coefficient (alpha=2 pi k/lambda) from reflectance measurements of particulates have been described; one relies upon Kubelka-Munk theory and the other Hapke theory. Both have been applied to estimate alpha and k for various materials. Neither enables determination of the wavelength dependence of n, n=f(lambda). Thus, a mechanism providing this ability is desirable. Using Hapke-theory to estimate k from reflectance measurements requires two additional quantities be known or assumed: 1) n=f(lambda) and 2) d, the sample particle diameter. Typically n is assumed constant (c) or modestly varying with lambda; referred to here as n(sub 0). Assuming n(sub 0), at each lambda an estimate of k is used to calculate the reflectance and is iteratively adjusted until the difference between the model and measured reflectance is minimized. The estimated k's (k(sub l)) are the final results, and this concludes the typical analysis. Additional information is included in the original extended abstract.

Roush, T. L.↗

NASA NTRS2005

The Effect of Infrastructure Sharing in Estimating Operations Cost of Future Space Transportation Systems

NASA and the aerospace industry are extremely serious about reducing the cost and improving the performance of launch vehicles both manned or unmanned. In the aerospace industry, sharing infrastructure for manufacturing more than one type spacecraft is becoming a trend to achieve economy of scale. An example is the Boeing Decatur facility where both Delta II and Delta IV launch vehicles are made. The author is not sure how Boeing estimates the costs of each spacecraft made in the same facility. Regardless of how a contractor estimates the cost, NASA in its popular cost estimating tool, NASA Air force Cost Modeling (NAFCOM) has to have a method built in to account for the effect of infrastructure sharing. Since there is no provision in the most recent version of NAFCOM2002 to take care of this, it has been found by the Engineering Cost Community at MSFC that the tool overestimates the manufacturing cost by as much as 30%. Therefore, the objective of this study is to develop a methodology to assess the impact of infrastructure sharing so that better operations cost estimates may be made.

Sundaram, Meenakshi↗