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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Estimating the Modified Allan Variance

The third-difference approach to modified Allan variance (MVAR) leads to a tractable formula for a measure of MVAR estimator confidence, the equivalent degrees of freedom (edf), in the presence of power-law phase noise. The effect of estimation stride on edf is tabulated. A simple approximation for edf is given, and its errors are tabulated. A theorem allowing conservative estimates of edf in the presence of compound noise processes is given.

Allan Variance↗
NASA NTRS2012

On the Transition and Migration of Flight Functions in the Airspace System

Since ~400 BC, when man first replicated flying behavior with kites, up until the turn of the 20th century, when the Wright brothers performed the first successful powered human flight, flight functions have become available to man via significant support from man-made structures and devices. Over the past 100 years or so, technology has enabled several flight functions to migrate to automation and/or decision support systems. This migration continues with the United States NextGen and Europe s Single European Sky (a.k.a. SESAR) initiatives. These overhauls of the airspace system will be accomplished by accommodating the functional capabilities, benefits, and limitations of technology and automation together with the unique and sometimes overlapping functional capabilities, benefits, and limitations of humans. This paper will discuss how a safe and effective migration of any flight function must consider several interrelated issues, including, for example, shared situation awareness, and automation addiction, or over-reliance on automation. A long-term philosophical perspective is presented that considers all of these issues by primarily asking the following questions: How does one find an acceptable level of risk tolerance when allocating functions to automation versus humans? How does one measure or predict with confidence what the risks will be? These two questions and others will be considered from the two most-discussed paradigms involving the use of increasingly complex systems in the future: humans as operators and humans as monitors.

Morris, Allan Terry↗
NASA NTRS2013

On the Statistical Analysis of X-ray Polarization Measurements

In many polarimetry applications, including observations in the X-ray band, the measurement of a polarization signal can be reduced to the detection and quantification of a deviation from uniformity of a distribution of measured angles of the form alpha plus beta cosine (exp 2)(phi - phi(sub 0) (0 (is) less than phi is less than pi). We explore the statistics of such polarization measurements using both Monte Carlo simulations as well as analytic calculations based on the appropriate probability distributions. We derive relations for the number of counts required to reach a given detection level (parameterized by beta the "number of sigma's" of the measurement) appropriate for measuring the modulation amplitude alpha by itself (single interesting parameter case) or jointly with the position angle phi (two interesting parameters case). We show that for the former case when the intrinsic amplitude is equal to the well known minimum detectable polarization (MDP) it is, on average, detected at the 3sigma level. For the latter case, when one requires a joint measurement at the same confidence level, then more counts are needed, by a factor of approximately equal to 2.2, than that required to achieve the MDP level. We find that the position angle uncertainty at 1sigma confidence is well described by the relation sigma(sub pi) equals 28.5(degrees) divided by beta.

Strohmayer, T. E.↗
NASA NTRS2017

A Large Ordinary Chondrite Shower in the Dominion Range

The US Antarctic Meteorite Program has visited the Dominion Range in the Transantarctic Mountains during several different seasons, including the 1985, 2003, 2008, 2010, and 2014 seasons. Total recovered meteorites from this region is over 2000. The 2008 and 2010 seasons have been fully classified and, respectively) revealing the presence of a large meteorite shower that comprises approximately 60% of all samples recovered in those two seasons. The oil immersion classification suggests that this shower is LL chondrite material, whereas published magnetic susceptibility (MS; log chi) measurements yield L chondrite values. However, usually random sampling of a large collection like this would uncover EOC material for which we have prepared thin sections. In this case, no LL chondrite materials have been found in thin section, suggesting that the shower might instead be an L chondrite. L and LL chondrites are notoriously difficult to distinguish using oil immersion techniques. To better characterize this large group of samples, we have decided to examine some of the large members of this group, using EMPA analysis of the olivines to verify the classifications. With a compositional link between this subset of samples, and the MS measurements, we can more confidently classify the samples making up this pairing group. Subsequently, more accurate and meaningful comparisons may be drawn between this pairing group and some other Antarctic pairing groups such as from the Queen Alexandra Range (QUE), and Lewis Cliffs Ice Tongue (LEW). electron microprobe analysis

Satterwhite, C. E.↗
NASA NTRS2019

Detector Based Calibration of a Portable Imaging Spectrometer for CLARREO Pathfinder Mission

The Climate Absolute Refractivity and Reflectance Observatory (CLARREO) Pathfinder (CPF) mission is being developed to demonstrate SI-traceable retrievals of reflectance at unprecedented accuracies for global satellite observations. An Independent Calibration of the CPF sensor using the Goddard Laser for Absolute Measurement of Radiance (GLAMR) is planned to allow validation of CPF accuracies. GLAMR is a detector-based calibration system relies on a set of NIST-calibrated transfer radiometers to assess the spectral radiance from the GLAMR sphere source to better than 0.3 % (k=2). The current work describes the calibration of the Solar, Lunar Absolute Reflectance Imaging Spectroradiometer (SOLARIS) that was originally developed as a calibration demonstration system for the CLARREO mission and is now being used to assess the independent calibration being developed for CPF. The methodology for the radiometric calibration of SOLARIS is presented as well as results from the GLAMR-based calibration of SOLARIS. The portability of SOLARIS makes it capable of collecting field measurements of earth scenes and direct solar and lunar irradiance similar to those expected during the on-orbit operation of the CPF sensor. Results of SOLARIS field measurements are presented. The use of SOLARIS in this effort also allows the testing protocols for GLAMR to be improved and the field measurements by SOLARIS build confidence in the error budget for GLAMR calibrations. Results are compared to accepted solar irradiance models to demonstrate accuracy values giving confidence in the error budget for the CLARREO reflectance retrieval.

Aytac, Yigit↗
NASA NTRS2022

GJ 3929: High-precision Photometric and Doppler Characterization of an Exo-Venus and Its Hot, Mini-Neptune-mass Companion

We detail the follow-up and characterization of a transiting exo-Venus identified by TESS, GJ 3929b (TOI-2013b), and its nontransiting companion planet, GJ 3929c (TOI-2013c). GJ 3929b is an Earth-sized exoplanet in its star’s Venus zone ( P b = 2.616272 ± 0.000005 days; S b = 17.3 +0.8 -0.7 S ⊕ ) orbiting a nearby M dwarf. GJ 3929c is most likely a nontransiting sub-Neptune. Using the new, ultraprecise NEID spectrometer on the WIYN 3.5 m Telescope at Kitt Peak National Observatory, we are able to modify the mass constraints of planet b reported in previous works and consequently improve the significance of the mass measurement to almost 4σ confidence ( M b = 1.75 ± 0.45 M ⊕ ). We further adjust the orbital period of planet c from its alias at 14.30 ± 0.03 days to the likely true period of 15.04 ± 0.03 days, and we adjust its minimum mass to m sin i = 5.71 ± 0.92 M ⊕ . Using the diffuser-assisted ARCTIC imager on the ARC 3.5 m telescope at Apache Point Observatory, in addition to publicly available TESS and LCOGT photometry, we are able to constrain the radius of planet b to R p = 1.09 ± 0.04 R ⊕ . GJ 3929b is a top candidate for transmission spectroscopy in its size regime (TSM = 14 ± 4), and future atmospheric studies of GJ 3929b stand to shed light on the nature of small planets orbiting M dwarfs.

Exoplanets↗
NASA NTRS1999

Uncertainty Analysis of Inertial Model Attitude Sensor Calibration and Application with a Recommended New Calibration Method

Statistical tools, previously developed for nonlinear least-squares estimation of multivariate sensor calibration parameters and the associated calibration uncertainty analysis, have been applied to single- and multiple-axis inertial model attitude sensors used in wind tunnel testing to measure angle of attack and roll angle. The analysis provides confidence and prediction intervals of calibrated sensor measurement uncertainty as functions of applied input pitch and roll angles. A comparative performance study of various experimental designs for inertial sensor calibration is presented along with corroborating experimental data. The importance of replicated calibrations over extended time periods has been emphasized; replication provides independent estimates of calibration precision and bias uncertainties, statistical tests for calibration or modeling bias uncertainty, and statistical tests for sensor parameter drift over time. A set of recommendations for a new standardized model attitude sensor calibration method and usage procedures is included. The statistical information provided by these procedures is necessary for the uncertainty analysis of aerospace test results now required by users of industrial wind tunnel test facilities.

Tripp, John S.↗
NASA NTRS1978

Search for X-ray polarization in the Crab pulsar

Results of a search for X-ray polarization in the Crab pulsar are presented which were obtained by observing the pulsar at 2.6 and 5.2 keV with identical X-ray polarimeters aboard OSO 8. The polarization in different portions of the X-ray light curve is analyzed, the polarization contribution due to the nebula is removed, and the results of the analysis are given for isolated portions of both the primary pulse and the interpulse at 2.6 and 5.2 keV. No evidence for X-ray polarization is found at the 99% confidence level; 3-sigma upper limits to the polarization at 2.6 keV are given along with the largest polarization allowed at 5.2 keV by the 99% confidence counter. It is noted that the trailing edge of the interpulse at 2.6 keV is 26% polarized at the 92% confidence level, while the 5.2-keV polarization measurement of 40% in the leading edge of the primary pulse is different from zero at 96% confidence. X-ray and optical polarization measurements are compared.

Silver, E. H.↗
NASA NTRS2014

Obtaining Stokes Parameters from the SUMI Experiment

A sounding rocket experiment designed at the Marshall Space Flight Center, named the Solar Ultraviolet Magnetograph Investigation, had its second launch in July of 2012 to test the feasibility of measuring polarization signals of the ionized magnesium resonance doublet near 280 nm, originating from the transition region. The rocket housed a telescope at the front end and an imaging system at the rear end. Placed at the focal point of the self‐filtering telescope, a wave plate rotated through 12 predefined angular orientations to restrict the measurements to specific combinations of circular and linear polarization. Coupled with a double Wollaston analyzer, the linearly polarized ordinary and extraordinary beams were measured for the 12 combinations, each containing different fractions of the Stokes parameters (I, Q, U, V). A thorough analysis of the data has allowed us to come to several conclusions regarding the design of the experiment. 1) We are confident that polarization can be measured. A sunspot region was determined to exhibit similar results over multiple pixels. 2) Measurements are limited by resolution, i.e. regions smaller than the angular resolution per pixel cannot be resolved with any certainty. 3) Temporal evolution of magnetic features must be considered in future experimental designs. Measurements need to be taken in repeated cycles as opposed to a single cycle over the duration of the experiment. In our presentation, we will provide a summary of the observations along with the methods of our analysis, including the limitations that we've encountered.

Fayock, Brian↗
NASA NTRS2004

Prediction of Active-Region CME Productivity from Magnetograms

We report results of an expanded evaluation of whole-active-region magnetic measures as predictors of active-region coronal mass ejection (CME) productivity. Previously, in a sample of 17 vector magnetograms of 12 bipolar active regions observed by the Marshall Space Flight Center (MSFC) vector magnetograph, from each magnetogram we extracted a measure of the size of the active region (the active region s total magnetic flux a) and four measures of the nonpotentiality of the active region: the strong-shear length L(sub SS), the strong-gradient length L(sub SG), the net vertical electric current I(sub N), and the net-current magnetic twist parameter alpha (sub IN). This sample size allowed us to show that each of the four nonpotentiality measures was statistically significantly correlated with active-region CME productivity in time windows of a few days centered on the day of the magnetogram. We have now added a fifth measure of active-region nonpotentiality (the best-constant-alpha magnetic twist parameter (alpha sub BC)), and have expanded the sample to 36 MSFC vector magnetograms of 31 bipolar active regions. This larger sample allows us to demonstrate statistically significant correlations of each of the five nonpotentiality measures with future CME productivity, in time windows of a few days starting from the day of the magnetogram. The two magnetic twist parameters (alpha (sub 1N) and alpha (sub BC)) are normalized measures of an active region s nonpotentially in that they do not depend directly on the size of the active region, while the other three nonpotentiality measures (L(sub SS), L(sub SG), and I(sub N)) are non-normalized measures in that they do depend directly on active-region size. We find (1) Each of the five nonpotentiality measures is statistically significantly correlated (correlation confidence level greater than 95%) with future CME productivity and has a CME prediction success rate of approximately 80%. (2) None of the nonpotentiality measures is a significantly better CME predictor than the others. (3) The active-region phi shows some correlation with CME productivity, but well below a statistically significant level (correlation confidence level less than approximately 80%; CME prediction success rate less than approximately 65%). (4) In addition to depending on magnetic twist, CME productivity appears to have some direct dependence on active-region size (rather than only an indirect dependence through a correlation of magnetic twist with active-region size), but it will take a still larger sample of active regions (50 or more) to certify this. (5) Of the five nonpotentiality measures, L(sub SG) appears to be the best for operational CME forecasting because it is as good or better a CME predictor than the others and it alone does not require a vector magnetogram; L(sub SG) can be measured from a line-of-sight magnetogram such as from the Michelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory (SOHO).

Falconer, D. A.↗
NASA NTRS1975

Quantitative water quality with LANDSAT and Skylab

Correlation studies were completed between LANDSAT Multispectral Scanner (MSS) band ratios derived from computer compatible tape (CCT) and 170 water samples taken from three large Kansas reservoirs, coincident with 16 different LANDSAT passes over a 13 month period. The following conclusions were obtained: (1) LANDSAT MSS reflectance levels are useful for quantitative measurement of suspended solids up to at least 900 ppm, (2) MSS band ratios derived from CCT can measure suspended solids with 67% confidence level accuracy of 12 ppm over the range 0-80 ppm and 35 ppm over the range 0900 ppm, (3) suspended solids contour maps can be easily constructed from CCT for water bodies larger than approximately 100 acres, (4) rationing suppresses MSS reflectance level dependence on seasonal sun angle variation and permits measurement of suspended load the year round in the middle latitudes. SKYLAB imagery from a single pass over three reservoirs compares favorably to LANDSAT results up to 100 ppm.

Yarger, H. L.↗
NASA NTRS2012

Hypersonic Boundary Layer Measurements with Variable Blowing Rates Using Molecular Tagging Velocimetry

Measurements of mean and instantaneous streamwise velocity profiles in a hypersonic boundary layer with variable rates of mass injection (blowing) of nitrogen dioxide (NO2) were obtained over a 10-degree half-angle wedge model. The NO2 was seeded into the flow from a slot located 29.4 mm downstream of the sharp leading edge. The top surface of the wedge was oriented at a 20 degree angle in the Mach 10 flow, yielding an edge Mach number of approximately 4.2. The streamwise velocity profiles and streamwise fluctuating velocity component profiles were obtained using a three-laser NO2->NO photolysis molecular tagging velocimetry method. Observed trends in the mean streamwise velocity profiles and profiles of the fluctuating component of streamwise velocity as functions of the blowing rate are described. An effort is made to distinguish between the effect of blowing rate and wall temperature on the measured profiles. An analysis of the mean velocity profiles for a constant blowing rate is presented to determine the uncertainty in the measurement for different probe laser delay settings. Measurements of streamwise velocity were made to within approximately 120 gm of the model surface. The streamwise spatial resolution in this experiment ranged from 0.6 mm to 2.6 mm. An improvement in the spatial precision of the measurement technique has been made, with spatial uncertainties reduced by about a factor of 2 compared to previous measurements. For the quiescent flow calibration measurements presented, uncertainties as low as 2 m/s are obtained at 95% confidence for long delay times (25 gs). For the velocity measurements obtained with the wind tunnel operating, average single-shot uncertainties of less than 44 m/s are obtained at 95% confidence with a probe laser delay setting of 1 gs. The measurements were performed in the 31-inch Mach 10 Air Tunnel at the NASA Langley Research Center.

Bathel, Brett F.↗
NASA NTRS1987

Efficient computation of parameter confidence intervals

An important step in system identification of aircraft is the estimation of stability and control derivatives from flight data along with an assessment of parameter accuracy. When the maximum likelihood estimation technique is used, parameter accuracy is commonly assessed by the Cramer-Rao lower bound. It is known, however, that in some cases the lower bound can be substantially different from the parameter variance. Under these circumstances the Cramer-Rao bounds may be misleading as an accuracy measure. This paper discusses the confidence interval estimation problem based on likelihood ratios, which offers a more general estimate of the error bounds. Four approaches are considered for computing confidence intervals of maximum likelihood parameter estimates. Each approach is applied to real flight data and compared.

Murphy, Patrick C.↗
NASA NTRS1983

Determining Normal-Distribution Tolerance Bounds Graphically

Graphical method requires calculations and table lookup. Distribution established from only three points: mean upper and lower confidence bounds and lower confidence bound of standard deviation. Method requires only few calculations with simple equations. Graphical procedure establishes best-fit line for measured data and bounds for selected confidence level and any distribution percentile.

Mezzacappa, M. A.↗
NASA NTRS1999

Uncertainty Analysis of Instrument Calibration and Application

Experimental aerodynamic researchers require estimated precision and bias uncertainties of measured physical quantities, typically at 95 percent confidence levels. Uncertainties of final computed aerodynamic parameters are obtained by propagation of individual measurement uncertainties through the defining functional expressions. In this paper, rigorous mathematical techniques are extended to determine precision and bias uncertainties of any instrument-sensor system. Through this analysis, instrument uncertainties determined through calibration are now expressed as functions of the corresponding measurement for linear and nonlinear univariate and multivariate processes. Treatment of correlated measurement precision error is developed. During laboratory calibration, calibration standard uncertainties are assumed to be an order of magnitude less than those of the instrument being calibrated. Often calibration standards do not satisfy this assumption. This paper applies rigorous statistical methods for inclusion of calibration standard uncertainty and covariance due to the order of their application. The effects of mathematical modeling error on calibration bias uncertainty are quantified. The effects of experimental design on uncertainty are analyzed. The importance of replication is emphasized, techniques for estimation of both bias and precision uncertainties using replication are developed. Statistical tests for stationarity of calibration parameters over time are obtained.

Tripp, John S.↗
NASA NTRS1994

Development of a multicomponent force and moment balance for water tunnel applications, volume 1

The principal objective of this research effort was to develop a multicomponent strain gauge balance to measure forces and moments on models tested in flow visualization water tunnels. An internal balance was designed that allows measuring normal and side forces, and pitching, yawing and rolling moments (no axial force). The five-components to applied loads, low interactions between the sections and no hysteresis. Static experiments (which are discussed in this Volume) were conducted in the Eidetics water tunnel with delta wings and a model of the F/A-18. Experiments with the F/A-18 model included a thorough baseline study and investigations of the effect of control surface deflections and of several Forebody Vortex Control (FVC) techniques. Results were compared to wind tunnel data and, in general, the agreement is very satisfactory. The results of the static tests provide confidence that loads can be measured accurately in the water tunnel with a relatively simple multicomponent internal balance. Dynamic experiments were also performed using the balance, and the results are discussed in detail in Volume 2 of this report.

Suarez, Carlos J.↗
NASA NTRS2003

On the Confidence Limit of Hilbert Spectrum

Confidence limit is a routine requirement for Fourier spectral analysis. But this confidence limit is established based on ergodic theory: For stationary process, temporal average equals the ensemble average. Therefore, one can divide the data into n-sections and treat each section as independent realization. Most natural processes in general, and climate data in particular, are not stationary; therefore, there is a need for the Hilbert Spectral analysis for such processes. Here ergodic theory is no longer applicable. We propose to use various adjustable parameters in the shifting processes of the Empirical Mode Decomposition (EMD) method to obtain an ensemble of Intrinsic Mode Function 0 sets. Based on such an ensemble, we introduce a statistical measure in. a form of confidence limits for the Intrinsic Mode Functions, and consequently, the Hilbert spectra. The criterion of selecting the various adjustable parameters is based on the orthogonality test of the resulting M F sets. Length-of-day data from 1962 to 2001 will be used to illustrate this new approach. Its implication in climate data analysis will also be discussed.

Huang, Norden↗
NASA NTRS2006

Establishing and Verifying the Traceability of Remote-Sensing Measurements to International Standards

This viewgraph presentation reviews the principles of establishing and verifying the traceability of remote sensing measurements to national and international scales. Doing this allows comparisons to be made independent of time or locale, and improves understanding of instrument performance, provides confidence in the accuracy of the measurements, improves measurement accuracy and helps contractors understand and meet agency requirements, protecting contractor and customer.

Fraser, Gerald T.↗