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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Estimating normal mixture parameters from the distribution of a reduced feature vector

A FORTRAN computer program was written and tested. The measurements consisted of 1000 randomly chosen vectors representing 1, 2, 3, 7, and 10 subclasses in equal portions. In the first experiment, the vectors are computed from the input means and covariances. In the second experiment, the vectors are 16 channel measurements. The starting covariances were constructed as if there were no correlation between separate passes. The biases obtained from each run are listed.

Guseman, L. F.↗
NASA NTRS1991

Cosmic rays in the Large and Small Magellanic Clouds and the relationship to our Galaxy

Information on the cosmic rays in the Large and Small Magellanic Clouds may be obtained from measurements of the synchrotron radiation related to the energetic electrons, which are believed to contain only about 1 percent of the cosmic rays energy. Assuming the same ratio as in our Galaxy between the cosmic ray electrons and nucleons, the energy density distribution may be estimated. This prediction is compared to that deduced from the matter density distribution, the concept of dynamic balance, and an appropriate coupling scale. For the LMC, the condition of quasi-equilibrium seems satisfied as is required for dynamic balance to be a valid concept, but for the SMC, this seems not to be the case.

Fichtel, Carl E.↗
NASA NTRS1999

Parameter Estimation in Astronomy with Poisson-Distributed Data: The (CHI)2(gamma) Statistic - 1

Applying the standard weighted mean formula, [Sigma (sub i)n(sub i)ssigma(sub i, sup -2)], to determine the weighted mean of data, n(sub i), drawn from a Poisson distribution, will, on average, underestimate the true mean by approx. 1 for all true mean values larger than approx.3 when the common assumption is made that the error of the i th observation is sigma(sub i) = max square root of n(sub i), 1).This small, but statistically significant offset, explains the long-known observation that chi-square minimization techniques which use the modified Neyman'chi(sub 2) statistic, chi(sup 2, sub N) equivalent Sigma(sub i)((n(sub i) - y(sub i)(exp 2)) / max(n(sub i), 1), to compare Poisson - distributed data with model values, y(sub i), will typically predict a total number of counts that underestimates the true total by about 1 count per bin. Based on my finding that weighted mean of data drawn from a Poisson distribution can be determined using the formula [Sigma(sub i)[n(sub i) + min(n(sub i), 1)](n(sub i) + 1)(exp -1)] / [Sigma(sub i)(n(sub i) + 1)(exp -1))], I propose that a new chi(sub 2) statistic, chi(sup 2, sub gamma) equivalent, should always be used to analyze Poisson- distributed data in preference to the modified Neyman's chi(exp 2) statistic. I demonstrated the power and usefulness of,chi(sub gamma, sup 2) minimization by using two statistical fitting techniques and five chi(exp 2) statistics to analyze simulated X-ray power - low 15 - channel spectra with large and small counts per bin. I show that chi(sub gamma, sup 2) minimization with the Levenberg - Marquardt or Powell's method can produce excellent results (mean slope errors approx. less than 3%) with spectra having as few as 25 total counts.

Mighell, Kenneth J.↗
NASA NTRSDate not supplied

Flight Performance Estimates for the NASA X-57 Distributed Electric Propulsion Flight Demonstrator

The X-57 flight demonstrator concept featured four configurations starting with a conventional combustion-powered multiengine airplane and ending with a fully electric configuration with two forms of distributed propulsion and a highly modified wing. These configurations, called Mods, were designed to gain incremental insight into different aircraft propulsion configuration options and their impact on the aircraft performance. The gasoline-powered Mod I configuration consumed 2.6 to 2.9 times more stored energy in cruise than the electric but otherwise conventionally configured Mod II configuration. The highly loaded wing of Mod III led to an increase of 40% in the power-off lift-to-drag ratio as compared to Mod II at the project high-speed cruise target speed and altitude. The power-on lift-to-drag ratio of Mod III was 53% higher than Mod II due to the beneficial aero-propulsive interaction of the wingtip-mounted cruise propellers in Mod III. The high-lift propeller system of Mod IV recovered the low-speed performance of the conventional configuration in Mod II that was otherwise lost with the introduction of the highly loaded Mod III wing. The battery-electric configurations also benefitted from a lack of power lapse in the electric motors with increasing air density as compared to the combustion-powered baseline aircraft.

Distributed Performance↗
NASA NTRSDate not supplied

Flight Performance Estimates for the NASA X-57 Distributed Electric Propulsion Flight Demonstrator

The X-57 flight demonstrator concept featured four configurations starting with a conventional combustion-powered multiengine airplane and ending with a fully electric configuration with two forms of distributed propulsion and a highly modified wing. These configurations, called Mods, were designed to gain incremental insight into different aircraft propulsion configuration options and their impact on the aircraft performance. The gasoline-powered Mod I configuration consumed 2.6 to 2.9 times more stored energy in cruise than the electric but otherwise conventionally configured Mod II configuration. The highly loaded wing of Mod III led to an increase of 40% in the power-off lift-to-drag ratio as compared to Mod II at the project high-speed cruise target speed and altitude. The power-on lift-to-drag ratio of Mod III was 53% higher than Mod II due to the beneficial aero-propulsive interaction of the wingtip-mounted cruise propellers in Mod III. The high-lift propeller system of Mod IV recovered the low-speed performance of the conventional configuration in Mod II that was otherwise lost with the introduction of the highly loaded Mod III wing. The battery-electric configurations also benefitted from a lack of power lapse in the electric motors with increasing air density as compared to the combustion-powered baseline aircraft.

Distributed Performance↗
NASA NTRS2021

Radar-Based Bayesian Estimation of Ice Crystal Growth Parameters within a Microphysical Model

The potential for polarimetric Doppler radar measurements to improve predictions of ice microphysical processes within an idealized model–observational framework is examined. In an effort to more rigorously constrain ice growth processes (e.g., vapor deposition) with observations of natural clouds, a novel framework is developed to compare simulated and observed radar measurements, coupling a bulk adaptive-habit model of vapor growth to a polarimetric radar forward model. Bayesian inference on key microphysical model parameters is then used, via a Markov chain Monte Carlo sampler, to estimate the probability distribution of the model parameters. The statistical formalism of this method allows for robust estimates of the optimal parameter values, along with (non-Gaussian) estimates of their uncertainty. To demonstrate this framework, observations from Department of Energy radars in the Arctic during a case of pristine ice precipitation are used to constrain vapor deposition parameters in the adaptive habit model. The resulting parameter probability distributions provide physically plausible changes in ice particle density and aspect ratio during growth. A lack of direct constraint on the number concentration produces a range of possible mean particle sizes, with the mean size inversely correlated to number concentration. Consistency is found between the estimated inherent growth ratio and independent laboratory measurements, increasing confidence in the parameter PDFs and demonstrating the effectiveness of the radar measurements in constraining the parameters. The combined Doppler and polarimetric observations produce the highest-confidence estimates of the parameter PDFs, with the Doppler measurements providing a stronger constraint for this case.

Robert S. Schrom↗
NASA NTRS2011

Sensitivity of C-Band Polarimetric Radar-Based Drop Size Distribution Measurements to Maximum Diameter Assumptions

The estimation of rain drop size distribution (DSD) parameters from polarimetric radar observations is accomplished by first establishing a relationship between differential reflectivity (Z(sub dr)) and the central tendency of the rain DSD such as the median volume diameter (D0). Since Z(sub dr) does not provide a direct measurement of DSD central tendency, the relationship is typically derived empirically from rain drop and radar scattering models (e.g., D0 = F[Z (sub dr)] ). Past studies have explored the general sensitivity of these models to temperature, radar wavelength, the drop shape vs. size relation, and DSD variability. Much progress has been made in recent years in measuring the drop shape and DSD variability using surface-based disdrometers, such as the 2D Video disdrometer (2DVD), and documenting their impact on polarimetric radar techniques. In addition to measuring drop shape, another advantage of the 2DVD over earlier impact type disdrometers is its ability to resolve drop diameters in excess of 5 mm. Despite this improvement, the sampling limitations of a disdrometer, including the 2DVD, make it very difficult to adequately measure the maximum drop diameter (D(sub max)) present in a typical radar resolution volume. As a result, D(sub max) must still be assumed in the drop and radar models from which D0 = F[Z(sub dr)] is derived. Since scattering resonance at C-band wavelengths begins to occur in drop diameters larger than about 5 mm, modeled C-band radar parameters, particularly Z(sub dr), can be sensitive to D(sub max) assumptions. In past C-band radar studies, a variety of D(sub max) assumptions have been made, including the actual disdrometer estimate of D(sub max) during a typical sampling period (e.g., 1-3 minutes), D(sub max) = C (where C is constant at values from 5 to 8 mm), and D(sub max) = M*D0 (where the constant multiple, M, is fixed at values ranging from 2.5 to 3.5). The overall objective of this NASA Global Precipitation Measurement Mission (GPM/PMM Science Team)-funded study is to document the sensitivity of DSD measurements, including estimates of D0, from C-band Z(sub dr) and reflectivity to this range of D(sub max) assumptions. For this study, GPM Ground Validation 2DVD's were operated under the scanning domain of the UAHuntsville ARMOR C-band dual-polarimetric radar. Approximately 7500 minutes of DSD data were collected and processed to create gamma size distribution parameters using a truncated method of moments approach. After creating the gamma parameter datasets the DSD's were then used as input to a T-matrix model for computation of polarimetric radar moments at C-band. All necessary model parameterizations, such as temperature, drop shape, and drop fall mode, were fixed at typically accepted values while the D(sub max) assumption was allowed to vary in sensitivity tests. By hypothesizing a DSD model with D(sub max) (fit) from which the empirical fit to D0 = F[Z(sub dr)] was derived via non-linear least squares regression and a separate reference DSD model with D(sub max) (truth), bias and standard error in D0 retrievals were estimated in the presence of Z(sub dr) measurement error and hypothesized mismatch in D(sub max) assumptions. Although the normalized standard error for D0 = F[Z(sub dr)r] can increase slightly (as much as from 11% to 16% for all 7500 DSDs) when the D(sub max) (fit) does not match D(sub max) (truth), the primary impact of uncertainty in D(sub max) is a potential increase in normalized bias error in D0 (from 0% to as much as 10% over all 7500 DSDs, depending on the extent of the mismatch between D(sub max) (fit) and D(sub max) (truth)). For DSDs characterized by large Z(sub dr) (Z(sub dr) > 1.5 to 2.0 dB), the normalized bias error for D0 estimation at C-band is sometimes unacceptably large (> 10%), again depending on the extent of the hypothesized D(sub max) mismatch. Modeled errors in D0 retrievals from Z(sub dr) at C-band are demonstrated in detail and comparedo similar modeled retrieval errors at S-band and X-band where the sensitivity to D(sub max) is expected to be less. The impact of D(sub max) assumptions to the retrieval of other DSD parameters such as Nw, the liquid water content normalized intercept parameter, are also explored. Likely implications for DSD retrievals using C-band polarimetric radar for GPM are assessed by considering current community knowledge regarding D(sub max) and quantifying the statistical distribution of Z(sub dr) from ARMOR over a large variety of meteorological conditions. Based on these results and the prevalence of C-band polarimetric radars worldwide, a call for more emphasis on constraining our observational estimate of D(sub max) within a typical radar resolution volume is made

Carey, Lawrence D.↗
NASA NTRS2013

Method for Estimating Operational Loads on Aerospace Structures Using Span-Wisely Distributed Surface Strains

This report presents a new method for estimating operational loads (bending moments, shear loads, and torques) acting on slender aerospace structures using distributed surface strains (unidirectional strains). The surface strain-sensing stations are to be evenly distributed along each span-wise strain-sensing line. A depth-wise cross section of the structure along each strain-sensing line can then be considered as an imaginary embedded beam. The embedded beam was first evenly divided into multiple small domains with domain junctures matching the strain-sensing stations. The new method is comprised of two steps. The first step is to determine the structure stiffness (bending or torsion) using surface strains obtained from a simple bending (or torsion) loading case, for which the applied bending moment (or torque) is known. The second step is to use the strain-determined structural stiffness (bending or torsion), and a new set of surface strains induced by any other loading case to calculate the associated operational loads (bending moments, shear loads, or torques). Performance of the new method for estimating operational loads was studied in light of finite-element analyses of several example structures subjected to different loading conditions. The new method for estimating operational loads was found to be fairly accurate, and is very promising for applications to the flight load monitoring of flying vehicles with slender wings.

Ko, William L.↗
NASA NTRS1973

Comparison between photogrammetric and bistatic-radar slope frequency distributions

A comparison was made of the results for lunar surface roughness estimates and slope frequency distributions obtained by using photogrammetric techniques with those obtained by using bistatic radar. Three topics were discussed: (1) the form of the slope frequency distributions, (2) the change of roughness estimates of the lunar surface with scale, and (3) the magnitude of surface roughness.

Moore, H. J.↗
NASA NTRS1977

The distribution of seismic velocities and attenuation in the earth

Estimates of the radial distribution of seismic velocities and density and of seismic attenuation within the earth are obtained through inversion of body wave, surface wave, and normal mode data. The effect of attenuation related dispersion on gross earth structure, and on the reliability of eigenperiod identifications is discussed. The travel time baseline discrepancies between body waves and free oscillation models are examined and largely resolved.

Hart, R. S.↗
NASA NTRS1982

A comparison of minimum distance and maximum likelihood techniques for proportion estimation

The estimation of mixing proportions P sub 1, P sub 2,...P sub m in the mixture density f(x) = the sum of the series P sub i F sub i(X) with i = 1 to M is often encountered in agricultural remote sensing problems in which case the p sub i's usually represent crop proportions. In these remote sensing applications, component densities f sub i(x) have typically been assumed to be normally distributed, and parameter estimation has been accomplished using maximum likelihood (ML) techniques. Minimum distance (MD) estimation is examined as an alternative to ML where, in this investigation, both procedures are based upon normal components. Results indicate that ML techniques are superior to MD when component distributions actually are normal, while MD estimation provides better estimates than ML under symmetric departures from normality. When component distributions are not symmetric, however, it is seen that neither of these normal based techniques provides satisfactory results.

Woodward, W. A.↗
NASA NTRS1988

A unified framework for approximation in inverse problems for distributed parameter systems

A theoretical framework is presented that can be used to treat approximation techniques for very general classes of parameter estimation problems involving distributed systems that are either first or second order in time. Using the approach developed, one can obtain both convergence and stability (continuous dependence of parameter estimates with respect to the observations) under very weak regularity and compactness assumptions on the set of admissible parameters. This unified theory can be used for many problems found in the recent literature and in many cases offers significant improvements to existing results.

Banks, H. T.↗
NASA NTRS1975

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions, Addendum

New results and insights concerning a previously published iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions were discussed. It was shown that the procedure converges locally to the consistent maximum likelihood estimate as long as a specified parameter is bounded between two limits. Bound values were given to yield optimal local convergence.

Peters, B. C., Jr.↗
NASA NTRS2015

Coupled Inertial Navigation and Flush Air Data Sensing Algorithm for Atmosphere Estimation

This paper describes an algorithm for atmospheric state estimation that is based on a coupling between inertial navigation and flush air data sensing pressure measurements. In this approach, the full navigation state is used in the atmospheric estimation algorithm along with the pressure measurements and a model of the surface pressure distribution to directly estimate atmospheric winds and density using a nonlinear weighted least-squares algorithm. The approach uses a high fidelity model of atmosphere stored in table-look-up form, along with simplified models of that are propagated along the trajectory within the algorithm to provide prior estimates and covariances to aid the air data state solution. Thus, the method is essentially a reduced-order Kalman filter in which the inertial states are taken from the navigation solution and atmospheric states are estimated in the filter. The algorithm is applied to data from the Mars Science Laboratory entry, descent, and landing from August 2012. Reasonable estimates of the atmosphere and winds are produced by the algorithm. The observability of winds along the trajectory are examined using an index based on the discrete-time observability Gramian and the pressure measurement sensitivity matrix. The results indicate that bank reversals are responsible for adding information content to the system. The algorithm is then applied to the design of the pressure measurement system for the Mars 2020 mission. The pressure port layout is optimized to maximize the observability of atmospheric states along the trajectory. Linear covariance analysis is performed to assess estimator performance for a given pressure measurement uncertainty. The results indicate that the new tightly-coupled estimator can produce enhanced estimates of atmospheric states when compared with existing algorithms.

Karlgaard, Christopher D.↗
NASA NTRS2016

Predicting Real-Time Safety of the National Airspace System

To gain the situational awareness necessary for informed decision making regarding avoidance of airspace hazards, each operator must consolidate operations-relevant information from disparate sources and apply extensive domain knowledge to correctly interpret not just the current state of the NAS but forecast its (combined) evolution over the duration of the operation. This time- and workload-intensive process is periodically repeated throughout the operation so that changes can be managed in a timely manner.The imprecision, inaccuracies, inconsistency, and incompleteness of the incoming data further challenges the process. To facilitate informed decision making, this paper presents a model-based framework for the textitautomated real-time monitoring and prediction of possible effects of airspace hazards on the safety of the National Airspace System (NAS). First, hazards to flight are identified and transformed into sms, that is, quantities of interest that could be evaluated based on available data and are predictive of an unsafe event. The sms and associated thresholds that specify when an event transitions from emphsafe to emphunsafe are combined with models of airspace operations and aircraft dynamics. The framework can include any hazard to flight that can be modeled quantitatively. Models can be detailed and complex, or they can be considerably simplifed, as appropriate to the application. Real-time NAS safety monitoring and prediction begins with an estimate of the state of the NAS using the dynamic models. Given the state estimate and a probability distribution of future inputs to the NAS, we can then predict the evolution of the NAS - the future state - and the occurrence of hazards and unsafe events. The entire probability distribution of airspace sms is computed, not just point estimates, without significant assumptions regarding the distribution type andor parameters. We demonstrate our overall approach through a simulated scenario in which we predict the occurrence of some unsafe events and show how these predictions evolve in time as flight operations progress. Predictions accounting for common sources of uncertainty are included and it is shown how the predictions improve in time, become more confident, and change dynamically as new information is made available to the prediction algorithm.

safety↗
NASA NTRS1969

Comments on bistatic lidar

The use of bistatic lidar to determine the size and concentration of atmospheric aerosols is discussed. It is shown that bistatic measurements made at several scattering angles coupled with logical assumptions about the size distribution can provide estimates of the aerosol concentration, and by polarization measurements, meteorological parameters that influence the vertical distribution of particulates can be determined.

Reagan, J. A.↗