Results for “Function Estimation” — Page 34

NASA NTRS1994

Time scales of pattern evolution from cross-spectrum analysis of advanced very high resolution radiometer and coastal zone color scanner imagery

We have selected square subareas (110 km on a side) from coastal zone color scanner (CZCS) and advanced very high resolution radiometer (AVHRR) images for 1981 in the California Current region off northern California for which we could identify sequences of cloud-free data over periods of days to weeks. We applied a two-dimensional fast Fourier transformation to images after median filtering, (x, y) plane removal, and cosine tapering. We formed autospectra and coherence spectra as functions of a scalar wavenumber. Coherence estimates between pairs of images were plotted against time separation between images for several wide wavenumber bands to provide a temporal lagged coherence function. The temporal rate of loss of correlation (decorrelation time scale) in surface patterns provides a measure of the rate of pattern change or evolution as a function of spatial dimension. We found that patterns evolved (or lost correlation) approximately twice as rapidly in upwelling jets as in the 'quieter' regions between jets. The rapid evolution of pigment patterns (lifetime of about 1 week or less for scales of 50-100 km) ought to hinder biomass transfer to zooplankton predators compared with phytoplankton patches that persist for longer times. We found no significant differences between the statistics of CZCS and AVHRR images (spectral shape or rate of decorrelation). In addition, in two of the three areas studied, the peak correlation between AVHRR and CZCS images from the same area occurred at zero lag, indicating that the patterns evolved simutaneously. In the third area, maximum coherence between thermal and pigment patterns occurred when pigment images lagged thermal images by 1-2 days, mirroring the expected lag of high pigment behind low temperatures (and high nutrients) in recently upwelled water. We conclude that in dynamic areas such as coastal upwelling systems, the phytoplankton cells (identified by pigment color patterns) behave largely as passive scalars at the mesoscale and that growth, death, and sinking of phytoplankton collectively play at most a mariginal role in determining the spectral statistics of the pigment patterns.

Denman, Kenneth L.↗

NASA NTRS1997

Functional specializations in human cerebral cortex analyzed using the Visible Man surface-based atlas

We used surface-based representations to analyze functional specializations in the human cerebral cortex. A computerized reconstruction of the cortical surface of the Visible Man digital atlas was generated and transformed to the Talairach coordinate system. This surface was also flattened and used to establish a surface-based coordinate system that respects the topology of the cortical sheet. The linkage between two-dimensional and three-dimensional representations allows the locations of published neuroimaging activation foci to be stereotaxically projected onto the Visible Man cortical flat map. An analysis of two activation studies related to the hearing and reading of music and of words illustrates how this approach permits the systematic estimation of the degree of functional segregation and of potential functional overlap for different aspects of sensory processing.

Non-NASA Center↗

NASA NTRS2015

Observing System Simulations for Small Satellite Formations Estimating Bidirectional Reflectance

The bidirectional reflectance distribution function (BRDF) gives the reflectance of a target as a function of illumination geometry and viewing geometry, hence carries information about the anisotropy of the surface. BRDF is needed in remote sensing for the correction of view and illumination angle effects (for example in image standardization and mosaicing), for deriving albedo, for land cover classification, for cloud detection, for atmospheric correction, and other applications. However, current spaceborne instruments provide sparse angular sampling of BRDF and airborne instruments are limited in the spatial and temporal coverage. To fill the gaps in angular coverage within spatial, spectral and temporal requirements, we propose a new measurement technique: Use of small satellites in formation flight, each satellite with a VNIR (visible and near infrared) imaging spectrometer, to make multi-spectral, near-simultaneous measurements of every ground spot in the swath at multiple angles. This paper describes an observing system simulation experiment (OSSE) to evaluate the proposed concept and select the optimal formation architecture that minimizes BRDF uncertainties. The variables of the OSSE are identified; number of satellites, measurement spread in the view zenith and relative azimuth with respect to solar plane, solar zenith angle, BRDF models and wavelength of reflection. Analyzing the sensitivity of BRDF estimation errors to the variables allow simplification of the OSSE, to enable its use to rapidly evaluate formation architectures. A 6-satellite formation is shown to produce lower BRDF estimation errors, purely in terms of angular sampling as evaluated by the OSSE, than a single spacecraft with 9 forward-aft sensors. We demonstrate the ability to use OSSEs to design small satellite formations as complements to flagship mission data. The formations can fill angular sampling gaps and enable better BRDF products than currently possible.

small satellite↗

NASA NTRSDate not supplied

Near Rectilinear Halo Orbit Determination with Simulated DSN Observations

This paper presents the results of a high-fidelity simulation of spacecraft orbit determination in a near rectilinear halo orbit (NRHO). Others in the literature have examined this problem with linear covariance analysis, but the highly-nonlinear dynamics of this orbit challenge the assumptions underlying such analyses. The present work builds on similar analysis performed by other authors to contribute a fuller understanding of the operational requirements for NRHO navigation. The present work serves as a check to the assumptions of previous studies and an independent verification of those results. The results from the literature are extended by quantifying the space of orbital states from which a spacecraft with given control authority can safely return to the nominal path. Spacecraft state uncertainty estimates are evaluated as a function of time. Simulated range and range-rate measurements with the Deep Space Network (DSN) ground stations are used to model orbit determination accuracy. Orbit maintenance maneuvers are performed using both short-horizon and long-horizon stationkeeping targeting. Monte Carlo analysis of orbit determination and stationkeeping is performed. This paper quantifies the achievable state uncertainty with deep space network (DSN)-only range and range-rate observations. This paper also addresses requirements on the frequency of DSN observation periods and correlates ground contact frequency with navigation accuracy. The results of several related studies are presented and discussed: the effect of missing ground station passes, the effect of missing stationkeeping maneuvers, the sensitivity of the spacecraft state estimate to realistic error sources, and stationkeeping propellant budget.

Nathan L Parrish↗

NASA NTRS1991

Approximate effect of parameter pseudonoise intensity on rate of convergence for EKF parameter estimators

When using parameter estimation methods based on extended Kalman filter (EKF) theory, it is common practice to assume that the unknown parameter values behave like a random process, such as a random walk, in order to guarantee their identifiability by the filter. The present work is the result of an ongoing effort to quantitatively describe the effect that the assumption of a fictitious noise (called pseudonoise) driving the unknown parameter values has on the parameter estimate convergence rate in filter-based parameter estimators. The initial approach is to examine a first-order system described by one state variable with one parameter to be estimated. The intent is to derive analytical results for this simple system that might offer insight into the effect of the pseudonoise assumption for more complex systems. Such results would make it possible to predict the estimator error convergence behavior as a function of the assumed pseudonoise intensity, and this leads to the natural application of the results to the design of filter-based parameter estimators. The results obtained show that the analytical description of the convergence behavior is very difficult.

Hill, Bryon K.↗

NASA NTRS2001

Cloud Spatial Structure and 3D Radiative Transfer

Cloud radiative properties are sensitive to drop size and other parameters of cloud micro-structure, but also to cloud shape, spacing, and other parameters of cloud macro-structure, including internal fractal structure. New information on cloud structure is being derived from a variety of cloud radars and lidars. Ongoing field programs such as DoE/ARM are improving the measurement and modelling of physical and radiative properties of clouds. A parallel effort is underway to improve cloud remote sensing, especially from the new suite of EOS (Earth Observing System) instruments which are beginning to provide higher spectral, spatial resolution, and/or angular resolution. Key parameters for improving pixel-scale retrievals are cloud thickness and photon mean-free-path, which together determine the scale of "radiative smoothing" of cloud fluxes and radiances. This scale has been observed as a change in the spatial spectrum of Landsat cloud radiances, and was also recently found with the Goddard micropulse lidar, by searching for returns from directions nonparallel to the incident beam. "Offbeam" Lidar returns are now being used to estimate the cloud "radiative Green's function", (G). G depends on cloud thickness and may be used to retrieve that important quantity. G is also being applied to improving simple estimates of cloud radiative properties that are based on the "Independent Pixel Approximation" or IPA. This and other measurements of 3D transfer in clouds, coupled with Monte Carlo and other 3D transfer methods, are beginning to provide a better understanding of the dependence of radiation on cloud inhomogeneity, and to suggest new retrieval and parameterization algorithms which take account of cloud inhomogeneity. An international "Intercomparison of 3D Radiation Codes" or I3RC, program is underway to coordinate and evaluate the variety of 3D radiative transfer methods now available, and to make them more widely available. Information is on the Web at: http://climate.gsfc.nasa.gov/I3RC. Input consists of selected cloud fields derived from data sources such as radar, microwave and satellite, and from models involved in the GEWEX Cloud Systems Studies. Output is selected radiative quantities that characterize the large-scale properties of the fields of radiative fluxes and heating. Several example cloud fields will be used to illustrate the effects of cloud inhomogeneity and 3D radiation.

Cahalan, Robert F.↗

NASA NTRS2001

Cloud Spatial Structure and 3D Radiative Transfer

Cloud radiative properties are sensitive to drop size and other parameters of cloud micro-structure, but also to cloud shape, spacing, and other parameters of cloud macro-structure, including internal fractal structure. New information on cloud structure is being derived from a variety of cloud radars and lidars. Ongoing field programs such as DoE/ARM (atmospheric radiation measurement) are improving the measurement and modelling of physical and radiative properties of clouds. A parallel effort is underway to improve cloud remote sensing, especially from the new suite of EOS (Earth observing system) instruments which are beginning to provide higher spectral, spatial resolution, and/or angular resolution. Key parameters for improving pixel-scale retrievals are cloud thickness and photon mean-free-path, which together determine the scale of 'radiative smoothing' of cloud fluxes and radiances. This scale has been observed as a change in the spatial spectrum of Landsat cloud radiances, and was also recently found with the Goddard micropulse lidar, by searching for returns from directions nonparallel to the incident beam. 'Offbeam' Lidar returns are now being used to estimate the cloud 'radiative Green's function' (G). G depends on cloud thickness and may be used to retrieve that important quantity. G is also being applied to improving simple estimates of cloud radiative properties that are based on the 'Independent Pixel Approximation' or IPA. This and other measurements of 3D (three dimensional) transfer in clouds, coupled with Monte Carlo and other 3D transfer methods, are beginning to provide a better understanding of the dependence of radiation on cloud inhomogeneity, and to suggest new retrieval and parameterization algorithms which take account of cloud inhomogeneity. An international 'Intercomparison of 3D Radiation Codes' (I3RC) program is underway to coordinate and evaluate the variety of 3D radiative transfer methods now available, and to make them more widely available. Information is on the Web at: http://climate.gsfc.nasa.gov/I3RC. Input consists of selected cloud fields derived from data sources such as radar, microwave and satellite, and from models involved in the GEWEX Cloud Systems Studies. Output is selected radiative quantities that characterize the large-scale properties of the fields of radiative fluxes and heating. Several example cloud fields will be used to illustrate the effects of cloud inhomogeneity and 3D radiation.

Cahalan, Robert F.↗

NASA NTRS1999

Cloud Spatial Structure and 3D Radiative Transfer

Cloud radiative properties are sensitive to drop size and other parameters of cloud micro-structure, but also to cloud shape,spacing, and other parameters of cloud macro-structure, including internal fractal structure. New information on cloud structure is being derived from a variety of cloud radars, and ongoing field programs such as DoE/ARM. These programs are improving the measurement and modelling of physical and radiative properties of clouds. A parallel effort is underway to improve cloud remote sensing, especially from the new suite of EOS-AM1 instruments which will provide higher spectral, spatial resolution, and/or angular resolution. Key parameters for improving pixel-scale retrievals are cloud thickness and photon mean-free-path, which together determine the scale of "radiative smoothing" of cloud fluxes and radiances. This scale has been observed as a change in the spatial spectrum of Landsat cloud radiances, and was also recently found with the Goddard micropulse lidar, by searching for returns from directions nonparallel to the incident beam. "Offbeam" Lidar returns are now being used to estimate the cloud "radiative Green's function", G,which depends on cloud thickness and may be used to retrieve that important quantity. G is also being applied to improving simple IPA estimates of cloud radiative properties. This and other measurements of 3D transfer in clouds, coupled with Monte Carlo and other 3D transfer methods, are beginning to provide a better understanding of the dependence of radiation on cloud inhomogeneity, and to suggest new retrieval and parameterization algorithms which take account of cloud inhomogeneity.

Cahalan, Robert F.↗

NASA NTRS1999

Cloud Spatial Structure and 3D Radiative Transfer

Cloud radiative properties are sensitive to drop size and other parameters of cloud micro-structure, but also to cloud shape,spacing, and other parameters of cloud macro-structure, including internal fractal structure. New information on cloud structure is being derived from a variety of cloud radars. Ongoing field programs such as Department of Energy's Atmospheric Radiation Measurement (DoE/ARM) are improving the measurement and modelling of physical and radiative properties of clouds. A parallel effort is underway to improve cloud remote sensing, especially from the new suite of EOS-AM1 instruments which will provide higher spectral, spatial resolution, and/or angular resolution. Key parameters for improving pixel-scale retrievals are cloud thickness and photon mean-free-path, which together determine the scale of "radiative smoothing" of cloud fluxes and radiances. This scale has been observed as a change in the spatial spectrum of Landsat cloud radiances, and was also recently found with the Goddard micropulse lidar, by searching for returns from directions nonparallel to the incident beam. "Offbeam" Lidar returns are now being used to estimate the cloud "radiative Green's function", G,which depends on cloud thickness and may be used to retrieve that important quantity. G is also being applied to improving simple IPA estimates of cloud radiative properties. This and other measurements of 3D transfer in clouds, coupled with Monte Carlo and other 3D transfer methods, are beginning to provide a better understanding of the dependence of adiation on cloud inhomogeneity, and to suggest new retrieval and parameterization algorithms which take account of cloud inhomogeneity. An international "Intercomparison of 3D Radiation Codes" or I3RC, program is beginning to coordinate and evaluate the variety of 3D radiative transfer methods now available, and to make them more widely available. Information is on the Web at: http://climate.qsfc.nasa.crov/I3RC. Input consists of selected cloud fields derived from data sources such as radar, microwave and satellite, and from models involved in the GEWEX Cloud Systems Studies. Output is selected radiative quantities that characterize the large- scale properties of the fields of radiative fluxes and heating. Several example cloud fields will be used to illustrate.

Cahalan, Robert F.↗

NASA NTRS1978

On least squares collocation

It is shown that the least squares collocation approach to estimating geodetic parameters is identical to conventional minimum variance estimation. Hence, the least squares collocation estimator can be derived either by minimizing the usual least squares quadratic loss function or by computing a conditional expectation by means of the regression equation. When a deterministic functional relationship between the data and the parameters to be estimated is available, one can implement a least squares solution using the functional relation to obtain an equation of condition. It is proved the solution so obtained is identical to what is obtained through least squares collocation. The implications of this equivalance for the estimation of mean gravity anomalies are discussed.

Argentiero, P. D.↗

NASA NTRSDate not supplied

Operational Modal Analysis of the Artemis I Dynamic Rollout Test and Wet Dress Rehearsal

NASA has developed an expendable heavy lift launch vehicle capability, the Space Launch System (SLS), to support lunar and deep space exploration. The uncrewed Artemis I was the first flight of this new launch vehicle and tested critical systems for the upcoming crewed Artemis II flight to the moon. Accelerations were recorded at a multitude of locations on Artemis, the Mobile Launcher (ML), and the Crawler Transporter (CT)during the rollout of Artemis I from the Vehicle Assembly Building (VAB) to Launch Pad 39B March 2022 and is referred to as the Artemis I Dynamic Rollout Test (DRT). While Artemis I was at Launch Pad 39B, the Wet Dress Rehearsal (WDR) was performed to demonstrate launch readiness and acceleration measurements were also recorded. Finally, Artemis I rolled back from Launch Pad 39B to the VAB in April 2022, where acceleration measurements were also recorded and is referred to as the rollback portion of DRT. Because the forces during rollout and at the launch pad acting on Artemis I, the ML, and the CT are not directly measurable, Operational Modal Analysis (OMA) techniques, instead of traditional Experimental Modal Analysis (EMA) techniques, were used to identify modal characteristics. The OMA analysis of DRT and WDR directly builds upon the lessons learned from the OMA analysis of an earlier rollout of the ML from the VAB. DRT and WDR dynamic characteristics will be used to support SLS Integrated Modal Test finite element model correlation efforts and Exploration Ground System ML and CT finite element model verification and validation, which are part of the Building Block approach the Space Launch System program has implemented. The dynamic characteristics extracted from DRT as well as the rollout acceleration time histories themselves will be used in the development of generic rollout forcing functions that will provide refined estimates of the Artemis IV rollout forces, which will have the heavier and larger SLS Block 1B launch vehicle and Mobile Launcher 2 (ML-2). This paper briefly describes Artemis I, the ML, and the CT physical characteristics, DRT rollout/rollback and WDR data collection, the challenges in implementing OMA techniques due in part to the CT harmonics, and how these challenges were overcome to obtain the Artemis I DRT configuration and WDR configuration modal characteristics.

Apollo↗

NASA NTRS1971

Design of optimal probing signals for vector parameter estimation.

In the design of optimal inputs or probing signals for parameter estimation, it is more natural to consider functions of the Fisher information matrix as the criterion of optimality instead of some function of the error covariance matrix. The input which maximizes the Fisher information measure for efficient estimation of a scalar parameter also provides the minimum error variance. The information is thus a logical choice for the optimality criterion in scalar problems. No such obvious choice is apparent for vector parameter estimation. A number of performance measures are examined and compared in the present study, and a useful criterion is selected. The design of an optimal probing signal using this criterion is shown to be equivalent to an optimal control problem in which certain equality constraints must be satisfied. This problem may be solved by conventional techniques of deterministic or stochastic optimal control.

Nahi, N. E.↗

NASA NTRS1975

Estimates of saltation threshold and erosion rates on Mars

The Mariner 9 photographs of the Martian surface include many which show crater-associated streaks caused by atmospheric winds. Due to the low density atmosphere of Mars, the wind speeds necessary to move surface particles and thus cause the streaks are apparently very high. The atmospheric-boundary-layer wind tunnel has been used to determine threshold speeds for particles of varying density and diameter and the results for small particles have been extrapolated to estimate somewhat lower threshold speeds on Mars than previous estimates. A series of streak modeling tests is used to derive an erosion-rate correlation function, which is in turn used to estimate erosion rates to the lee of some of the craters on Mars which exhibited time-dependent streak behavior during the mission.

Iversen, J. D.↗

NASA NTRS1992

Studies on spectral analysis of randomly sampled signals: Application to laser velocimetry data

Spectral analysis is very useful in determining the frequency characteristics of many turbulent flows, for example, vortex flows, tail buffeting, and other pulsating flows. It is also used for obtaining turbulence spectra from which the time and length scales associated with the turbulence structure can be estimated. These estimates, in turn, can be helpful for validation of theoretical/numerical flow turbulence models. Laser velocimetry (LV) is being extensively used in the experimental investigation of different types of flows, because of its inherent advantages; nonintrusive probing, high frequency response, no calibration requirements, etc. Typically, the output of an individual realization laser velocimeter is a set of randomly sampled velocity data. Spectral analysis of such data requires special techniques to obtain reliable estimates of correlation and power spectral density functions that describe the flow characteristics. FORTRAN codes for obtaining the autocorrelation and power spectral density estimates using the correlation-based slotting technique were developed. Extensive studies have been conducted on simulated first-order spectrum and sine signals to improve the spectral estimates. A first-order spectrum was chosen because it represents the characteristics of a typical one-dimensional turbulence spectrum. Digital prefiltering techniques, to improve the spectral estimates from randomly sampled data were applied. Studies show that the spectral estimates can be increased up to about five times the mean sampling rate.

Sree, David↗

NASA NTRSDate not supplied

Operational Modal Analysis of the Artemis I Dynamic Rollout Test and Wet Dress Rehearsal

NASA has developed an expendable heavy lift launch vehicle capability, the Space Launch System (SLS), to support lunar and deep space exploration. The uncrewed Artemis I was the first flight of this new launch vehicle and tested critical systems for the upcoming crewed Artemis II flight to the moon. Accelerations were recorded at a multitude of locations on Artemis, the Mobile Launcher (ML), and the Crawler Transporter (CT)during the rollout of Artemis I from the Vehicle Assembly Building (VAB) to Launch Pad 39B March 2022 and is referred to as the Artemis I Dynamic Rollout Test (DRT). While Artemis I was at Launch Pad 39B, the Wet Dress Rehearsal (WDR) was performed to demonstrate launch readiness and acceleration measurements were also recorded. Finally, Artemis I rolled back from Launch Pad 39B to the VAB in April 2022, where acceleration measurements were also recorded and is referred to as the rollback portion of DRT. Because the forces during rollout and at the launch pad acting on Artemis I, the ML, and the CT are not directly measurable, Operational Modal Analysis (OMA) techniques, instead of traditional Experimental Modal Analysis (EMA) techniques, were used to identify modal characteristics. The OMA analysis of DRT and WDR directly builds upon the lessons learned from the OMA analysis of an earlier rollout of the ML from the VAB. DRT and WDR dynamic characteristics will be used to support SLS Integrated Modal Test finite element model correlation efforts and Exploration Ground System ML and CT finite element model verification and validation, which are part of the Building Block approach the Space Launch System program has implemented. The dynamic characteristics extracted from DRT as well as the rollout acceleration time histories themselves will be used in the development of generic rollout forcing functions that will provide refined estimates of the Artemis IV rollout forces, which will have the heavier and larger SLS Block 1B launch vehicle and Mobile Launcher 2 (ML-2). This paper briefly describes Artemis I, the ML, and the CT physical characteristics, DRT rollout/rollback and WDR data collection, the challenges in implementing OMA techniques due in part to the CT harmonics, and how these challenges were overcome to obtain the Artemis I DRT configuration and WDR configuration modal characteristics.

Apollo↗

NASA NTRS2000

A Review of Electrical Impedance Spectrometry Methods for Parametric Estimation of Physiologic Fluid Volumes

Electrical impedance spectrometry involves measurement of the complex resistance of a load at multiple frequencies. With this information in the form of impedance magnitude and phase, or resistance and reactance, basic structure or function of the load can be estimated. The "load" targeted for measurement and estimation in this study consisted of the water-bearing tissues of the human calf. It was proposed and verified that by measuring the electrical impedance of the human calf and fitting this data to a model of fluid compartments, the lumped-model volume of intracellular and extracellular spaces could be estimated, By performing this estimation over time, the volume dynamics during application of stimuli which affect the direction of gravity can be viewed. The resulting data can form a basis for further modeling and verification of cardiovascular and compartmental modeling of fluid reactions to microgravity as well as countermeasures to the headward shift of fluid during head-down tilt or spaceflight.

Dewberry, B.↗

NASA NTRS1993

Maximum-likelihood analysis of the COBE angular correlation function

We have used maximum-likelihood estimation to determine the quadrupole amplitude Q(sub rms-PS) and the spectral index n of the density fluctuation power spectrum at recombination from the COBE DMR data. We find a strong correlation between the two parameters of the form Q(sub rms-PS) = (15.7 +/- 2.6) exp (0.46(1 - n)) microK for fixed n. Our result is slightly smaller than and has a smaller statistical uncertainty than the 1992 estimate of Smoot et al.

Seljak, Uros↗

NASA NTRS1982

Capillary surface discontinuities above reentrant corners

A particular configuration of a vertical capillary tube for which S is the equilibrium interface between two fluids in the presence of a downward pointing gravitational field was investigated. S is the graph a function u whose domain is the (horizontal) cross section gamma of the tube. The mean curvature of S is proportional to its height above a fixed reference plane and lambda is a prescribed constant and may be taken between zero and pi/2. Domains gamma for which us is a bounded function but does not extend continuously to d gamma are sought. Simple domains are found and the behavior of u in those domains is studied. An important comparison principle that has been used in the literature to derive many of the results in capillarity is reviewed. It allows one to deduce the approximate shape of a capillary surface by constructing comparison surfaces with mean curvature and contact angle close to those of the (unknown) solution surface. In the context of nonparametric problems the comparison principle leads to height estimates above and below for the function u. An example from the literature where these height estimates have been used successfully is described. The promised domains for which the bounded u does not extend continuously to the boundary are constructed. The point on the boundary at which u has a jump discontinuity will be the vertext of a re-entrant corner having any interior angle theta pi. Using the comparison principle the behavior of u near this point is studied.

Korevaar, H. J.↗