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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Improvement of structural models using covariance analysis and nonlinear generalized least squares

The next generation of large, flexible space structures will be too light to support their own weight, requiring a system of structural supports for ground testing. The authors have proposed multiple boundary-condition testing (MBCT), using more than one support condition to reduce uncertainties associated with the supports. MBCT would revise the mass and stiffness matrix, analytically qualifying the structure for operation in space. The same procedure is applicable to other common test conditions, such as empty/loaded tanks and subsystem/system level tests. This paper examines three techniques for constructing the covariance matrix required by nonlinear generalized least squares (NGLS) to update structural models based on modal test data. The methods range from a complicated approach used to generate the simulation data (i.e., the correct answer) to a diagonal matrix based on only two constants. The results show that NGLS is very insensitive to assumptions about the covariance matrix, suggesting that a workable NGLS procedure is possible. The examples also indicate that the multiple boundary condition procedure more accurately reduces errors than individual boundary condition tests alone.

Glaser, R. J.↗
NASA NTRS1993

Covariant harmonic oscillators: 1973 revisited

Using the relativistic harmonic oscillator, a physical basis is given to the phenomenological wave function of Yukawa which is covariant and normalizable. It is shown that this wave function can be interpreted in terms of the unitary irreducible representations of the Poincare group. The transformation properties of these covariant wave functions are also demonstrated.

Noz, M. E.↗
NASA NTRS1995

Using dark current data to estimate AVIRIS noise covariance and improve spectral analyses

Starting in 1994, all AVIRIS data distributions include a new product useful for quantification and modeling of the noise in the reported radiance data. The 'postcal' file contains approximately 100 lines of dark current data collected at the end of each data acquisition run. In essence this is a regular spectral-image cube, with 614 samples, 100 lines and 224 channels, collected with a closed shutter. Since there is no incident radiance signal, the recorded DN measure only the DC signal level and the noise in the system. Similar dark current measurements, made at the end of each line are used, with a 100 line moving average, to remove the DC signal offset. Therefore, the pixel-by-pixel fluctuations about the mean of this dark current image provide an excellent model for the additive noise that is present in AVIRIS reported radiance data. The 61,400 dark current spectra can be used to calculate the noise levels in each channel and the noise covariance matrix. Both of these noise parameters should be used to improve spectral processing techniques. Some processing techniques, such as spectral curve fitting, will benefit from a robust estimate of the channel-dependent noise levels. Other techniques, such as automated unmixing and classification, will be improved by the stable and scene-independence noise covariance estimate. Future imaging spectrometry systems should have a similar ability to record dark current data, permitting this noise characterization and modeling.

Boardman, Joseph W.↗
NASA NTRS1993

Orbit determination covariance analysis for the Deep Space Program Science Experiment mission

To define an appropriate orbit support procedure for the DSPSE mission, detailed permission orbit determination covariance analyses have been performed for the translunar and trans-Geographos mission phases. Preliminary analyses were also performed for the lunar mapping mission phase. These analyses are designed to assess the tracking patterns and the amount of tracking data needed to obtain orbit solutions of required accuracy for each mission phase and before and after each major orbit perturbation, such as orbit maneuvers and flybys of the Earth and Moon. In addition to operational orbit determination procedures, these analyses identify major error sources, estimate their contribution to orbital errors, and address possible strategies to reduce orbit determination error. For the lunar orbit phase, several lunar gravity error modeling approaches have been investigated. The covariance analysis results presented in this paper will serve as a guide for providing orbit determination support for the DSPSE mission.

Beckman, M.↗
NASA NTRS1996

Analysis of Compressible Mixing Layers Using Dilatational Covariances Model

Compressible mixing layers are analyzed using a dilatational covariances model based on a pseudo-sound constitutive relation. The calculations are used to evaluate the different physical phenomena affecting compressible mixing layers. The rate of growth of the mixing layer is retarded by both the compressible dissipation and the pressure-dilatational covariances. The pressure-dilatational, essentially a nonequilibrium effect, reduces the amount of excess production over dissipation available for the turbulence energy growth. The pseudo-sound model also includes a history dependent portion: this is also investigated. All constants in the model and used in these computations are predicted by the theory.

Thangam, S.↗
NASA NTRS2002

Covariance Propagation and Partial Eigendecomposition Filtering on the Continuum: The Cases of Advective Dynamics

As a motivation for this lecture, we begin by stating a paradox that challenges our fundamental understanding of covariance evolution (at least it challenged my own). Attempting to resolve this 'divergence paradox' leads us to introduce the continuum fundamental solution operator for the dynamics under consideration, which will be advection dynamics in this lecture. This operator is the object that is approximated by the discrete 'tangent linear model. We then show how the fundamental solution operator can be used to describe the solution of the continuum covariance evolution equation. This description is complete enough to resolve fully the divergence paradox.

Cohn, S.↗
NASA NTRS2007

Generalized Squashing Factors for Covariant Description of Magnetic Connectivity in the Solar Corona

The study of magnetic connectivity in the solar corona reveals a need to generalize the field line mapping technique to arbitrary geometry of the boundaries and systems of coordinates. Indeed, the global description of the connectivity in the corona requires the use of the photospheric and solar wind boundaries. Both are closed surfaces and therefore do not admit a global regular system of coordinates. At least two overlapping regular systems of coordinates for each of the boundaries are necessary in this case to avoid spherical-pole-like singularities in the coordinates of the footpoints. This implies that the basic characteristic of magnetic connectivity-the squashing degree or factor Q of elemental flux tubes, according to Titov and coworkers-must be rewritten in covariant form. Such a covariant expression of Q is derived in this work. The derived expression is very flexible and highly efficient for describing the global magnetic connectivity in the solar corona. In addition, a general expression for a new characteristic Q1, which defines a squashing of the flux tubes in the directions perpendicular to the field lines, is determined. This new quantity makes it possible to filter out the quasi-separatrix layers whose large values of Q are caused by a projection effect at the field lines nearly touching the photosphere. Thus, the value Q1 provides a much more precise description of the volumetric properties of the magnetic field structure. The difference between Q and Q1 is illustrated by comparing their distributions for two configurations, one of which is the Titov-Demoulin model of a twisted magnetic field.

Titov, V. S.↗
NASA NTRS2008

Quantifying the Effect of Component Covariances in CMB Extraction from Multi-frequency Data

Linear combination methods provide a global method for component separation of multi-frequency data. We present such a method that allows for consideration of possible covariances between the desired cosmic microwave background signal and various foreground signals that are also present. We also recover information on the foregrounds including the number of foregrounds, their spectra and templates. In all this, the covariances, which we would only expect to vanish 'in the mean' are included as parameters expressing the fundamental uncertainty due to this type of cosmic variance. When we make the reasonable assumption that the CMB is Gaussian, we can compute both a mean recovered CMB map and also an RMS error map, The mean map coincides with WMAP's Internal Linear Combination map.

Phillips, Nicholas G.↗
NASA NTRS2009

Covariant C and O Isotope Trends in Arctic Carbonate Crusts and ALH 84001: Potential Biomarker or Indicator of Cryogenic Formation Environment?

This work seeks to use the chemical, isotopic, and mineralogical characteristics of secondary carbonate minerals produced during brief aqueous events to identify the conditions of the aqueous environment in which they formed. Liquid water near the surface of Mars is subject to either rapid freezing and/or evaporation. These processes are also active on Earth, and produce secondary minerals that have complex chemical, mineralogical, and isotopic textures and compositions that can include covariant relationships between Delta C-13 (sub VPDB) and delta O-18 (sub VSMOW). The extremely well studied four billion year old carbonates preserved in martian meteorite ALH 84001 also show covariant delta C-13 and delta O-18 compositions, but these variations are manifested on a micro-scale in a single thin section while the variation observed so far in terrestrial carbonates is seen between different hand samples.

Socki, Richard A.↗
NASA NTRS2013

Covariance Analysis Tool (G-CAT) for Computing Ascent, Descent, and Landing Errors

G-CAT is a covariance analysis tool that enables fast and accurate computation of error ellipses for descent, landing, ascent, and rendezvous scenarios, and quantifies knowledge error contributions needed for error budgeting purposes. Because GCAT supports hardware/system trade studies in spacecraft and mission design, it is useful in both early and late mission/ proposal phases where Monte Carlo simulation capability is not mature, Monte Carlo simulation takes too long to run, and/or there is a need to perform multiple parametric system design trades that would require an unwieldy number of Monte Carlo runs. G-CAT is formulated as a variable-order square-root linearized Kalman filter (LKF), typically using over 120 filter states. An important property of G-CAT is that it is based on a 6-DOF (degrees of freedom) formulation that completely captures the combined effects of both attitude and translation errors on the propagated trajectories. This ensures its accuracy for guidance, navigation, and control (GN&C) analysis. G-CAT provides the desired fast turnaround analysis needed for error budgeting in support of mission concept formulations, design trade studies, and proposal development efforts. The main usefulness of a covariance analysis tool such as G-CAT is its ability to calculate the performance envelope directly from a single run. This is in sharp contrast to running thousands of simulations to obtain similar information using Monte Carlo methods. It does this by propagating the "statistics" of the overall design, rather than simulating individual trajectories. G-CAT supports applications to lunar, planetary, and small body missions. It characterizes onboard knowledge propagation errors associated with inertial measurement unit (IMU) errors (gyro and accelerometer), gravity errors/dispersions (spherical harmonics, masscons), and radar errors (multiple altimeter beams, multiple Doppler velocimeter beams). G-CAT is a standalone MATLAB- based tool intended to run on any engineer's desktop computer.

Boussalis, Dhemetrios↗
NASA NTRS2014

Use of an OSSE to Evaluate Background Error Covariances Estimated by the 'NMC Method'

The NMC method has proven utility for prescribing approximate background-error covariances required by variational data assimilation systems. Here, untunedNMCmethod estimates are compared with explicitly determined error covariances produced within an OSSE context by exploiting availability of the true simulated states. Such a comparison provides insights into what kind of rescaling is required to render the NMC method estimates usable. It is shown that rescaling of variances and directional correlation lengths depends greatly on both pressure and latitude. In particular, some scaling coefficients appropriate in the Tropics are the reciprocal of those in the Extratropics. Also, the degree of dynamic balance is grossly overestimated by the NMC method. These results agree with previous examinations of the NMC method which used ensembles as an alternative for estimating background-error statistics.

Data Assimilation↗
NASA NTRS2015

Covariability in the Monthly Mean Convective and Radiative Diurnal Cycles in the Amazon

The diurnal cycle of convective clouds greatly influences the radiative energy balance in convectively active regions of Earth, through both direct presence, and the production of anvil and stratiform clouds. Previous studies show that the frequency and properties of convective clouds can vary on monthly timescales as a result of variability in the monthly mean atmospheric state. Furthermore, the radiative budget in convectively active regions also varies by up to 7 Wm-2 in convectively active regions. These facts suggest that convective clouds connect atmospheric state variability and radiation variability beyond clear sky effects alone. Previous research has identified monthly covariability between the diurnal cycle of CERES-observed top-of-atmosphere radiative fluxes and multiple atmospheric state variables from reanalysis over the Amazon region. ASVs that enhance (reduce) deep convection, such as CAPE (LTS), tend to shift the daily OLR and cloud albedo maxima earlier (later) in the day by 2-3 hr. We first test the analysis method using multiple reanalysis products for both the dry and wet seasons to further investigate the robustness of the preliminary results. We then use CloudSat data as an independent cloud observing system to further evaluate the relationships of cloud properties to variability in radiation and atmospheric states. While CERES can decompose OLR variability into clear sky and cloud effects, it cannot determine what variability in cloud properties lead to variability in the radiative cloud effects. Cloud frequency, cloud top height, and cloud microphysics all contribute to the cloud radiative effect, all of which are observable by CloudSat. In addition, CloudSat can also observe the presence and variability of deep convective cores responsible for the production of anvil clouds. We use these capabilities to determine the covariability of convective cloud properties and the radiative diurnal cycle.

Dodson, Jason B.↗
NASA NTRS2016

Position Error Covariance Matrix Validation and Correction

In order to calculate operationally accurate collision probabilities, the position error covariance matrices predicted at times of closest approach must be sufficiently accurate representations of the position uncertainties. This presentation will discuss why the Gaussian distribution is a reasonable expectation for the position uncertainty and how this assumed distribution type is used in the validation and correction of position error covariance matrices.

Frisbee, Joe, Jr.↗
NASA NTRS2017

Assessment of the Gaussian Covariance Approximation over an Earth-Asteroid Encounter Period

In assessing the risk an asteroid may pose to the Earth, the asteroids state is often predicted for many years, often decades. Only by accounting for the asteroids initial state uncertainty can a measure of the risk be calculated. With the asteroids state uncertainty growing as a function of the initial velocity uncertainty, orbit velocity at the last state update, and the time from the last update to the epoch of interest, the asteroids position uncertainties can grow to many times the size of the Earth when propagated to the encounter risk corridor. This paper examines the merits of propagating the asteroids state covariance as an analytical matrix. The results of this study help to bound the efficacy of applying different metrics for assessing the risk an asteroid poses to the Earth. Additionally, this work identifies a criterion for when different covariance propagation methods are needed to continue predictions after an Earth-encounter period.

planetary defense↗
NASA NTRS2017

Assessment of the Gaussian Covariance Approximation over an Earth-Asteroid Encounter Period

In assessing the risk an asteroid may pose to the Earth, the asteroids state is often predicted for many years, often decades. Only by accounting for the asteroids initial state uncertainty can a measure of the risk be calculated. With the asteroids state uncertainty growing as a function of the initial velocity uncertainty, orbit velocity at the last state update, and the time from the last update to the epoch of interest, the asteroids position uncertainties can grow to many times the size of the Earth when propagated to the encounter risk corridor. This paper examines the merits of propagating the asteroids state covariance as an analytical matrix. The results of this study help to bound the efficacy of applying different metrics for assessing the risk an asteroid poses to the Earth. Additionally, this work identifies a criterion for when different covariance propagation methods are needed to continue predictions after an Earth-encounter period.

uncertainty characterization↗
NASA NTRS2018

Analyzing the Relationship between Tracking and Covariance for Satellite Collision Avoidance

This presentation will display statistical analysis performed with over 150,000 Conjunction Data Messages (CDMs) received for the Earth Observing System (EOS) Aqua, Aura and Terra satellites within the three year period of March 2015 through February 2018. The analysis performed demonstrates the relationship between the covariance of a secondary object and the amount of tracks it receives, as a function of Time to Closest Approach (TCA). The examination indicates that higher tracking frequencies result in lower uncertainties inclusively from the time the data is screened up until TCA. Further investigation displays the impacts of how additional observations of secondary objects lower their position uncertainties and what period of time prior to TCA convergence of the covariance can be expected depending on how well the objects are tracked. Data points from several recent EOS High Interest Events (HIEs) are used to exemplify this analysis.

Collision Avoidance↗
NASA NTRS2020

Spatial Heterogeneity in CO2, CH4, and Energy Fluxes: Insights from Airborne Eddy Covariance Measurements Over the Mid-Atlantic Region

The exchange of carbon between the Earth’s atmosphere and biosphere influences the atmospheric abundances of carbon dioxide (CO2) and methane (CH4). Airborne eddy covariance can quantify surface-atmosphere exchange from landscape-to-regional scales, offering a unique perspective on carbon cycle dynamics. We use extensive airborne measurements to quantify fluxes of sensible heat, latent heat, CO2, and CH4across multiple ecosystems in the Mid-Atlantic region during September 2016 and May 2017. In conjunction with footprint analysis and land cover information, we use the airborne dataset to explore the effects of landscape heterogeneity on measured fluxes. Our results demonstrate large variability in CO2 uptake over mixed agricultural and forested sites, with fluxes ranging from -3.4 ± 0.7 to -11.5 ± 1.6μmol m-2s-1 for croplands and -9.1 ± 1.5 to -22.7 ± 3.2μmol m-2s-1for forests. We also report substantial CH4emissions of 32.3 ± 17.0to 76.1 ± 29.4nmol m-2s-1 from a brackish herbaceous wetland and 58.4± 12.0 to 181.2 ± 36.8nmol m-2s-1 from a freshwater forested wetland. Comparison of ecosystem-specific aircraft observations with measurements from eddy covariance flux towers along the flight path demonstrate that towers capture ~30–75% of the regional variability in ecosystem fluxes. Diel patterns measured at the tower sites suggest that peak, midday flux measurements from aircraft accurately predicts net daily CO2exchange. We discuss next steps in applying airborne observations to evaluate bottom-up flux models and improve understanding of the biophysical processes that drive carbon exchange from landscape-to-regional scales.

airborne measurements to quantify fluxes of sensib↗
NASA NTRSDate not supplied

Continuum Covariance Propagation for Understanding Variance Loss in Advective Systems

We demonstrate for state dynamics governed by the continuity equation and related hyperbolic partial differential equations that significant, spurious variance loss occurs during covariance propagation by traditional methods used in data assimilation, even at full rank. This inaccurate variance evolution is caused not by numerical dissipation, but rather by a discontinuous change in the continuum covariance dynamics as correlation lengths tend to zero.

Shay Gilpin↗