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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

Performance evaluation for transform coding using a nonseparable covariance model

Intraframe transform coding of pictures for the case of a nonseparable covariance model is considered. Performances of the Walsh-Hadamard, discrete-cosine, and Karhunen-Loeve transforms are compared based on the compaction of signal energy in the transform components and the degree of decorrelation of the data. The results demonstrate that the performances of the discrete-cosine and Karhunen-Loeve transforms compare closely, as is the case with a separable covariance model. The corresponding performance of the Walsh-Hadamard transform is inferior.

Natarajan, T. R.↗
NASA NTRS1980

A VLBI variance-covariance analysis interactive computer program

An interactive computer program (in FORTRAN) for the variance covariance analysis of VLBI experiments is presented for use in experiment planning, simulation studies and optimal design problems. The interactive mode is especially suited to these types of analyses providing ease of operation as well as savings in time and cost. The geodetic parameters include baseline vector parameters and variations in polar motion and Earth rotation. A discussion of the theroy on which the program is based provides an overview of the VLBI process emphasizing the areas of interest to geodesy. Special emphasis is placed on the problem of determining correlations between simultaneous observations from a network of stations. A model suitable for covariance analyses is presented. Suggestions towards developing optimal observation schedules are included.

Bock, Y.↗
NASA NTRS1981

Scale covariant gravitation. V - Kinetic theory. VI - Stellar structure and evolution

A scale covariant kinetic theory for particles and photons is developed. The mathematical framework of the theory is given by the tangent bundle of a Weyl manifold. The Liouville equation is derived, and solutions to corresponding equilibrium distributions are presented and shown to yield thermodynamic results identical to the ones obtained previously. The scale covariant theory is then used to derive results of interest to stellar structure and evolution. A radiative transfer equation is derived that can be used to study stellar evolution with a variable gravitational constant. In addition, it is shown that the sun's absolute luminosity scales as L approximately equal to GM/kappa, where kappa is the stellar opacity. Finally, a formula is derived for the age of globular clusters as a function of the gravitational constant using a previously derived expression for the absolute luminosity.

Hsieh, S.-H.↗
NASA NTRS1983

Covariance hypotheses for LANDSAT data

Two covariance hypotheses are considered for LANDSAT data acquired by sampling fields, one an autoregressive covariance structure and the other the hypothesis of exchangeability. A minimum entropy approximation of the first structure by the second is derived and shown to have desirable properties for incorporation into a mixture density estimation procedure. Results of a rough test of the exchangeability hypothesis are presented.

Decell, H. P.↗
NASA NTRS1985

An efficient algorithm for estimating noise covariances in distributed systems

An efficient computational algorithm for estimating the noise covariance matrices of large linear discrete stochatic-dynamic systems is presented. Such systems arise typically by discretizing distributed-parameter systems, and their size renders computational efficiency a major consideration. The proposed adaptive filtering algorithm is based on the ideas of Belanger, and is algebraically equivalent to his algorithm. The earlier algorithm, however, has computational complexity proportional to p to the 6th, where p is the number of observations of the system state, while the new algorithm has complexity proportional to only p-cubed. Further, the formulation of noise covariance estimation as a secondary filter, analogous to state estimation as a primary filter, suggests several generalizations of the earlier algorithm. The performance of the proposed algorithm is demonstrated for a distributed system arising in numerical weather prediction.

Dee, D. P.↗
NASA NTRS1987

Errors in plate rotations as described by covariance matrices and their combination in reconstructions

The use of covariance matrices to describe the errors in plate rotations and to combine the contributions of individual plate pairs for plate reconstructions is discussed. Particular attention is given to finite rotations and the combination of covariance matrices for a circuit of successive plate pair rotations. Examples of errors in plate reconstructions in which the position of the Pacific plate relative to North America is reconstructed are presented.

Jurdy, Donna M.↗
NASA NTRS1987

Covariance and the hierarchy of frame bundles

This is an essay on the general concept of covariance, and its connection with the structure of the nested set of higher frame bundles over a differentiable manifold. Examples of covariant geometric objects include not only linear tensor fields, densities and forms, but affinity fields, sectors and sector forms, higher order frame fields, etc., often having nonlinear transformation rules and Lie derivatives. The intrinsic, or invariant, sets of forms that arise on frame bundles satisfy the graded Cartan-Maurer structure equations of an infinite Lie algebra. Reduction of these gives invariant structure equations for Lie pseudogroups, and for G-structures of various orders. Some new results are introduced for prolongation of structure equations, and for treatment of Riemannian geometry with higher-order moving frames. The use of invariant form equations for nonlinear field physics is implicitly advocated.

Estabrook, Frank B.↗
NASA NTRS1989

A covariant multiple scattering series for elastic projectile-target scattering

A covariant formulation of the multiple scattering series for the optical potential is presented. The case of a scalar nucleon interacting with a spin zero isospin zero A-body target through meson exchange, is considered. It is shown that a covariant equation for the projectile-target t-matrix can be obtained which sums the ladder and crossed ladder diagrams efficiently. From this equation, a multiple scattering series for the optical potential is derived, and it is shown that in the impulse approximation, the two-body t-matrix associated with the first order optical potential is the one in which one particle is kept on mass-shell. The meaning of various terms in the multiple scattering series is given. The construction of the first-order optical potential for elastic scattering calculations is described.

Gross, Franz↗
NASA NTRS1990

A numerical algorithm to propagate navigation error covariance matrices associated with generalized strapdown inertial measurement units

The design and operation of a Strapdown Navigation Analysis Program (SNAP) developed to perform covariance analysis on spacecraft inertial-measurement-unit (IMU) navigation errors are described and demonstrated. Consideration is given to the IMU modeling subroutine (with user-specified sensor characteristics), the data input procedures, state updates and the simulation of instrument failures, the determination of the nominal trajectory, the mapping-matrix and Monte Carlo covariance-matrix propagation methods, and aided-navigation simulation. Numerical results are presented in tables for sample applications involving (1) the Galileo/IUS spacecraft from its deployment from the Space Shuttle to a point 10 to the 8th ft from the center of the earth and (2) the TDRS-C/IUS spacecraft from Space Shuttle liftoff to a point about 2 h before IUS deployment. SNAP is shown to give reliable results for both cases, with good general agreement between the mapping-matrix and Monte Carlo predictions.

Weir, Kent A.↗
NASA NTRS1990

Gravity field improvement using GPS data from Topex/Poseidon - A covariance analysis

A covariance analysis is performed using a realistic scenario for processing 10 days of GPS data, to obtain the expected improvement to the GEM-T2 gravity field. The gravity bin technique has been refined to compute the covariance matrix associated with the spherical harmonic gravity field. It is shown that the GPS data from one ten-day arc of Topex/Poseidon with no a priori can improve medium degree and order (3-26) sigmas for the parameters in the GEM-T2 gravity field by more than an order of magnitude.

Bertiger, Willy I.↗
NASA NTRS1991

Relative-Error-Covariance Algorithms

Two algorithms compute error covariance of difference between optimal estimates, based on data acquired during overlapping or disjoint intervals, of state of discrete linear system. Provides quantitative measure of mutual consistency or inconsistency of estimates of states. Relative-error-covariance concept applied, to determine degree of correlation between trajectories calculated from two overlapping sets of measurements and construct real-time test of consistency of state estimates based upon recently acquired data.

Bierman, Gerald J.↗
NASA NTRS1991

Constant covariance in local vertical coordinates for near-circular orbits

A method is presented for devising a covariance matrix that either remains constant or grows in keeping with the presence of a period error in a rotating local-vertical coordinate system. The solution presented may prove useful in the initialization of simulation covariance matrices for near-circular-orbit problems. Use is made of the Clohessy-Wiltshire equations and the travelling-ellipse formulation.

Shepperd, Stanley W.↗
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.↗