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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

GRAVSAT/GEOPAUSE covariance analysis including geopotential aliasing

A conventional covariance analysis for the GRAVSAT/GEOPAUSE mission is described in which the uncertainties of approximately 200 parameters, including the geopotential coefficients to degree and order 12, are estimated over three different tracking intervals. The estimated orbital uncertainties for both GRAVSAT and GEOPAUSE reach levels more accurate than presently available. The adjusted measurement bias errors approach the mission goal. Survey errors in the low centimeter range are achieved after ten days of tracking. The ability of the mission to obtain accuracies of geopotential terms to (12, 12) one to two orders of magnitude superior to present accuracy levels is clearly shown. A unique feature of this report is that the aliasing structure of this (12, 12) field is examined. It is shown that uncertainties for unadjusted terms to (12, 12) still exert a degrading effect upon the adjusted error of an arbitrarily selected term of lower degree and order. Finally, the distribution of the aliasing from the unestimated uncertainty of a particular high degree and order geopotential term upon the errors of all remaining adjusted terms is listed in detail.

Koch, D. W.↗
NASA NTRS1976

An algorithm for propagating the square-root covariance matrix in triangular form

A method for propagating the square root of the state error covariance matrix in lower triangular form is described. The algorithm can be combined with any triangular square-root measurement update algorithm to obtain a triangular square-root sequential estimation algorithm. The triangular square-root algorithm compares favorably with the conventional sequential estimation algorithm with regard to computation time.

Tapley, B. D.↗
NASA NTRS1976

The covariance of temperature and ozone due to planetary-wave forcing

The cross-spectra of temperature and ozone mass mixing ratio at 42 km and 28 km has been determined for spring (1971) and summer (1971-2) over Christchurch, New Zealand (44 S, 172 E). The sources of data are the SCR and BUV experiments on Nimbus 4. The observed covariances are compared with a model in which the temperature and ozone perturbations are forced by an upward propagating planetary wave. The agreement between the observations and the model is reasonable. It is suggested that this cross-spectral method permits an estimate of the meridional gradient of ozone mass mixing ratio from measurements of the vertical profile of ozone mass mixing ratio at one location, supported by temperature profiles from at least two locations.

Fraser, G. J.↗
NASA NTRS1978

A triangular covariance factorization for sequential filtering algorithms

A method for propagating the square-root of the state error covariance matrix in lower triangular UDU form is described. This update method can be combined with the UDU transformation used by Bierman to obtain the equations of a square-root free triangular estimation algorithm. The method is compared with the state transition matrix time update algorithm on the basis of integration accuracy, computational efficiency and storage requirements.

Tapley, B. D.↗
NASA NTRS1979

Implications of general covariance and maximum four-dimensional Yang-Mills gauge symmetry

General covariance and maximum four-dimensional Yang-Mills gauge symmetry lead to these results: (1) gravity is characterized by a dimensionless constant F of the order of 10 to the -19th; (2) the Newtonian force is always attractive; (3) space-time has a torsion; and (4) gravitational spin-force between two protons is about 10 to the 19th times stronger than the corresponding Newtonian force. A possible experimental test is discussed.

Hsu, J. P.↗
NASA NTRS1979

Scale covariance and G-varying cosmology. II - Thermodynamics, radiation, and the 3 K background

Within the framework of a scale-covariant theory of gravitation, a semiclassical description of particles and photons is given. Thermodynamic relations consistent with the modified conservation equations are derived. Application to a system of radiation shows that the observed 3-K background radiation can be interpreted, within the present framework, as a remnant of equilibrium radiation in the past. As the theory postulates a nonstandard coupling between gravitation and electrodynamics, the assumption that Einstein's theory of gravitation is unchanged forces modifications at the atomic level. The use of Minkowskian spacetime in atomic physics is found to be adequate only over small, but not large, time scales compared with the age of the universe. As a result, a relation between energy and the frequency of a free photon is demonstrated. Possible observational consequences of this relation are discussed.

Canuto, V. M.↗
NASA NTRS1979

Scale covariance and G-varying cosmology. III - The /m, z/, /theta sub m, z/, /theta sub i, z/, and /N/m/, m/ tests

The Einstein gravitational equations in atomic units are fully solved for a matter-dominated universe in the context of a recently proposed scale-covariant cosmology. The magnitude-redshift relation for elliptical galaxies is studied, the evolutionary parameter used in such a study is derived, and the relation between isophotal angular diameters and redshifts is investigated, along with the relation between metric angular diameters and redshifts, the N(m)-magnitude relation for QSOs, and the magnitude-redshift relation for QSOs. Results are presented for four gauges (i.e., relations between G and the scale function beta (t)), and no contradictions are found between the proposed theory and the observational data. It is shown that only an open universe can fit the data if certain gauges suggested by a recent analysis of the time variation of the moon's period are selected and that observations made with atomic instruments do not necessarily yield geometrical parameters unless specific assumptions are made regarding the relation between atomic and gravitational dynamics.

Canuto, V. M.↗
NASA NTRS1979

Scale covariance and G-varying cosmology. IV - The log N-log S relation

The traditional radio counts N(S) and radio source models are studied within the framework of the scale-covariant cosmology developed to investigate whether the relative strength of the gravitational and electromagnetic constants is a function of cosmological epoch. It is found that a gravitational constant G varying as the inverse of t, where t is the epoch in atomic units, is consistent with all the data analyzed. For a wide class of models the present cosmology allows a finer discrimination of the deceleration parameter than does standard theory. The results, when combined with those of previous papers, namely, those from radio and optical flux and angular-diameter data analysis, favor an open universe.

Canuto, V. M.↗
NASA NTRS1980

Evaluation of orbits with incomplete knowledge of the mathematical expectancy and the matrix of covariation of errors

The problem of selecting the optimal algorithm of filtration and the optimal composition of the measurements is examined assuming that the precise values of the mathematical expectancy and the matrix of covariation of errors are unknown. It is demonstrated that the optimal algorithm of filtration may be utilized for making some parameters more precise (for example, the parameters of the gravitational fields) after preliminary determination of the elements of the orbit by a simpler method of processing (for example, the method of least squares).

Bakhshiyan, B. T.↗
NASA NTRS1981

Identifiability of unknown noise covariance matrices for some special cases of a linear, time-invariant, discrete-time dynamic system

Two off-line schemes are proposed for the identification of unknown noise covariance matrices Q and R of a discrete-time dynamic system. The first scheme is based on a maximum a posteriori cost function utilizing smoothed state estimates, while the second is based on a maximum likelihood cost function utilizing filtered state estimates. Sensitivity of the cost functions to Q and R is analyzed for the following cases: (1) single-input single-output systems; (2) multiinput single-output systems; and (3) single-input multioutput systems with a diagonal R. Identifiability criteria are presented for the cases considered and demonstrated by examples.

Tsang, W. L.↗
NASA NTRS1983

A Covariance Analysis for the Determination of Baseline Observing GPS Satellites

Results of covariance analyses are presented for the determination of baseline vectors of length from 150 m to 4000 km. The data are doubly differenced ranges derived from the signals transmitted by the satellites of the Global Positioning System. The modeling of various error sources is described. The results indicate the low cost baseline determination system is capable of subdecimeter accuracy for baselines up to 1000 km in length.

Wu, S. C.↗
NASA NTRS1985

Covariances and spectra of the kinematics and dynamics of nonlinear waves

Using the Stokes waves as a model of nonlinear waves and considering the linear component as a narrow-band Gaussian process, the covariances and spectra of velocity and acceleration components and pressure for points in the vicinity of still water level were derived taking into consideration the effects of free surface fluctuations. The results are compared with those obtained earlier using linear Gaussian waves.

Tung, C. C.↗
NASA NTRS1987

A covariance analysis algorithm for interconnected systems

A covariance analysis algorithm for propagation of signal statistics in arbitrarily interconnected nonlinear systems is presented which is applied to six-degree-of-freedom systems. The algorithm uses statistical linearization theory to linearize the nonlinear subsystems, and the resulting linearized subsystems are considered in the original interconnection framework for propagation of the signal statistics. Some nonlinearities commonly encountered in six-degree-of-freedom space-vehicle models are referred to in order to illustrate the limitations of this method, along with problems not encountered in standard deterministic simulation analysis. Moreover, the performance of the algorithm shall be numerically exhibited by comparing results using such techniques to Monte Carlo analysis results, both applied to a simple two-dimensional space-intercept problem.

Cheng, Victor H. L.↗
NASA NTRS1988

Storage and computationally efficient permutations of factorized covariance and square-root information arrays

A unified method to permute vector stored Upper triangular Diagonal factorized covariance and vector stored upper triangular Square Root Information arrays is presented. The method involves cyclic permutation of the rows and columns of the arrays and retriangularization with fast (slow) Givens rotations (reflections). Minimal computation is performed, and a one dimensional scratch array is required. To make the method efficient for large arrays on a virtual memory machine, computations are arranged so as to avoid expensive paging faults. This method is potentially important for processing large volumes of radio metric data in the Deep Space Network.

Muellerschoen, R. J.↗
NASA NTRS1988

Storage and computationally efficient permutations of factorized covariance and square-root information matrices

A unified method to permute vector-stored upper-triangular diagonal factorized covariance (UD) and vector stored upper-triangular square-root information filter (SRIF) arrays is presented. The method involves cyclical permutation of the rows and columns of the arrays and retriangularization with appropriate square-root-free fast Givens rotations or elementary slow Givens reflections. A minimal amount of computation is performed and only one scratch vector of size N is required, where N is the column dimension of the arrays. To make the method efficient for large SRIF arrays on a virtual memory machine, three additional scratch vectors each of size N are used to avoid expensive paging faults. The method discussed is compared with the methods and routines of Bierman's Estimation Subroutine Library (ESL).

Muellerschoen, R. J.↗
NASA NTRS1991

Generalized Covariance Analysis For Remote Estimators

Technique developed to predict true covariance of stochastic process at remote location when control applied to process both by autonomous (local-estimator) control subsystem and remote (non-local-estimator) control subsystem. Intended orginally for design and evaluation of ground-based schemes for estimation of gyro parameters of Magellan spacecraft. Applications include variety of remote-control systems with and without delays. Potential terrestrial applications include navigation and control of industrial processes.

Boone, Jack N.↗