Product mean values and convection speed
Applying relationship of beam intensity covariances and local extinction coefficient covariances to calculation of convection velocity in crossed-beam methodology
Heybey, W. H.↗
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Results for “covariance”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Navigation analysis for Viking 1979, option B
A parametric study performed for 48 trans-Mars reference missions in support of the Viking program is reported. The launch dates cover several months in the year 1979, and each launch date has multiple arrival dates in 1980. A plot of launch versus arrival dates with case numbers designated for reference purposes is included. The analysis consists of the computation of statistical covariance matrices based on certain assumptions about the ground-based tracking systems. The error model statistics are listed in tables. Tracking systems were assumed at three sites: Goldstone, California; Canberra, Australia; and Madrid, Spain. The tracking data consisted of range and Doppler measurements taken during the tracking intervals starting at E-30(d) and ending at E-10(d) for the control data and ending at E-18(h) for the knowledge data. The control and knowledge covariance matrices were delivered to the Planetary Mission Analysis Branch for inputs into a delta V dispersion analysis.
Mitchell, P. H.↗
Wave propagation in a random medium
A simple technique is used to derive statistical characterizations of the perturbations imposed upon a wave (plane, spherical or beamed) propagating through a random medium. The method is essentially physical rather than mathematical, and is probably equivalent to the Rytov method. The limitations of the method are discussed in some detail; in general they are restrictive only for optical paths longer than a few hundred meters, and for paths at the lower microwave frequencies. Situations treated include arbitrary path geometries, finite transmitting and receiving apertures, and anisotropic media. Results include, in addition to the usual statistical quantities, time-lagged functions, mixed functions involving amplitude and phase fluctuations, angle-of-arrival covariances, frequency covariances, and other higher-order quantities.
Lee, R. W.↗
Mars gravitational field estimation error
The error covariance matrices associated with a weighted least-squares differential correction process have been analyzed for accuracy in determining the gravitational coefficients through degree and order five in the Mars gravitational potential junction. The results are presented in terms of standard deviations for the assumed estimated parameters. The covariance matrices were calculated by assuming Doppler tracking data from a Mars orbiter, a priori statistics for the estimated parameters, and model error uncertainties for tracking-station locations, the Mars ephemeris, the astronomical unit, the Mars gravitational constant (G sub M), and the gravitational coefficients of degrees six and seven. Model errors were treated by using the concept of consider parameters.
Compton, H. R.↗
A bound on the rate-distortion function and application to images.
An upper bound on the rate-distortion function for discrete ergodic sources with memory is developed by partitioning the source sample space into a finite number of disjoint subsets and bounding the rates for each subset. The bound depends only on the mean vectors and covariance matrices for the subsets and is easy to compute. It is tighter than the Gaussian bound for sources that exhibit clustering of either the values or covariances of successive source outputs. The bound is evaluated for a certain class of pictorial data using both one-dimensional and two-dimensional blocks of picture elements. Two-dimensional blocks yield a tighter bound than one-dimensional blocks; both result in a significantly tighter bound than the Gaussian bound.
Tasto, M.↗
Recursive filter initialization.
Description of an initialization technique which partially accounts for the interrelation between the true-state vector errors when recursive filtering is applied in space navigation systems. The technique reduces the undesirable transient effects of the first few measurements and inhibits filter divergence when the interval between measurements is inordinately large. The key feature of this technique is the inclusion of the effect of a number of pseudo-measurements of certain orbital parameters into the initial covariance matrix. The pseudo-measurement technique has been shown to be useful when reinitialization of the error covariance matrix is required to prevent filter divergence.
Battin, R. H.↗
A comparison of the effects of small nonlinearities on several estimation schemes.
A variety of techniques are available for estimating the states of nonlinear dynamic systems from noisy data. These procedures are generally equivalent when applied to linear systems. This paper investigates the difference between several of these procedures in the presence of small dynamic and observational nonlinearities. In particular, it examines one least square batch processing algorithm, and three recursive algorithms similar to the Kalman filter. To first order, all the estimators have the same covariance. Expressions for the means, however, show that each estimator has a different bias. The examples presented show that the biases can be a strong function of such parameters as initial covariances and number of data points being considered.
Conrad, B.↗
Development of a standardized battery of performance tests for the assessment of noise stress effects
A set of 36 relatively independent categories of human performance were identified. These categories encompass human performance in the cognitive, perceptual, and psychomotor areas, and include diagnostic measures and sensitive performance metrics. Then a prototype standardized test battery was constructed, and research was conducted to obtain information on the sensitivity of the tests to stress, the sensitivity of selected categories of performance degradation, the time course of stress effects on each of the selected tests, and the learning curves associated with each test. A research project utilizing a three factor partially repeated analysis of covariance design was conducted in which 60 male subjects were exposed to variations in noise level and quality during performance testing. Effects of randomly intermittent noise on performance of the reaction time tests were observed, but most of the other performance tests showed consistent stability. The results of 14 analyses of covariance of the data taken from the performance of the 60 subjects on the prototype standardized test battery provided information which will enable the final development and test of a standardized test battery and the associated development of differential sensitivity metrics and diagnostic classificatory system.
Theologus, G. C.↗
Retrieval of dispersive and convective transport phenomena in fluids using stationary and nonstationary time domain analysis
Simultaneously occuring dispersive and convective components of fluid kinematics are obtained by a time domain analysis of optically retrieved temporal histories of the transport phenomena. Utilizing triangulation of collimated optical fields of view from two radiometers to obtain the temporal histories of the intensity fluctuations associated with the transport phenomena has enabled investigators to retrieve the local convective transport by employing correlation statistics. The location of the peak in the covariance curve determines the transit time from which the convection velocity is calculated; whereas, the change in shape of the peak in the covariance curve determines the change in average frequency of the wave packet from which the dispersion velocity is calculated. Thus, two-component analysis requires the maximum possible enhancement of the delineation for the transport. The convection velocity is the result of a fixed reference frame calculation whereas, the dispersion velocity is the result of a moving reference frame calcuation.
Stephens, J. B.↗
HYMPS: Numerical Techniques
The digital calculations that drive the classification portion of the Hybrid Pattern Recognition System (HYMPS) are considered. A revision of these calculations is suggested that involves three items: matrix inversion, det calculations and singularity, and covariance factorization. It is shown that it is more economical to first factor the covariance matrix, and by so doing, delete the matrix inversion routine. In addition, the necessary det calculations can be more easily realized by use of simple theoretical facts about the factorization.
Decell, H. P., Jr.↗
Pattern Recognition and Linear Discriminant Function
The properties of a linear discriminant function are discussed for the case of arbitrary distributions with equal covariance matrices. Using two examples, a comparison is made showing how the difference of the means relates to the covariance matrices.
Finch, L. H.↗
SYMAT, COVAR: Test Procedures for Matrix Calculations
The FORTRAN subroutine SYMAT and related subroutines are described. In essence SYMAT is an iterative algorithm in which the problem of finding eigenvalues and eigenvectors of a real symmetric matrix is transformed into an equivalent problem of finding eigenvalues and eigenvectors of an infinite sequence of matrices of order two. A DEMO PROGRAM contains a subroutine COVAR which is used to compute the covariance matrix (denoted by A) of a data matrix (denoted by X). Since a covariance matrix is symmetric it can be analyzed by using subroutine SYMAT.
Morris, W. L.↗
Estimation strategies for orbit determination of applications satellites
A procedure for applying covariance analysis to determine the most efficient estimation strategy for satisfying the stringent mission requirements of long arc orbit determination of applications satellites is presented. The procedure is applied to the problem of satisfying mission requirements with respect to altitude determination of GEOS-C. It is shown that requirements are met when twelve dominant geopotential coefficients are estimated along with satellite state. This application of covariance analysis is general and can be applied to future applications satellites. Recommendations for future studies are also given.
Argentiero, P.↗
Results on the two population feature selection problem using probability of correct classification as a criterion
Variational equations are presented for maximizing the probability of correct classification as a function of a 1xn feature selection matrix B for the two-population problem. For the special case of equal covariance matrices the optimal B is unique up to scalar multiples and rank one sufficient. For equal population means, the best 1xn B is an eigenvector corresponding either to the largest or smallest eigenvalue of sigma sub 2 to the minus 1 power sigma sub 1 where sigma sub 1 and sigma sub 2 are the nxn covariance matrices of the two populations. The transformed probability of correct classification depends only on the eigenvalue. Finally, a procedure is proposed for constructing an optimal or nearly optimal kxn matrix of rank k without solving the k-dimensional variational equation.
Peters, B. C.↗
Mariner/Jupiter/Saturn navigation in the presence of massive planetary satellites
Orbit determination accuracies attainable during a Mariner/Jupiter/Saturn encounter have been established by means of covariance analyses. Advanced earth-based multistation radiometric data, optical data consisting of star/satellite pictures provided by a narrow-angle TV camera on board the spacecraft, and batch sequential filtering methods were employed. An evaluation of sequential filter sensitivities to errors in modeling small nongravitational spacecraft accelerations is presented. Selected covariances developed in the orbit determination analysis are used in an investigation of the trajectory correction costs associated with a close Ganymede encounter. The 99 percentile Delta V contours in the Ganymede aiming plane are obtained for satellite encounters before or after Jupiter closed approach, and the sources of the dominant contributions to the Delta V costs are identified.
Hildebrand, C. E.↗
Weighted adaptive algorithms for estimation of Gaussian distribution parameters
Two weighted adaptive algorithms are proposed for updating the estimates of the mean vector and the covariance matrix, respectively, in a multispectral pattern recognition system. To achieve computational efficiency, the auxiliary matrices have been utilized in the algorithm for covariance matrix updating. Enhancements in the performance accuracy of a multispectral processing system and extensions of the Gaussian maximum likelihood classification capabilities to larger scale surveys are the motivations in developing the algorithms presented herein.
Chang, C. Y.↗
Design/cost tradeoff studies. Appendix A. Supporting analyses and tradeoffs, book 2. Earth Observatory Satellite system definition study (EOS)
Attitude reference systems for use with the Earth Observatory Satellite (EOS) are described. The systems considered are fixed and gimbaled star trackers, star mappers, and digital sun sensors. Covariance analyses were performed to determine performance for the most promising candidate in low altitude and synchronous orbits. The performance of attitude estimators that employ gyroscopes which are periodically updated by a star sensor is established by a single axis covariance analysis. The other systems considered are: (1) the propulsion system design, (2) electric power and electrical integration, (3) thermal control, (4) ground data processing, and (5) the test plan and cost reduction aspects of observatory integration and test.
Source record↗
A prefiltering version of the Kalman filter with new numerical integration formulas for Riccati equations
A prefiltering version of the Kalman filter is derived for both discrete and continuous measurements. The derivation consists of determining a single discrete measurement that is equivalent to either a time segment of continuous measurements or a set of discrete measurements. This prefiltering version of the Kalman filter easily handles numerical problems associated with rapid transients and ill-conditioned Riccati matrices. Therefore, the derived technique for extrapolating the Riccati matrix from one time to the next constitutes a new set of integration formulas which alleviate ill-conditioning problems associated with continuous Riccati equations. Furthermore, since a time segment of continuous measurements is converted into a single discrete measurement, Potter's square root formulas can be used to update the state estimate and its error covariance matrix. Therefore, if having the state estimate and its error covariance matrix at discrete times is acceptable, the prefilter extends square root filtering with all its advantages, to continuous measurement problems.
Womble, M. E.↗