SEARCH · Engineering Papers

Results for “Covariance Matrix”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 343 records · Page 19

All sources NASA NTRS DOE OSTI

NASA NTRS1979

CLASSY: An adaptive maximum likelihood clustering algorithm

The CLASSY clustering method alternates maximum likelihood iterative techniques for estimating the parameters of a mixture distribution with an adaptive procedure for splitting, combining, and eliminating the resultant components of the mixture. The adaptive procedure is based on maximizing the fit of a mixture of multivariate normal distributions to the observed data using its first through fourth central moments. It generates estimates of the number of multivariate normal components in the mixture as well as the proportion, mean vector, and covariance matrix for each component. The basic mathematical model for CLASSY and the actual operation of the algorithm as currently implemented are described. Results of applying CLASSY to real and simulated LANDSAT data are presented and compared with those generated by the iterative self-organizing clustering system algorithm on the same data sets.

Lennington, R. K.↗

NASA NTRS1980

A study of autonomous satellite navigation methods using the global positioning satellite system

Special orbit determination algorithms were developed to accommodate the size and speed limitations of on-board computer systems of the NAVSTAR Global Positioning System. The algorithms use square root sequential filtering methods. A new method for the time update of the square root covariance matrix was also developed. In addition, the time update method was compared with another square root convariance propagation method to determine relative performance characteristics. Comparisions were based on the results of computer simulations of the LANDSAT-D satellite processing pseudo range and pseudo range-rate measurements from the phase one GPS. A summary of the comparison results is presented.

Tapley, B. D.↗

NASA NTRS1980

STS-1 operational flight profile. Volume 5: Descent cycle 3. Appendix D: GRTLS six degree of freedom Monte Carlo dispersion analysis

The results of a six degree of freedom (6-DOF) nonlinear Monte Carlo dispersion analysis for the latest glide return to landing site (GRTLS) abort trajectory for the Space Transportation System 1 Flight are presented. For this GRTLS, the number two main engine fails at 262.5 seconds ground elapsed time. Fifty randomly selected simulations, initialized at external tank separation, are analyzed. The initial covariance matrix is a 20 x 20 matrix and includes navigation errors and dispersions in position and velocity, time, accelerometer bias, and inertial platform misalinements. In all 50 samples, speedbrake, rudder, elevon, and body flap hinge moments are acceptable. Transitions to autoland begin before 9,000 feet and there are no tailscrapes. Navigation derived dynamic pressure accuracies exceed the flight control system constraints above Mach 2.5. Three out of 50 landings exceeded tire specification limit speed of 222 knots. Pilot manual landings are expected to reduce landing speed by landing farther downrange.

Montez, M. N.↗

NASA NTRS1979

On the overlapping plate method in astrometry

A method is proposed for the simplification of the algorithms of Eichhorn and Russell (1976) for obtaining the solutions of astrometric problems using the overlapping plate method. The method provides the parameter vector (consisting of 'star constants' and plate constants) as well as the covariance matrix of the parameters. A considerable reduction in the amount of matrix algebra required is obtained with the present method.

Jefferys, W. H.↗

NASA NTRS1980

Parameter identification of linear discrete stochastic systems with time delays

An identification algorithm that uses the maximum likelihood technique to identify the unknown time delays, plant parameters, and noise covariances of linear discrete stochastic systems is presented. Cases of additive white noise and colored measurement noises are considered. The likelihood function is evaluated using either a minimum-variance (Kalman) filter or a minimal-order observer. The Kalman filter is used in the identification algorithm to provide minimum-variance estimates. The minimal-order observer is a lower-dimensional and computationally simpler filter, and is advantageous especially for systems with long delays. It provides a less optimal solution to the minimum-mean-square state estimation problem. The colored-noise observer algorithm has the disadvantage of having to compute an extra error covariance matrix of lower order.

Wong, E. C.↗

NASA NTRS1981

Three-axis attitude determination from vector observations

Two computationally efficient algorithms are presented for determining three-axis attitude from two or more vector observations. The first of these, the TRIAD algorithm, provides a deterministic (i.e., nonoptimal) solution for the attitude based on two vector observations. The second, the QUEST algorithm, is an optimal algorithm which determines the attitude that achieves the best weighted overlap of an arbitrary number of reference and observation vectors. Analytical expressions are given for the covariance matrices for the two algorithms using a fairly realistic model for the measurement errors. The mathematical relationship of the two algorithms and their relative merits are discussed and numerical examples are given. The advantage of computing the covariance matrix in the body frame rather than in the inertial frame (e.g., in terms of Euler angles) is emphasized. These results are valuable when a single-frame attitude must be computed frequently. They will also be useful to the mission analyst or spacecraft engineer for the evaluation of launch-window constraints or of attitude accuracies for different attitude sensor configurations.

Shuster, M. D.↗

NASA NTRS1981

Saturn gravity results obtained from Pioneer 11 tracking data and earth-based Saturn satellite data

Improved gravity coefficients for Saturn, its satellites and rings are calculated on the basis of a combination of Pioneer 11 spacecraft Doppler tracking data and earth-based determinations of Saturn natural satellite apse and node rates. Solutions are first obtained separately from the coherent Doppler tracking data obtained for the interval from August 20 to September 4, surrounding the time of closest approach, with the effects of solar plasma on radio signal propagation taken into account, and from secular rates for Mimas, Enceladus, Tethys, Dione, Rhea and Titan determined from astrometric data by Kozai (1957, 1976) and Garcia (1972). Combination of the data by the use of the Pioneer solution and corresponding unadjusted covariance matrix as a priori information for a secular rate analysis results in values for the total ring mass of essentially zero at a standard error level of 1.7 x 10 to the -6th Saturn masses, a ratio of solar mass to that of the Saturn system of 3498.09 + or - 0.22, masses of Rhea, Titan and Iapetus of 4.0 + or - 0.9, 238.8 + or - 3, and 3.4 + or - 1.3 x 10 to the -6th Saturn masses, respectively, and second and fourth zonal harmonics of 16,479 + or - 18 and -937 + or - 38, respectively. The harmonic coefficients are noted to be important as boundary conditions in the modeling of the Saturn interior.

Null, G. W.↗

NASA NTRS1981

Multiobjective insensitive design of airplane control systems with uncertain parameters

A multiobjective computer-aided design algorithm has been developed which minimizes the sensitivity of the design objectives to uncertainties in system parameters. The more important uncertain parameters are described by a gaussian random vector with known covariance matrix, and a vector sensitivity objective function is defined as the probabilities that the design objectives will violate specified requirements constraints. Control system parameters are found which minimize the sensitivity vector in a Pareto-optimal sense, using constrained minimization algorithms. Example results are shown for lateral stability augmentation system (SAS) design for three Shuttle flight conditions.

Schy, A. A.↗

NASA NTRS1981

The influence of autocorrelation in signature extraction: An example from a geobotanical investigation of Cotter Basin, Montana

The presence of positive serial correlation (autocorrelation) in remotely sensed data results in an underestimate of the variance-covariance matrix when calculated using contiguous pixels. This underestimate produces an inflation in F statistics. For a set of Thematic Mapper Simulator data (TMS), used to test the ability to discriminate a known geobotanical anomaly from its background, the inflation in F statistics related to serial correlation is between 7 and 70 times. This means that significance tests of means of the spectral bands initially appear to suggest that the anomalous site is very different in spectral reflectance and emittance from its background sites. However, this difference often disappears and is always dramatically reduced when compared to frequency distributions of test statistics produced by the comparison of simulated training sets possessing equal means, but which are composed of autocorrelated observations.

Labovitz, M. L.↗

NASA NTRS1982

Predicting the required number of training samples

A criterion which measures the quality of the estimate of the covariance matrix of a multivariate normal distribution is developed. Based on this criterion, the necessary number of training samples is predicted. Experimental results which are used as a guide for determining the number of training samples are included.

Kalayeh, H. M.↗

NASA NTRS1981

An autonomous Nimbus Doppler positioning system

A single-pass Doppler positioning system was developed at the GSFC in support of the Nimbus-6 mission. The system was designed to satisfy the following requirements: compatibility with the PDP 11/70 minicomputer; single-pass recovery of up to 250 positions with a two-sigma accuracy of 5 km; high reliability with a minimum of human interaction; and near real-time responsiveness. The system consists of a numerical integrator which includes only the J2 term (earth flattening) of the earth's gravity field, an editing routine, a first guess algorithm, a least squares position recovery program, and a routine for generating a 95% confidence circle based on a computer covariance matrix. An analysis and quantification of the following error sources that limit system accuracy are presented: orbit error, radial aliasing, computational difficulties with overhead passes, oscillator drift, and ambiguity problems. Results of system reliability tests and sample outputs are included.

Garza-Robles, R.↗

NASA NTRS1982

Sampling errors in the estimation of empirical orthogonal functions

Empirical Orthogonal Functions (EOF's), eigenvectors of the spatial cross-covariance matrix of a meteorological field, are reviewed with special attention given to the necessary weighting factors for gridded data and the sampling errors incurred when too small a sample is available. The geographical shape of an EOF shows large intersample variability when its associated eigenvalue is 'close' to a neighboring one. A rule of thumb indicating when an EOF is likely to be subject to large sampling fluctuations is presented. An explicit example, based on the statistics of the 500 mb geopotential height field, displays large intersample variability in the EOF's for sample sizes of a few hundred independent realizations, a size seldom exceeded by meteorological data sets.

North, G. R.↗

NASA NTRS1981

The magnifying glass - A feature space local expansion for visual analysis

The Magnifying Glass Transformation (MGT) technique is proposed, as a multichannel spectral operation yielding visual imagery which is enhanced in a specified spectral vicinity, guided by the statistics of training samples. An application example is that in which the discrimination among spectral neighbors within an interactive display may be increased without altering distant object appearances or overall interpretation. A direct histogram specification technique is applied to the channels within the multispectral image so that a subset of the spectral domain occupies an increased fraction of the domain. The transformation is carried out by obtaining the training information, establishing the condition of the covariance matrix, determining the influenced solid, and initializing the lookup table. Finally, the image is transformed.

Juday, R. D.↗

NASA NTRS1983

Feature selection methodologies using simulated Thematic Mapper data

The present investigation is concerned with the determination of the intrinsic dimensionality of a simulated Thematic Mapper data set. In addition, the effectiveness and sensitivity of 'standard' statistics separability measures (i.e., transformed divergence) is evaluated in comparison to eigenvectors for identifying the optimum subset of the original Thematic Mapper Simulator (TMS) bands for classifying the various cover types. TMS data were collected on May 2, 1979 by NASA's NS001 aircraft multispectral scanner over a bottomland forested area in South Carolina near the city of Camden. It is found that the eigenvectors and eigenvalues of a covariance matrix from a multispectral scanner system (MSS) data set can be obtained without having to actually transform the data.

Dean, M. E.↗

NASA NTRS1982

The influence of autocorrelation in signature extraction - An example from a geobotanical investigation of Cotter Basin, MT

Labovitz, M. L.↗

NASA NTRS1983

Predicting the required number of training samples

Kalayeh, H. M.↗

NASA NTRS1983

Light extinction by aerosols during summer air pollution

In order to utilize satellite measurements of optical thickness over land for estimating aerosol properties during air pollution episodes, the optical thickness was measured from the surface and investigated. Aerosol optical thicknesses have been derived from solar transmission measurements in eight spectral bands within the band lambda 440-870 nm during the summers of 1980 and 1981 near Washington, DC. The optical thicknesses for the eight bands are strongly correlated. It was found that first eigenvalue of the covariance matrix of all observations accounts for 99 percent of the trace of the matrix. Since the measured aerosol optical thickness was closely proportional to the wavelength raised to a power, the aerosol size distribution derived from it is proportional to the diameter (d) raised to a power for the range of diameters between 0.1 to 1.0 micron. This power is insensitive to the total optical thickness. Changes in the aerosol optical thickness depend on several aerosol parameters, but it is difficult to identify the dominant one. The effects of relative humidity and accumulation mode concentration on the optical thickness are analyzed theoretically, and compared with the measurements.

Kaufman, Y. J.↗

NASA NTRS1983

Standard ozone profiles from balloon and satellite data sets

Standard profiles based on upper level averaged profiles from BUV and lower level averaged profiles from balloon measurements are presented in a parametric representation as a function of time of year and latitude. The representation is a simple 4-parameter function representing the ozone amount (m-atm-cm) in each of 12 atmospheric layers defined following the standard Umkehr convention. The same parameterization is applied to the Nimbus-7 SBUV data and is compared to the BUV/balloon parameterization. The ozone variance unaccounted for by the representation is presented and discussed. The season-latitude representation reduces considerably the ozone variance at all levels and explains much of the correlation between layers. This simple representation and corresponding covariance matrix have been used as a priori information in the ozone vertical profile inversion of the Nimbus-7 SBUV experimental measurements.

Klenk, K. F.↗