The minimal bound on the estimation error covariance matrix in the presence of correlated driving noise
Increase approximation of estimation errors covariance between discrete measurements due to random forcing function uncertainty
Deckert, J. C.↗
SEARCH · Engineering Papers
Results for “Covariance and correlation”
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Computation of the factorized error covariance of the difference between correlated estimators
A state estimation problem where some of the measurements may be common to two or more data sets is considered. Two approaches for computing the error covariance of the difference between filtered estimates (for each data set) are discussed. The first algorithm is based on postprocessing of the Kalman gain profiles of two correlated estimators. It uses UD factors of the covariance of the relative error. The second algorithm uses a square root information filter applied to relative error analysis. In the absence of process noise, the square root information filter is computationally more efficient and more flexible than the Kalman gain (covariance update) method. Both the algorithms (covariance and information matrix based) are applied to a Venus orbiter simulation, and their performances are compared.
Wolff, Peter J.↗
Determination of statistics for any rotation of axes of a bivariate normal elliptical distribution
Determination of mean, variance, covariance, and correlation estimates for axes rotation of bivariate normal elliptical distribution
Crutcher, H. L.↗
Probabilistic finite elements for fracture mechanics
The probabilistic finite element method (PFEM) is developed for probabilistic fracture mechanics (PFM). A finite element which has the near crack-tip singular strain embedded in the element is used. Probabilistic distributions, such as expectation, covariance and correlation stress intensity factors, are calculated for random load, random material and random crack length. The method is computationally quite efficient and can be expected to determine the probability of fracture or reliability.
Besterfield, Glen↗
A quick look method of detecting water of hydration in small solar system bodies
The action of aqueous alteration of the near-subsurface material on asteroids and probably some satellites in the Solar System constitutes part of the formation history of the Solar System. The C-class asteroids (and subclasses B, G, and F) were initially believed to have undergone aqueous alteration based on their low albedos and neutral broadband visible and near-infrared colors. These spectra exhibit a sharp drop at wavelengths shorter than 0.55 microns due to a strong ferric oxide intervalence change transfer transition. This IVCT comprises multiple absorptions that are not uniquely indicative of phyllosilicates, but rather are present in the spectrum of any object containing Fe(2+) and Fe(3+) in its surface material. A definitive indication of aqueous alteration came when the broad IR absorption feature having a minimum near 3.0 microns indicative of structural hydroxyl (OH) and interlayer and and absorbed water in phyllosilicates was identified in the IR photometry of many C-class asteroids. Additional mineralogical compositional evidence of aqueously-altered asteroids has come as the result of high SNR narrowband spectrophotometry in the visible and near-infrared spectral regions taken using a CCD/spectrograph combination. An absorption feature centered at 0.7 microns indicative of an Fe(2+) - Fe(3+) charge transfer transition in oxidized iron in phyllosilicates in spectra of some low-albedo asteroids, especially C and G class, and CM2 carbonaceous chondrite meteorites was identified in the CCD spectra. The correlation and covariance of the 0.7-micron and 3.0-micron features were examined by comparing observations of asteroids common to both the CCD reflectance spectra and the 3.0-micron multicolor photometry data sets. Thirty-one pairs of observations were included in this training group. The results of the statistical study indicate that with a 95% confidence level, 84% of the objects observed either having or not having the 0.7-micron feature will correspondingly have the 3.0-micron water of hydration feature.
Vilas, F.↗
A novel ozone sensor for various environmental applications
A small, lightweight, and fast-response ozone sensor for various environmental applications is described. At a flow rate of 100 l/min(-1) the ozone sensor has a response time of significantly better than 0.1 s with a detection limit lower than 100 pptv. The ozone sensor was successfully tested in various environmental applications, i.e. in measuring directly the vertical ozone flux onto agricultural land utilizing the eddy correlation or covariance technique and in monitoring horizontal and vertical ozone profiles in the troposphere and stratosphere.
Guesten, H.↗
A conservative bound on the estimation error covariance matrix in the presence of correlated driving noise and correlated discrete measurement noise.
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Potter, J. E.↗
Electromagnetic wave scattering in a two-layer anisotropic random medium
For electromagnetic wave propagation and scattering in an anisotropic random medium, the Dyson equation for the mean field and the Bethe-Salpeter equation for the correlation or the covariance of the field were derived. With the random permittivity expressed in a general anisotropic form, the bilocal and the nonlinear approximations are employed to solve the Dyson equation, and the ladder approximation to solve the Bethe-Salpeter equation. The mean dyadic Green's function for a two-layer anisotropic random medium with arbitrary three-dimensional correlation functions has been investigated with the zeroth-order solutions to the Dyson equation under the nonlinear approximation. The effective propagation constants are calculated for the four characteristic waves associated with the coherent vector fields, propagating in an anisotropic random-medium layer, which are the ordinary and extraordinary waves with upward- and downward-propagating vectors.
Lee, J. K.↗
Remote sensing of earth terrain
Progress on the investigation of the anisotropy of the terrain media, such as vegetation canopy and sea ice, and the study of the fluctuation-dissipation theorem in conjunction with the application of strong fluctuation theory for passive remote sensing of snowpacks is reported. The Feynman diagrammatic technique is used to derive the Dyson equation for the mean field and the Bethe-Salpeter equation for the correlation or the covariance of the field for electromagnetic wave propagation and scattering in an anisotropic random medium. With the random permittivity expressed in a general form, the bilocal and the nonlinear approximations are employed to solve the Dyson equation and the ladder approximation to the Bethe-Salpeter equation. The mean dyadic Green's function for a two layer anisotropic random medium with arbitrary three dimensional correlation function was investigated with the zeroth-order solutions to the Dyson equation under the four characteristic waves associated with the coherent vector fields propagating in an anisotropic random medium layer, which are the ordinary and extraordinary waves with upward and downward propagating vectors.
Kong, J. A.↗
A dual frequency radar for ocean roughness sampling
A microwave technique for determining the roughness (rms wave height) of a randomly varying air-water interface has been developed theoretically, verified with laboratory wavetank studies and is currently being implemented for ocean surface measurements in a series of applications flight experiments. These aircraft observations will be near the Chesapeake Light Tower and will include a range of altitudes and sea conditions. The measurement concept involves cross-correlating the envelope fluctuations on two received carriers that are monochromatic when transmitted in a normal direction to the interface and are observed in a backscatter direction after reflection by the large number of randomly distributed specular points on the surface. The measured correlation coefficient (normalized covariance) as a function of carrier frequency separation will depend on the surface roughness, specifically the probability density function of the specular point height. Details of the flight system are discussed, and preliminary flight results are presented.
Weissman, D. E.↗
A study of sound generation in subsonic rotors, volume 2
Computer programs were developed for use in the analysis of sound generation by subsonic rotors. Program AIRFOIL computes the spectrum of radiated sound from a single airfoil immersed in a laminar flow field. Program ROTOR extends this to a rotating frame, and provides a model for sound generation in subsonic rotors. The program also computes tone sound generation due to steady state forces on the blades. Program TONE uses a moving source analysis to generate a time series for an array of forces moving in a circular path. The resultant time series are than Fourier transformed to render the results in spectral form. Program SDATA is a standard time series analysis package. It reads in two discrete time series and forms auto and cross covariances and normalizes these to form correlations. The program then transforms the covariances to yield auto and cross power spectra by means of a Fourier transformation.
Chalupnik, J. D.↗
The crossed-beam correlation technique.
Local turbulent properties of shear layer derived from covariance of two crossed perpendicular beams of radiation
TURBULENCE MEASURING APPARATUS↗
Airborne remote sensing measurements with a pulsed CO2 DIAL system
The present investigation is concerned with an optical radar instrument which has been developed for airborne remote sensing of atmospheric trace species at infrared wavelengths. The instrument makes use of compact, pulsed carbon dioxide lasers. It was designed for conducting differential absorption lidar (DIAL) measurements. The backscatter of laser pulse energy from the ocean and terrain surface is utilized to determine trace species column content. The instrument, which is carried by the NASA P3 aircraft, is used in a flight test program started in July 1981. The results obtained with the instrument in this program are discussed, taking into account ocean surface backscatter statistics, the ratio of ocean to terrain backscatter, the dual-wavelength correlation coefficient, the dual-wavelength cross-covariance, and the dependence of un-correlated noise variance on the mean backscatter signal.
Bufton, J. L.↗
Data compression properties of the Hartley transform
The data compression performance of the Hartley transform on a Markov-1 signal is theoretically compared to that of the Fourier transform. Covariance distribution and residue correlation measurements have been computed for the Hartley, Fourier, and cosine transforms. The Hartley transform achieves better coding performance than the Fourier transform, but is inferior to the cosine transform.
Yeh, Pen-Shu↗
Kalman estimation for SEDS measurements
The first on-orbit experiment of the Small Expendable Deployer System (SEDS) for tethered satellites will collect telemetry data for tethered length, rate of deployment, and tether tension. The post-flight analysis will use this data to reconstruct the deployment history and determine payload position and tether shape. Two Kalman estimator algorithms were written, and output using simulated measurement data was compared. Both estimators exhibited the same estimated state histories, indicating that numerical instability in the traditional algorithm was not the cause of filter divergence. Estimation of acceleration biases was added, which reduced the error but did not correct the divergence. An add-a-bead estimator that adds lumped masses as the tether is deployed was written, which provides a state model that matches the BEADSIM simulation providing the true measurements and states. This twenty-one bead estimator produced state histories similar to those of the two-bead estimator, indicating that the filter divergence was not caused by a reduced-order model. The noise models used to date are relatively simple and may be the source of estimator divergence. The investigation of colored noise models, cross-correlated measurement and process covariances, and noise-adaptive filter techniques is recommended.
Carrington, Connie K.↗
Correlated noise in the COBE DMR sky maps
The Cosmic Background Explorer Satellite Differential Radiometer (COBE DMR) sky maps contain low-level correlated noise. We obtain estimates of the amplitude and pattern of the correlated noise from three techniques: angular averages of the covariance matrix, Monte Carlo simulations of two-point correlation functions and direct analysis of the DMR maps. The results from the three methods are mutually consistent. The noise covariance matrix of a DMR sky maps is diagonal to an accuracy of better than 1%. For a given sky pixel, the dominant noise covariance occure with the ring of pixels at an angular separation of 60 deg due to the 60 deg separation of the DMR horns. The mean covariance at 60 deg is 0.45%((sup +0.18)(sub -0.14)) of the mean variance. Additionally, the variance in a given pixel is 0.7% greater than would be expected from a single beam experiment with the same noise properties. Autocorrelation functions suffer from a approximately 1.5 sigma positive bias at 60 deg while cross-correlations have no bias. Published COBE DMR results are not significantly affected by correlated noise.
Lineweaver, C. H.↗
Efficient recursive estimation - application to estimating the parameters of a covariance function.
Estimating parameters of covariance function with modified stochastic approximation
STATISTICAL CORRELATION↗
Correlation, Cost Risk, and Geometry
The geometric viewpoint identifies the choice of a correlation matrix for the simulation of cost risk with the pairwise choice of data vectors corresponding to the parameters used to obtain cost risk. The correlation coefficient is the cosine of the angle between the data vectors after translation to an origin at the mean and normalization for magnitude. Thus correlation is equivalent to expressing the data in terms of a non orthogonal basis. To understand the many resulting phenomena requires the use of the tensor concept of raising the index to transform the measured and observed covariant components into contravariant components before vector addition can be applied. The geometric viewpoint also demonstrates that correlation and covariance are geometric properties, as opposed to purely statistical properties, of the variates. Thus, variates from different distributions may be correlated, as desired, after selection from independent distributions. By determining the principal components of the correlation matrix, variates with the desired mean, magnitude, and correlation can be generated through linear transforms which include the eigenvalues and the eigenvectors of the correlation matrix. The conversion of the data to a non orthogonal basis uses a compound linear transformation which distorts or stretches the data space. Hence, the correlated data does not have the same properties as the uncorrelated data used to generate it. This phenomena is responsible for seemingly strange observations such as the fact that the marginal distributions of the correlated data can be quite different from the distributions used to generate the data. The joint effect of statistical distributions and correlation remains a fertile area for further research. In terms of application to cost estimating, the geometric approach demonstrates that the estimator must have data and must understand that data in order to properly choose the correlation matrix appropriate for a given estimate. There is a general feeling by employers and managers that the field of cost requires little technical or mathematical background. Contrary to that opinion, this paper demonstrates that a background in mathematics equivalent to that needed for typical engineering and scientific disciplines at the masters or doctorate level is appropriate within the field of cost risk.
Dean, Edwin B.↗