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NASA NTRS2017

Using Dispersed Modes During Model Correlation

The model correlation process for the modal characteristics of a launch vehicle is well established. After a test, parameters within the nominal model are adjusted to reflect structural dynamics revealed during testing. However, a full model correlation process for a complex structure can take months of man-hours and many computational resources. If the analyst only has weeks, or even days, of time in which to correlate the nominal model to the experimental results, then the traditional correlation process is not suitable. This paper describes using model dispersions to assist the model correlation process and decrease the overall cost of the process. The process creates thousands of model dispersions from the nominal model prior to the test and then compares each of them to the test data. Using mode shape and frequency error metrics, one dispersion is selected as the best match to the test data. This dispersion is further improved by using a commercial model correlation software. In the three examples shown in this paper, this dispersion based model correlation process performs well when compared to models correlated using traditional techniques and saves time in the post-test analysis.

Stewart, Eric C.↗
NASA NTRS1975

A generalized correlation of experimental flat-plate collector performance

A generalized correlation of flat-plate collector performance obtained by outdoor and indoor test methods is presented. This correlation shows that the indoor (simulator) test approach is a special case of the general situation of variable solar conditions. The important feature of the generalized correlation is that it permits a separation of the solar variables (flux, incident angle, etc.) which affect collector performance from the collector parameters (absorptance, transmittance, heat loss, etc.) which also affect collector performance and which are uniquely part of a given collector design. The correlation permits an evaluation of the relative merits of using instantaneous, hourly and daily collector efficiencies in obtaining a good collector correlation. The question of the transient behavior outdoors of a collector is an important part of determining whether to use instantaneous, hourly or daily efficiency values in a correlation approach. Correlation of the experimental performance of collectors allows the following: (1) comparisons of different collector designs, (2) collector performance prediction under conditions that differ from the conditions of the test program, and (3) monitoring performance degradation effects.

Simon, F. F.↗
NASA NTRS1983

Remote sensing of ice phenomena from orbit by signal correlation of multiple receiver responses

The method of signal correlation of microwave responses as applied to the measurement of Earth-surface ice temperatures from orbit is explained and summarized. Ice temperatures are estimated by a correlation function that is derived from the processes of a forward stepwise correlator. Subsets of the post-detected outputs of microwave receiving channels are combined in a multivariate cross-correlation function which operates as a spatial filter and serves to improve the spatial resolution of the thermal gradients in ice structures. The correlator is designed to selectively identify the correlative components among the microwave responses and to strongly suppress or cancel the non-correlative components appearing in the post-detected outputs.

Stacey, J. M.↗
NASA NTRS1984

Assessment of Thematic Mapper Band-to-band Registration by the Block Correlation Method

The design of the Thematic Mapper (TM) multispectral radiometer makes it susceptible to band-to-band misregistration. To estimate band-to-band misregistration a block correlation method is employed. This method is chosen over other possible techniques (band differencing and flickering) because quantitative results are produced. The method correlates rectangular blocks of pixels from one band against blocks centered on identical pixels from a second band. The block pairs are shifted in pixel increments both vertically and horizontally with respect to each other and the correlation coefficient for each shift position is computed. The displacement corresponding to the maximum correlation is taken as the best estimate of registration error for each block pair. Subpixel shifts are estimated by a bi-quadratic interpolation of the correlation values surrounding the maximum correlation. To obtain statistical summaries for each band combination post processing of the block correlation results performed. The method results in estimates of registration error that are consistent with expectations.

Card, D. H.↗
NASA NTRS1984

A SAR correlation algorithm which accommodates large-range migration

This paper presents an algorithm for azimuth correlation of synthetic aperture radar (SAR) data with extraordinarily large-range migration which cannot be accommodated by the existing frequency domain interpolation approach used in current Seasat SAR processing. A mathematical model is provided for the SAR range-correlated point-target response both in the spatial and frequency domains. A simple and efficient processing algorithm derived from the exact two-dimensional correlation algorithm is given. This algorithm enables azimuth correlation by two cascaded one-dimensional correlation steps. The first step is to transform the range-correlated SAR data into the frequency domain in azimuth, followed by a newly developed range convolution filter to correct the range-dispersed spectrum of the range-correlated point-target response (RCPTR). The second step is the frequency-domain range migration correction approach for the azimuth compression. Simulation results provided here indicate that this processing algorithm yields a satisfactory compressed impulse response for SAR data with large-range migration whereas previous methods were subject to a broadening of the impulse response along range.

Jin, M. Y.↗
NASA NTRS1986

Analysis/forecast experiments with a flow-dependent correlation function using FGGE data

The use of a flow-dependent correlation function to improve the accuracy of an optimum interpolation (OI) scheme is examined. The development of the correlation function for the OI analysis scheme used for numerical weather prediction is described. The scheme uses a multivariate surface analysis over the oceans to model the pressure-wind error cross-correlation and it has the ability to use an error correlation function that is flow- and geographically-dependent. A series of four-day data assimilation experiments, conducted from January 5-9, 1979, were used to investigate the effect of the different features of the OI scheme (error correlation) on forecast skill for the barotropic lows and highs. The skill of the OI was compared with that of a successive correlation method (SCM) of analysis. It is observed that the largest difference in the correlation statistics occurred in barotropic and baroclinic lows and highs. The comparison reveals that the OI forecasts were more accurate than the SCM forecasts.

Baker, W. E.↗
NASA NTRS1988

The discrete correlation function: A new method for analyzing unevenly sampled variability data

A method of measuring correlation functions without interpolating in the temporal domain, the discrete correlation function, is introduced. It provides an assumption-free representation of the correlation measured in the data, and allows meaningful error estimates. This method does not produce spurious correlations at zero lag due to correlated errors. It is shown that physical interpretation of active galactic nuclei cross-correlation functions requires knowledge of the input function's fluctuation power spectrum, involves model-dependence in the form of symmetry assumptions, and must take into account intrinsic scale bias. This technique was used to find a correlation in published IUE data for NGC 4151, which indicates that the broad C IV feature emanates from a shell 15 to 75 light-days in radius, assuming spherical symmetry.

Edelson, R. A.↗
NASA NTRS1989

Geographically correlated orbit error

The dominant error source in estimating the orbital position of a satellite from ground based tracking data is the modeling of the Earth's gravity field. The resulting orbit error due to gravity field model errors are predominantly long wavelength in nature. This results in an orbit error signature that is strongly correlated over distances on the size of ocean basins. Anderle and Hoskin (1977) have shown that the orbit error along a given ground track also is correlated to some degree with the orbit error along adjacent ground tracks. This cross track correlation is verified here and is found to be significant out to nearly 1000 kilometers in the case of TOPEX/POSEIDON when using the GEM-T1 gravity model. Finally, it was determined that even the orbit error at points where ascending and descending ground traces cross is somewhat correlated. The implication of these various correlations is that the orbit error due to gravity error is geographically correlated. Such correlations have direct implications when using altimetry to recover oceanographic signals.

Rosborough, G. W.↗
NASA NTRS1992

The effects of correlated noise in intra-complex DSN arrays for S-band Galileo telemetry reception

A number of the proposals for supporting a Galileo S-band (2.3-GHz) mission involve arraying several antennas to maximize the signal-to-noise ratio (and bit rate) obtainable from a given set of antennas. Arraying is no longer a new idea, having been used successfully during the Voyager encounters with Uranus and Neptune. However, arraying for Galileo's tour of Jupiter is complicated by Jupiter's strong radio emission, which produces correlated noise effects. This article discusses the general problem of correlated noise due to a planet, or other radio source, and applies the results to the specific case of an array of antennas at the DSN's Tidbinbilla, Australia, complex (DSS 42, DSS 43, DSS 45, and the yet-to-be-built DSS 34). The effects of correlated noise are highly dependent on the specific geometry of the array and on the spacecraft-planet configuration; in some cases, correlated noise effects produce an enhancement, rather than a degradation, of the signal-to-noise ratio. For the case considered here--an array of the DSN's Australian antennas observing Galileo and Jupiter--there are three regimes of interest. If the spacecraft-planet separation is approximately less than 75 arcsec, the average effect of correlated noise is a loss of signal to noise (approximately 0.2 dB as the spacecraft-planet separation approaches zero). For spacecraft-planet separations approximately greater than 75 arcsec, but approximately less than 400 arcsec, the effects of correlated noise cause signal-to-noise variations as large as several tenths of a decibel over time scales of hours or changes in spacecraft-planet separation of tens of arcseconds; however, on average its effects are small (less than 0.01 dB). When the spacecraft is more than 400 arcsec from Jupiter (as is the case for about half of Galileo's tour), correlated noise is a less than 0.05-dB effect.

Dewey, R. J.↗
NASA NTRS1991

Object enhanced optical correlation

A major drawback of optical correlator systems is the poor quality of correlation signals. Background noise is one of the many sources of false correlation peaks. However, by reconstructing an input scene with the object's amplitude function, an object-enhanced scene - used as input to the optical correlators - (with respect to background) can be obtained. Thus, the optical correlation of this enhanced image improves the signal-to-noise ratio in the correlation image. Furthermore, construction of a filter plane mask that permits simultaneous scene enhancement and cross-correlation operations is described. Experimental results demonstrate the practicality of this approach.

Scholl, Marija S.↗
NASA NTRS1993

On the estimation of the correlation dimension and its application to radar reflector discrimination

Recently, system theorists have recognized that low order systems of nonlinear differential equations can give rise to solutions which are neither periodic, constant, nor predictable in steady state, but which are nonetheless bounded and deterministic. This behavior, which was first described in the study of weather systems, has been termed 'chaotic.' Much study of chaotic systems has concentrated on analysis of the systems' phase space attractors. It has been recognized that invariant measures of the attractor possess inherent information about the system. One such measure is the dimension of the attractors. The dimension of a chaotic attractor has been shown to be noninteger, leading to the term 'strange attractor;' the attractor is said to have a fractal structure. The correlation dimension has become one of the most popular measures of dimension. However, many problems have been identified in correlation dimension estimation from time sequences. The most common methods for obtaining the correlation dimension have been least squares curves fitting to find the slope of the correlation integral and the Takens Estimator. However, these estimates show unacceptable sensitivity to the upper limit on the distance chosen. Here, a new method is proposed which is shown to be rather insensitive to the upper limit and to perform in a very stable manner, at least in the absence of noise. The correlation dimension is also shown to be an effective discriminant in distinguishing between radar returns resulting from weather and those from the ground. The weather returns are shown to have a correlation dimension generally between 2.0 and 3.0, while ground returns have a correlation dimension exceeding 3.0.

Barnett, Kevin D.↗
NASA NTRS1994

Redshift distortions of galaxy correlation functions

To examine how peculiar velocities can affect the two-, three-, and four-point redshift correlation functions, we evaluate volume-average correlations for configurations that emphasize and minimize redshift distortions for four different volume-limited samples from each of the CfA, SSRS, and IRAS redshift catalogs. We present the results as the correlation length r(sub 0) and power index gamma of the two-point correlations, bar-xi(sub 0) = (r(sub 0)/r)(exp gamma), and as the hierarchical amplitudes of the three- and four-point functions, S(sub 3) = bar-xi(sub 3)/bar-xi(exp 2)(sub 2) and S(sub 4) = bar-xi(sub 4)/bar-xi(exp 3)(sub 2). We find a characteristic distortion for bar-xi(sub 2), the slope gamma is flatter and the correlation length is larger in redshift space than in real space; that is, redshift distortions 'move' correlations from small to large scales. At the largest scales (up to 12 Mpc), the extra power in the redshift distribution is compatible with Omega(exp 4/7)/b approximately equal to 1. We estimate Omega(exp 4/7)/b to be 0.53 +/- 0.15, 1.10 +/- 0.16, and 0.84 +/- 0.45 for the CfA, SSRS, and IRAS catalogs. Higher order correlations bar-xi(sub 3) and bar-xi(sub 4) suffer similar redshift distortions but in such a way that, within the accuracy of our ananlysis, the normalized amplitudes S(sub 3) and S(sub 4) are insensitive to this effect. The hierarchical amplitudes S(sub 3) and S(sub 4) are constant as a function of scale between 1 and 12 Mpc and have similar values in all samples and catalogs, S(sub 3) approximately equal to 2 and S(sub 4) approximately equal to 6, despite the fact that bar-xi(sub 2), bar-xi(sub 3), and bar-xi(sub 4) differ from one sample to another by large factors (up to a factor of 4 in bar-xi(sub 2), 8 for bar-xi(sub 3), and 12 for bar-xi(sub 4)). The agreement between the independent estimations of S(sub 3) and S(sub 4) is remarkable given the different criteria in the selection of galaxies and also the difference in the resulting range of densities, luminosities, and locations between samples.

Fry, J. N.↗
NASA NTRS1994

Correlated environmental corrections in TOPEX/POSEIDON, with a note on ionospheric accuracy

Estimates of the effectiveness of an altimetric correction, and interpretation of sea level variability as a response to atmospheric forcing, both depend upon assuming that residual errors in altimetric corrections are uncorrelated among themselves and with residual sea level, or knowing the correlations. Not surprisingly, many corrections are highly correlated since they involve atmospheric properties and the ocean surface's response to them. The full corrections (including their geographically varying time mean values), show correlations between electromagnetic bias (mostly the height of wind waves) and either atmospheric pressure or water vapor of -40%, and between atmospheric pressure and water vapor of 28%. In the more commonly used collinear differences (after removal of the geographically varying time mean), atmospheric pressure and wave height show a -30% correlation, atmospheric pressure and water vapor a -10% correlation, both pressure and water vapor a 7% correlation with residual sea level, and a bit surprisingly, ionospheric electron content and wave height a 15% correlation. Only the ocean tide is totally uncorrelated with other corrections or residual sea level. The effectiveness of three ionospheric corrections (TOPEX dual-frequency, a smoothed version of the TOPEX dual-frequency, and Doppler orbitography and radiopositioning integrated by satellite (DORIS) is also evaluated in terms of their reduction in variance of residual sea level. Smooth (90-200 km along-track) versions of the dual-frequency altimeter ionosphere perform best both globally and within 20 deg in latitude from the equator. The noise variance in the 1/s TOPEX inospheric samples is approximately (11 mm) squared, about the same as noise in the DORIS-based correction; however, the latter has its error over scales of order 10(exp 3) km. Within 20 deg of the equator, the DORIS-based correction adds (14 mm) squared to the residual sea level variance.

Zlotnicki, V.↗
NASA NTRS2001

Effects of Eddy Viscosity on Time Correlations in Large Eddy Simulation

Subgrid-scale (SGS) models for large. eddy simulation (LES) have generally been evaluated by their ability to predict single-time statistics of turbulent flows such as kinetic energy and Reynolds stresses. Recent application- of large eddy simulation to the evaluation of sound sources in turbulent flows, a problem in which time, correlations determine the frequency distribution of acoustic radiation, suggest that subgrid models should also be evaluated by their ability to predict time correlations in turbulent flows. This paper compares the two-point, two-time Eulerian velocity correlation evaluated from direct numerical simulation (DNS) with that evaluated from LES, using a spectral eddy viscosity, for isotropic homogeneous turbulence. It is found that the LES fields are too coherent, in the sense that their time correlations decay more slowly than the corresponding time. correlations in the DNS fields. This observation is confirmed by theoretical estimates of time correlations using the Taylor expansion technique. Tile reason for the slower decay is that the eddy viscosity does not include the random backscatter, which decorrelates fluid motion at large scales. An effective eddy viscosity associated with time correlations is formulated, to which the eddy viscosity associated with energy transfer is a leading order approximation.

He, Guowei↗
NASA NTRS2002

Measurement of Correlation Between Flow Density, Velocity, and Density*velocity(sup 2) with Far Field Noise in High Speed Jets

To locate noise sources in high-speed jets, the sound pressure fluctuations p', measured at far field locations, were correlated with each of radial velocity v, density rho, and phov(exp 2) fluctuations measured from various points in jet plumes. The experiments follow the cause-and-effect method of sound source identification, where correlation is related to the first, and correlation to the second source terms of Lighthill's equation. Three fully expanded, unheated plumes of Mach number 0.95, 1.4 and 1.8 were studied for this purpose. The velocity and density fluctuations were measured simultaneously using a recently developed, non-intrusive, point measurement technique based on molecular Rayleigh scattering. It was observed that along the jet centerline the density fluctuation spectra S(sub rho) have different shapes than the radial velocity spectra S(sub v), while data obtained from the peripheral shear layer show similarity between the two spectra. Density fluctuations in the jet showed significantly higher correlation, than either rhov(sub 2) or v fluctuations. It is found that a single point correlation from the peak sound emitting region at the end of the potential core can account for nearly 10% of all noise at 30 to the jet axis. The correlation, representing the effectiveness of a longitudinal quadrupole in generating noise 90 to the jet axis, is found to be zero within experimental uncertainty. In contrast rhov(exp 2) fluctuations were better correlated with sound pressure fluctuation at the 30 location. The strongest source of sound is found to lie at the centerline and beyond the end of potential core.

Panda, Jayanta↗
NASA NTRS2003

Using Neural Networks to Describe Tracer Correlations

Neural networks are ideally suited to describe the spatial and temporal dependence of tracer-tracer correlations. The neural network performs well even in regions where the correlations are less compact and normally a family of correlation curves would be required. For example, the CH4-N2O correlation can be well described using a neural network trained with the latitude, pressure, time of year, and CH4 volume mixing ratio (v.m.r.). In this study a neural network using Quickprop learning and one hidden layer with eight nodes was able to reproduce the CH4-N2O correlation with a correlation co- efficient of 0.9995. Such an accurate representation of tracer-tracer correlations allows more use to be made of long-term datasets to constrain chemical models. Such as the dataset from the Halogen Occultation Experiment (HALOE) which has continuously observed CH4, (but not N2O) from 1991 till the present. The neural network Fortran code used is available for download.

Lary, D. J.↗
NASA NTRS2009

Version 2 of the Protuberance Correlations for the Shuttle-Orbiter Boundary Layer Transition Tool

Orbiter-specific transition data, acquired in four ground-based facilities (LaRC 20-Inch Mach 6 Air Tunnel, LaRC 31-Inch Mach 10 Air Tunnel, LaRC 20-Inch Mach 6 CF4 Tunnel, and CUBRC LENS-I Shock Tunnel) with three wind tunnel model scales (0.75, 0.90, and 1.8%) and from Orbiter historical flight data, have been analyzed to improve a pre-existing engineering tool for reentry transition prediction on the windward side of the Orbiter. Boundary layer transition (BLT) engineering correlations for transition induced by isolated protuberances are presented using a laminar Navier-Stokes (N-S) database to provide the relevant boundary-layer properties. It is demonstrated that the earlier version of the BLT correlation that had been developed using parameters derived from an engineering boundary-layer code has improved data collapse when developed with the N-S database. Of the new correlations examined, the proposed correlation 5, based on boundary-layer edge and wall properties, was found to provide the best overall correlation metrics when the entire database is employed. The second independent correlation (proposed correlation 7) selected is based on properties within the boundary layer at the protuberance height. The Aeroheating Panel selected a process to derive the recommended coefficients for Version 2 of the BLT Tool. The assumptions and limitations of the recommended protuberance BLT Tool V.2 are presented.

King, Rudolph A.↗
NASA NTRS2010

Implementation and Testing of VLBI Software Correlation at the USNO

The Washington Correlator (WACO) at the U.S. Naval Observatory (USNO) is a dedicated VLBI processor based on dedicated hardware of ASIC design. The WACO is currently over 10 years old and is nearing the end of its expected lifetime. Plans for implementation and testing of software correlation at the USNO are currently being considered. The VLBI correlation process is, by its very nature, well suited to a parallelized computing environment. Commercial off-the-shelf computer hardware has advanced in processing power to the point where software correlation is now both economically and technologically feasible. The advantages of software correlation are manifold but include flexibility, scalability, and easy adaptability to changing environments and requirements. We discuss our experience with and plans for use of software correlation at USNO with emphasis on the use of the DiFX software correlator.

Fey, Alan↗