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NASA NTRS1971

Optimal filtering in the presence of unmodeled time correlated driving disturbances.

In many realistic data filtering problems, the cross correlation of the state estimation error and the state forcing function is unknown due to the poor knowledge of the time history of the forcing function. In this paper, the conservative and minimal approximation to the cross correlation terms is presented. It requires only the knowledge of the estimation error covariance and the forcing function covariance, with the choice of an associated free parameter left to the user. If the estimation error covariance and/or the forcing function covariance are bounded from above but not known exactly, the cross correlation approximation using those upper bounds remains conservative. This cross correlation approximation leads to a conservative approximation to the estimation error covariance matrix differential equation between measurement times. The free parameter is determined as the analytic solution to an associated optimal control problem. The procedure is expanded to include discrete linear measurement incorporation.

Fraser, D. C.↗

NASA NTRS1972

Correlation of total sound power and peak sideline OASPL from jet exhausts.

An empirical analysis of jet noise is made for convergent exhaust nozzles. This study, conducted at the Lewis Research Center, presents an engineering approach to the correlation of total sound power and maximum sideline OASPL (at 200 ft) for both subsonic and supersonic jets based on available data. Data correlation for subsonic jets shows no dependency of total sound power and maximum sideline OASPL on jet density. The analysis for supersonic jets results in a correlation parameter for jet total sound power consisting of the conventional Lighthill parameter modified by considerations of jet Mach number and jet acoustic velocity. Similar parameters also correlate the maximum sideline OASPL for supersonic jets.

Von Glahn, U. H.↗

NASA NTRS1972

The correlation length for interplanetary magnetic field fluctuations

It is argued that it is appropriate to consider two correlation lengths for interplanetary magnetic field fluctuations. For particles with gyro-radii large enough to encounter and be scattered by large-scale tangential discontinuities in the field (particles with energies greater than or approximately equal to several GeV/nucleon) the appropriate correlation length is simply the mean spatial separation between the discontinuities, L approximately 2 x 10 to the 11th power. Particles with gyro-radii much less than this mean separation (energies less than or approximately equal to 100 MeV/nucleon) appear to be unaffected by the discontinuities and respond only to smaller-scale field fluctuations. For these particles the correlation length is shown to be L approximately 10 to the 10th power cm. With this system of two correlation lengths the cosmic-ray diffusion tensor may be altered from what was predicted by, for example, Jokipii and Coleman, and the objections raised recently by Klimas and Sandri to the diffusion analysis of Jokipii may apply only at relatively low energies (approximately 50 MeV/nucleon).

Fisk, L. A.↗

NASA NTRS1973

Correlation of ERTS-1 and aircraft optical data with water quality parameters of Charlotte Amalie Harbor, St. Thomas, Virgin Islands

The author has identified the following significant results. Attempts to correlate optical aircraft remote sensing of water quality with the optical data from the ERTS-1 satellite using calibrated imagery of Charlotte Amalie harbor, St. Thomas, Virgin Islands are reported. The harbor at Charlotte Amalie has a concentration of a number of factors affecting water quality: untreated sewage, land runoff, and sediment from navigation and dredging operations. Calibration procedures have been originated and applied to ERTS-1 and I2S camera imagery. The results indicate that the ERTS-1 and I2S imagery are correlated with optical in situ measurements of the harbor water. The aircraft green photographic and ERTS-1 MSS-4 bands have been found most suitable for monitoring the scattered light levels under the conditions of the investigation. The chemical parameters of the harbor water were found to be correlated to the optical properties for two stations investigated in detail. The biological properties of the harbor water (chlorophyll and carotenoids), correlate inversely with the optical data near the pollution sources compared to further away. Calibration procedures developed in this investigation were essential to the interpretation of the photographic and ERTS-1 photometric responses.

Coulbourn, W. C.↗

NASA NTRS1974

Cavitation in liquid cryogens. 4: Combined correlations for venturi, hydrofoil, ogives, and pumps

The results of a series of experimental and analytical cavitation studies are presented. Cross-correlation is performed of the developed cavity data for a venturi, a hydrofoil and three scaled ogives. The new correlating parameter, MTWO, improves data correlation for these stationary bodies and for pumping equipment. Existing techniques for predicting the cavitating performance of pumping machinery were extended to include variations in flow coefficient, cavitation parameter, and equipment geometry. The new predictive formulations hold promise as a design tool and universal method for correlating pumping machinery performance. Application of these predictive formulas requires prescribed cavitation test data or an independent method of estimating the cavitation parameter for each pump. The latter would permit prediction of performance without testing; potential methods for evaluating the cavitation parameter prior to testing are suggested.

Hord, J.↗

NASA NTRS1974

The effects of notch filters on the correlation properties of a PN signal

With wideband pseudo-noise (PN) communications systems, it is sometimes desirable to supplement the inherent interference rejection capabilities by adding notch filters to attenuate relatively narrowband interference. This correspondence presents an investigation of the effects of notch filters on the performance of PN correlation receivers. A theoretical analysis of the correlation drop due to filter distortion has been conducted and confirmed by experimentation. Additional measurements and analysis have established the trade-off between correlation drop and interference suppression as a function of interference bandwidth. A typical result is that by incurring a penalty of a 1-dB drop in correlation peak, interfering signals having bandwidths of 2 to 3% of the PN chip rate can be attenuated by 25 dB.

Sussman, S. M.↗

NASA NTRS1974

Correlation of 1.65 and 2.15 micron airglow emissions

The intense infrared airglow is due primarily to vibration-rotation bands of the OH molecule. This airglow has been observed with a 24-in. scanning photometer at two wavelengths. Narrow-band interference filters are used to limit observations to the (9,7) band at 2.15 microns and the (4,2) and (5,3) bands at 1.65 microns. If OH emission results from creation of the excited OH molecule in the v = 9 vibrational state and subsequent cascading through lower vibrational levels, the 1.65 and 2.15 micron radiation will be well correlated in space and time. However, if several mechanisms are involved in producing OH in a variety of initial excitation levels, there is no reason to expect good correlation. Sky maps obtained simultaneously at 1.65 and 2.15 microns show strongly correlated intensity fluctuations. Quantitative analysis of these maps and other investigations of smaller areas of the sky yield correlation coefficients typically in excess of 0.8.

Kieffaber, L. M.↗

NASA NTRS1973

The correlation of VLF propagation variations with atmospheric planetary-scale waves

Variations in the received daytime phase of long distance, cesium-controlled, VLF transmission were compared to the height variations of the 10-mb isobaric surface during the first three months of 1965 and 1969. The VLF phase values are also compared to height variations of constant electron densities in the E-region and to variations of f-min which have been shown to be well correlated with planetary-scale variations in the stratosphere by Deland and Cavalieri (1973). The VLF phase variations show good correlation with these previous ionospheric measurements and with the 10-mb surfaces. The planetary scale waves in the stratosphere are shown to be travelling on the average eastward in 1965 and westward in 1969. These correlations are interpreted as due to the propagation of travelling planetary scale waves with westward tilted wave fronts. Upward energy transport due to the vertical structure of those waves is also discussed. These correlations provide further evidence for the coupling between the lower ionosphere at about 70 km altitude (the daytime VLF reflection height and the stratosphere, and they demonstrate the importance of planetary wave phenomena to VLF propagation.

Cavalieri, D. J.↗

NASA NTRS1975

Flight transition data for angles of attack at Mach 22 with correlations of the data

Boundary-layer transition data for angles of attack from 2.5 to 47 deg from a flight experiment with a cone that reentered at angles of attack up to 75 deg were analyzed and their local flow conditions are presented. The transition data were obtained from both acoustic and electrostatic sensors. The data from the acoustic and electrostatic sensors were correlated by use of three different sets of correlating parameters. For each set of correlating parameters, the transitional and turbulent data from the acoustic and electrostatic sensors were plotted separately. Each of the correlations was compared with a linear curve fit of previous cone-flight data at near zero angle of attack. Results indicate that the data from acoustic sensors falls below the linear curve fits to the flight data and indicates the sensitivity of the sensors. It is shown that the transition data from the electrostatic sensors tends to scatter much more than the data from the acoustic sensors. However, the data from the electrostatic sensors tends to scatter about the linear curve fits based on previous flight data.

Johnson, C. B.↗

NASA NTRS1976

Strong scintillations in astrophysics. 4. Cross-correlation between different frequencies and finite bandwidth effects

The cross correlation of the intensity fluctuations between different frequencies and finite bandwidth effects on the intensity correlations based on the Markov approximation were calculated. Results may be applied to quite general turbulence spectra for an extended turbulent medium. Calculations of the cross-correlation function and of finite bandwidth effects are explicitly carried out for both Gaussian and Kolmogorov turbulence spectra. The increases of the correlation scale of intensity fluctuations are different for these two spectra and the difference can be used to determine whether the interstellar turbulent medium has a Gaussian or a Kolmogorov spectrum.

Lee, L. C.↗

NASA NTRS1976

Correlation of chlorophyll, suspended matter, and related parameters of waters in the lower Chesapeake Bay area to LANDSAT-1 imagery

The author has identified the following significant results. An effort to relate water parameters of the lower Chesapeake Bay area to multispectral scanner images of LANDSAT 1 has shown that some spectral bands can be correlated to water parameters, and has demonstrated the feasibility of synoptic mapping of estuaries by satellite. Bands 5 and 6 were shown to be useful for monitoring total particles. Band 5 showed high correlation with suspended sediment concentration. Attenuation coefficients monitored continuously by ship along three baselines were cross correlated with radiance values on three days. Improved correlations resulted when tidal conditions were taken into consideration. A contouring program was developed to display sediment variation in the lower Chesapeake Bay from the MSS bands.

Fleischer, P.↗

NASA NTRS1975

Correlation of displacement effects produced by electrons, protons and neutrons in silicon

The correlation of displacement effects produced by electrons, protons, and neutrons in silicon is studied. Available data from the literature is employed. In particular the scope of the study is limited to the degradation of excess carrier lifetime and device electrical parameters directly related to it. The degree to which displacement effects may be correlated in order to predict semiconductor device response based on response data to another type of radiation is discussed. Useful ranges of the correlation factors (lifetime damage constant ratios) as a function of device majority carrier type, device resistivity, and injection level are presented. A significant dependence on injection level for the correlation factors is found.

Van Lint, V. A. J.↗

NASA NTRS1976

The measurement of carbon monoxide and methane in the national capital air quality control region. III - Correlation interferometer results

Two types of experiments were performed with a correlation interferometer on-board a Bell Jet Ranger 206 Helicopter. The first consisted of simultaneous ground- and air-truth measurements as the instrumented helicopter passed over the Cheverly site. The second consisted of several measurement flights in and around the national capital air quality control region (Washington, D.C.). The correlation interferometer data, the infrared Fourier spectrometer data, and the integrated altitude sampling data showed agreement within the errors of the individual measurements. High values for CO were found from the D.C. flight data to be reproducible and concentrated in areas of stop-and-go traffic. It is concluded, that pollutants at low altitudes are detectable from an air-borne platform by remote correlation interferometry and that the correlation interferometer measurements agree with ground- and air-truth data.

Goldstein, H. W.↗

NASA NTRS1976

Correlation between microwave scattering and emission from land and sea at 13.9 GHz

Correlations have been calculated between active and passive microwave responses received by the S-193 radiometer-scatterometer on Skylab. Over both land and sea, the correlations between polarizations are high, but the correlation between radiometer and scatterometer response at 30-deg incidence is negligible. This suggests that multipolarization instruments with this crude resolution (greater than 10 km in all cases) are redundant, but a combination of radiometer and scatterometer is useful. Correlations among the responses at different angles suggest that the five angles used in Skylab are more than would be useful between zero and 48 deg in future instruments, but that instruments with three angles of measurement would be useful. In small areas, conclusions based on these large-data-set averages may need to be modified.

Sobti, A.↗

NASA NTRS1976

Strong scintillations in astrophysics. IV - Cross-correlation between different frequencies and finite bandwidth effects

The cross-correlation of the intensity fluctuations between different frequencies and finite-bandwidth effects on the intensity correlations are calculated based on the Markov approximation. The results may be applied to quite general turbulence spectra for an extended turbulent medium. Calculations of the cross-correlation function and of finite-bandwidth effects are explicitly carried out for both Gaussian and Kolmogorov turbulence spectra. The increases of the correlation scale of intensity fluctuations are different for these two spectra, and the difference can be used to determine whether the interstellar turbulent medium has a Gaussian or a Kolmogorov spectrum.

Lee, L. C.↗

NASA NTRS1976

A note on correlation description

The paper suggests some modifications to definitions of correlation functions made by Freeman and Bennett (1974) specifically for comparing measured quantities with those predicted by rotor theories, with reference to rotorcraft flight simulation. Special attention is paid to the quality of correlation, determined by a quality factor relating the measured and computed entities. Correlation criteria (mean load and rotor performance, overall amplitude and phase, harmonic altitude and harmonic phase) are examined, along with phase angle correlation criteria (harmonic phase defined by sine-cosine relation and harmonic phase defined by a first positive peak rotor azimuth position)

Mccloud, J. L., III↗

NASA NTRS1976

Correlation microphone for measuring airframe noise in large-scale wind tunnels

A correlation microphone arrangement was used in the test section of the Ames 7- by 10-Foot and 40- by 80-Foot Wind Tunnels in an attempt to reject the reverberant and wind noise. The tests in the 7- by 10-foot wind tunnel covered a frequency range from 400 Hz to 8 kHz while the tests in the 40- by 80-foot tunnel covered the range from 31.5 to 800 Hz. Examination of the experimental data plus calculations of cross-correlations due to reflective noise indicate that the correlation microphone is effective in rejecting microphone wind noise and reverberant noise even at low frequencies, and that the low-frequency background noise monitored by the correlation microphone is reflected noise with a preferred direction from the tunnel drive system. Design studies indicate that this tunnel drive noise can be reduced substantially through suitable modification of the drive fans and acoustical treatment of the nacelles that house these fans.

Ahtye, W. F.↗

NASA NTRS1975

Correlations by the entrainment theory of thermodynamic effects for developed cavitation in venturis and comparisons with ogive data

A semi-empirical entrainment theory was employed to correlate the measured temperature depression, Delta T, in a developed cavity for a venturi. This theory correlates Delta t in terms of the dimensionless numbers of Nusselt, Reynolds, Froude, Weber and Peclet, and dimensionless cavity length, L/D. These correlations are then compared with similar correlations for zero and quarter caliber ogives. In addition, cavitation number data for both limited and developed cavitation in venturis are presented.

Billet, M. L.↗