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NASA NTRS1994

Gain weighted eigenspace assignment

This report presents the development of the gain weighted eigenspace assignment methodology. This provides a designer with a systematic methodology for trading off eigenvector placement versus gain magnitudes, while still maintaining desired closed-loop eigenvalue locations. This is accomplished by forming a cost function composed of a scalar measure of error between desired and achievable eigenvectors and a scalar measure of gain magnitude, determining analytical expressions for the gradients, and solving for the optimal solution by numerical iteration. For this development the scalar measure of gain magnitude is chosen to be a weighted sum of the squares of all the individual elements of the feedback gain matrix. An example is presented to demonstrate the method. In this example, solutions yielding achievable eigenvectors close to the desired eigenvectors are obtained with significant reductions in gain magnitude compared to a solution obtained using a previously developed eigenspace (eigenstructure) assignment method.

Davidson, John B.↗

NASA NTRS2012

Correlation Between Analog Noise Measurements and the Expected Bit Error Rate of a Digital Signal Propagating Through Passive Components

A method of determining the bit error rate (BER) of a digital circuit from the measurement of the analog S-parameters of the circuit has been developed. The method is based on the measurement of the noise and the standard deviation of the noise in the S-parameters. Once the standard deviation and the mean of the S-parameters are known, the BER of the circuit can be calculated using the normal Gaussian function.

Warner, Joseph D.↗

NASA NTRS2004

Reducing Errors by Use of Redundancy in Gravity Measurements

A methodology for improving gravity-gradient measurement data exploits the constraints imposed upon the components of the gravity-gradient tensor by the conditions of integrability needed for reconstruction of the gravitational potential. These constraints are derived from the basic equation for the gravitational potential and from mathematical identities that apply to the gravitational potential and its partial derivatives with respect to spatial coordinates. Consider the gravitational potential in a Cartesian coordinate system {x1,x2,x3}. If one measures all the components of the gravity-gradient tensor at all points of interest within a region of space in which one seeks to characterize the gravitational field, one obtains redundant information. One could utilize the constraints to select a minimum (that is, nonredundant) set of measurements from which the gravitational potential could be reconstructed. Alternatively, one could exploit the redundancy to reduce errors from noisy measurements. A convenient example is that of the selection of a minimum set of measurements to characterize the gravitational field at n3 points (where n is an integer) in a cube. Without the benefit of such a selection, it would be necessary to make 9n3 measurements because the gravitygradient tensor has 9 components at each point. The problem of utilizing the redundancy to reduce errors in noisy measurements is an optimization problem: Given a set of noisy values of the components of the gravity-gradient tensor at the measurement points, one seeks a set of corrected values - a set that is optimum in that it minimizes some measure of error (e.g., the sum of squares of the differences between the corrected and noisy measurement values) while taking account of the fact that the constraints must apply to the exact values. The problem as thus posed leads to a vector equation that can be solved to obtain the corrected values.

Kulikov, Igor↗

NASA NTRS1988

On correcting radial orbit errors for altimetric satellites using crossover analysis

A method is proposed for correcting radial orbit error in measurements of sea surface height using a satellite altimeter. Traditionally, the orbit error is modeled in terms of a Fourier series with the Fourier coefficients determined by minimizing the residual crossover difference in a least-squares sense. In this method an a priori constraint must be imposed to obtain a unique solution. It is shown that by using singular value decomposition, no such constraint is needed. This proposed method leaves the geographically dependent errors unchanged and makes only those corrections warranted by the information contained in crossover differences. Thus, the resultant ocean topography is free from any undue distortion which might be incurred by an a priori constraint. It is suggested that the method is useful for application to high-accuracy altimetric mission, because the orbit error can be reduced without compromising the accuracy of the measured mean ocean topography.

Fu, Lee-Lueng↗

NASA NTRS1991

Using image area to control CCD systematic errors in spaceborne photometric and astrometric time-series measurements

The effect of some systematic errors for high-precision time-series spaceborne photometry and astrometry has been investigated with a CCD as the detector. The 'pixelization' of the images causes systematic error in astrometric measurements. It is shown that this pixelization noise scales as image radius r exp -3/2. Subpixel response gradients, not correctable by the 'flat field', and in conjunction with telescope pointing jitter, introduce further photometric and astrometric errors. Subpixel gradients are modeled using observed properties of real flat fields. These errors can be controlled by having an image span enough pixels. Large images are also favored by CCD dynamic range considerations. However, magnified stellar images can overlap, thus introducing another source of systematic error. An optimum image size is therefore a compromise between these competing factors.

Buffington, Andrew↗

NASA NTRS1991

Probable errors in width distributions of sea ice leads measured along a transect

The degree of error expected in the measurement of widths of sea ice leads along a single transect are examined in a probabilistic sense under assumed orientation and width distributions, where both isotropic and anisotropic lead orientations are examined. Methods are developed for estimating the distribution of 'actual' widths (measured perpendicular to the local lead orientation) knowing the 'apparent' width distribution (measured along the transect), and vice versa. The distribution of errors, defined as the difference between the actual and apparent lead width, can be estimated from the two width distributions, and all moments of this distribution can be determined. The problem is illustrated with Landsat imagery and the procedure is applied to a submarine sonar transect. Results are determined for a range of geometries, and indicate the importance of orientation information if data sampled along a transect are to be used for the description of lead geometries. While the application here is to sea ice leads, the methodology can be applied to measurements of any linear feature.

Key, J.↗

NASA NTRS1988

Some effects of finite spatial resolution on skin friction measurements in turbulent boundary layers

The effects of finite spatial resolution often cause serious errors in measurements in turbulent boundary layers, with particularly large effects for measurements of fluctuating skin friction and velocities within the sublayer. However, classical analyses of finite spatial resolution effects have generally not accounted for the substantial inhomogeneity and anisotropy of near-wall turbulence. The present study has made use of results from recent computational simulations of wall-bounded turbulent flows to examine spatial resolution effects for measurements made at a wall using both single-sensor probes and those employing two sensing volumes in a V shape. Results are presented to show the effects of finite spatial resolution on a variety of quantitites deduced from the skin friction field.

Westphal, Russell V.↗

NASA NTRS1977

LANDSAT/coastal processes

The author has identified the following significant results. Correlations between the satellite radiance values water color, Secchi disk visibility, turbidity, and attenuation coefficients were generally good. The residual was due to several factors including systematic errors in the remotely sensed data, errors, small time and space variations in the water quality measurements, and errors caused by experimental design. Satellite radiance values were closely correlated with the optical properties of the water.

James, W. P.↗

NASA NTRS1977

Prediction of pilot reserve attention capacity during air-to-air target tracking

Reserve attention capacity of a pilot was calculated using a pilot model that allocates exclusive model attention according to the ranking of task urgency functions whose variables are tracking error and error rate. The modeled task consisted of tracking a maneuvering target aircraft both vertically and horizontally, and when possible, performing a diverting side task which was simulated by the precise positioning of an electrical stylus and modeled as a task of constant urgency in the attention allocation algorithm. The urgency of the single loop vertical task is simply the magnitude of the vertical tracking error, while the multiloop horizontal task requires a nonlinear urgency measure of error and error rate terms. Comparison of model results with flight simulation data verified the computed model statistics of tracking error of both axes, lateral and longitudinal stick amplitude and rate, and side task episodes. Full data for the simulation tracking statistics as well as the explicit equations and structure of the urgency function multiaxis pilot model are presented.

Onstott, E. D.↗

NASA NTRS1990

Differential spacecraft tracking by interferometry

This study estimates measurement system errors for two space vehicles on the surface of Mars, and for two Mars orbiting spacecraft, which are being tracked by differential interferometry. In these examples, signals from all spacecraft lie within the same beamwidth of an earth-based radio antenna. The measurements of all spacecraft signals are made simultaneously; errors that scale with angular source separation or with temporal separation between measurement epochs are practically removed. It is shown that errors due to system thermal noise and to systematic effects within ground receiver electronics dominate, except for geometries when signals pass close to the sun, when solar plasma becomes the dominant error source. The instantaneous relative position of two orbiters may be measured to within ten meters, leading to 50-meter three-dimensional orbital accuracy.

Border, James S.↗

NASA NTRS1977

Compatibility check of measured aircraft responses using kinematic equations and extended Kalman filter

An extended Kalman filter smoother and a fixed point smoother were used for estimation of the state variables in the six degree of freedom kinematic equations relating measured aircraft responses and for estimation of unknown constant bias and scale factor errors in measured data. The computing algorithm includes an analysis of residuals which can improve the filter performance and provide estimates of measurement noise characteristics for some aircraft output variables. The technique developed was demonstrated using simulated and real flight test data. Improved accuracy of measured data was obtained when the data were corrected for estimated bias errors.

Klein, V.↗

NASA NTRS1991

The advanced receiver 2: Telemetry test results in CTA 21

Telemetry tests with the Advanced Receiver II (ARX II) in Compatibility Test Area 21 are described. The ARX II was operated in parallel with a Block-III Receiver/baseband processor assembly combination (BLK-III/BPA) and a Block III Receiver/subcarrier demodulation assembly/symbol synchronization assembly combination (BLK-III/SDA/SSA). The telemetry simulator assembly provided the test signal for all three configurations, and the symbol signal to noise ratio as well as the symbol error rates were measured and compared. Furthermore, bit error rates were also measured by the system performance test computer for all three systems. Results indicate that the ARX-II telemetry performance is comparable and sometimes superior to the BLK-III/BPA and BLK-III/SDA/SSA combinations.

Hinedi, S.↗

NASA NTRS1984

Fast decoding techniques for extended single-and-double-error-correcting Reed Solomon codes

A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. For example, some 256K-bit dynamic random access memories are organized as 32K x 8 bit-bytes. Byte-oriented codes such as Reed Solomon (RS) codes provide efficient low overhead error control for such memories. However, the standard iterative algorithm for decoding RS codes is too slow for these applications. Some special high speed decoding techniques for extended single and double error correcting RS codes. These techniques are designed to find the error locations and the error values directly from the syndrome without having to form the error locator polynomial and solve for its roots.

Costello, D. J., Jr.↗

NASA NTRS1980

Alignment techniques required by precise measurement of effective focal length

The characteristics of false color imagery produced by instrumentation on earth resource mapping satellites are examined. The spatial fidelity of the imagery is dependent upon the geometric accuracy (GA) and the band-to-band registration (BBR) with which the telescope instrument is assembled. BBR and GA require knowledge of telescope effective focal length (EFL) to one part in 10,000 in order that the next generation of earth mappers be able to carry out their missions. The basis for this level of precision is briefly considered, and a description is given of the means by which such precise EFL measurements have been carried out. Attention is given to accuracy requirements, the technique used to measure effective focal length, possible sources of error in the EFL measurement, approaches for eliminating errors, and the results of the efforts to control measurement errors in EFL determinations.

Wise, T. D.↗

NASA NTRS1977

The total hemispherical emittance of silicon-carbide coated reinforced carbon composites in the temperature range 100 K to 450 K

This paper deals with the measurement of the total hemispherical emittance of a silicon carbide coated carbon composite which is the thermal control material of the nose cone and leading edges of the Space Shuttle. In order to effect the thermal design of the spacecraft, it is desirable to have emittance data available for the temperature range 100 K to 2000 K to encompass the thermal extremes associated with orbiting and reentry conditions. Since the multiple thermal cycling associated with fifty to one hundred missions might result in substantial property changes, the data to be presented are for the low temperature regime 100 K to 450 K for both virgin material and material which was thermally treated to simulate multiple reentries. The discussion emphasizes the identification of possible sources of error in the measurement of equilibrium temperatures and the extent to which these measurement errors or uncertainties would alter the derived emittance values.

Mcgrath, J. J.↗

NASA NTRS1996

Optimal and robust control of transition

Optimal and robust control theories are used to determine feedback control rules that effectively stabilize a linearly unstable flow in a plane channel. Wall transpiration (unsteady blowing/suction) with zero net mass flux is used as the control. Control algorithms are considered that depend both on full flowfield information and on estimates of that flowfield based on wall skin-friction measurements only. The development of these control algorithms accounts for modeling errors and measurement noise in a rigorous fashion; these disturbances are considered in both a structured (Gaussian) and unstructured ('worst case') sense. The performance of these algorithms is analyzed in terms of the eigenmodes of the resulting controlled systems, and the sensitivity of individual eigenmodes to both control and observation is quantified.

Bewley, T. R.↗

NASA NTRS2010

Simulation Studies for a Space-Based CO2 Lidar Mission

We report results of initial space mission simulation studies for a laser-based, atmospheric CO2 sounder, which are based on real-time carbon cycle process modelling and data analysis. The mission concept corresponds to the Active Sensing of CO2 Emissions over Nights, Days and Seasons (ASCENDS) recommended by the US National Academy of Sciences' Decadal Survey. As a pre-requisite for meaningful quantitative evaluation, we employ a CO2 model that has representative spatial and temporal gradients across a wide range of scales. In addition, a relatively complete description of the atmospheric and surface state is obtained from meteorological data assimilation and satellite measurements. We use radiative transfer calculations, an instrument model with representative errors and a simple retrieval approach to quantify errors in 'measured' CO2 distributions, which are a function of mission and instrument design specifications along with the atmospheric/surface state. Uncertainty estimates based on the current instrument design point indicate that a CO2 laser sounder can provide data consistent with ASCENDS requirements and will significantly enhance our ability to address carbon cycle science questions. Test of a dawn/dusk orbit deployment, however, shows that diurnal differences in CO2 column abundance, indicative of plant photosynthesis and respiration fluxes, will be difficult to detect

Kawa, S. R.↗

NASA NTRS2010

Inferring Cirrus Size Distributions Through Satellite Remote Sensing and Microphysical Databases

Since cirrus clouds have a substantial influence on the global energy balance that depends on their microphysical properties, climate models should strive to realistically characterize the cirrus ice particle size distribution (PSD), at least in a climatological sense. To date, the airborne in situ measurements of the cirrus PSD have contained large uncertainties due to errors in measuring small ice crystals (D<60 m). This paper presents a method to remotely estimate the concentration of the small ice crystals relative to the larger ones using the 11- and 12- m channels aboard several satellites. By understanding the underlying physics producing the emissivity difference between these channels, this emissivity difference can be used to infer the relative concentration of small ice crystals. This is facilitated by enlisting temperature-dependent characterizations of the PSD (i.e., PSD schemes) based on in situ measurements. An average cirrus emissivity relationship between 12 and 11 m is developed here using the Moderate Resolution Imaging Spectroradiometer (MODIS) satellite instrument and is used to retrieve the PSD based on six different PSD schemes. The PSDs from the measurement-based PSD schemes are compared with corresponding retrieved PSDs to evaluate differences in small ice crystal concentrations. The retrieved PSDs generally had lower concentrations of small ice particles, with total number concentration independent of temperature. In addition, the temperature dependence of the PSD effective diameter De and fall speed Vf for these retrieved PSD schemes exhibited less variability relative to the unmodified PSD schemes. The reduced variability in the retrieved De and Vf was attributed to the lower concentrations of small ice crystals in the retrieved PSD.

Mitchell, David↗