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All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

A qualitative assessment of a random process proposed as an atmospheric turbulence model

A random process is formed by the product of two Gaussian processes and the sum of that product with a third Gaussian process. The resulting total random process is interpreted as the sum of an amplitude modulated process and a slowly varying, random mean value. The properties of the process are examined, including an interpretation of the process in terms of the physical structure of atmospheric motions. The inclusion of the mean value variation gives an improved representation of the properties of atmospheric motions, since the resulting process can account for the differences in the statistical properties of atmospheric velocity components and their gradients. The application of the process to atmospheric turbulence problems, including the response of aircraft dynamic systems, is examined. The effects of the mean value variation upon aircraft loads are small in most cases, but can be important in the measurement and interpretation of atmospheric turbulence data.

Sidwell, K.↗
NASA NTRS1993

Quasi-random narrow-band model fits to near-infrared low-temperature laboratory methane spectra and derived exponential-sum absorption coefficients

Near-infrared 10/cm resolution spectra of methane obtained at various temperatures, pressures, and abundances are fit to a quasi-random narrow-band model. Exponential-sum absorption coefficients for three temperatures (112, 188, and 295 K), and 20 pressures from 0.0001 to 5.6 bars, applicable to the cold environments of the major planets, are then derived from the band model for the 230 wavelengths measured from 1.6 to 2.5 microns. RMS deviations between the laboratory and the exponential-sum synthetic transmissions are reported for the best fitting 50 wavelengths. Deviations relevant to broadband, 1-percent spectral resolution observations are also presented. The validity of exponential-sum coefficients derived from broadband (10/cm) transmission data is demonstrated via direct comparison with line-by-line calculations. The complete atlas of coefficients is available from the Planetary Data System-Planetary Atmospheres Discipline Node.

Baines, Kevin H.↗
NASA NTRS1977

A mathematical study of a random process proposed as an atmospheric turbulence model

A random process is formed by the product of a local Gaussian process and a random amplitude process, and the sum of that product with an independent mean value process. The mathematical properties of the resulting process are developed, including the first and second order properties and the characteristic function of general order. An approximate method for the analysis of the response of linear dynamic systems to the process is developed. The transition properties of the process are also examined.

Sidwell, K.↗
NASA NTRS1996

Perceptually Lossless Wavelet Compression

The Discrete Wavelet Transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter, which we call DWT uniform quantization noise. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2(exp -1), where r is display visual resolution in pixels/degree, and L is the wavelet level. Amplitude thresholds increase rapidly with spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from low-pass to horizontal/vertical to diagonal. We propose a mathematical model for DWT noise detection thresholds that is a function of level, orientation, and display visual resolution. This allows calculation of a 'perceptually lossless' quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.

Watson, Andrew B.↗
NASA NTRS1995

Visibility of Wavelet Quantization Noise

The Discrete Wavelet Transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter, which we call DWT uniform quantization noise. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2(exp)-L , where r is display visual resolution in pixels/degree, and L is the wavelet level. Amplitude thresholds increase rapidly with spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from low-pass to horizontal/vertical to diagonal. We describe a mathematical model to predict DWT noise detection thresholds as a function of level, orientation, and display visual resolution. This allows calculation of a "perceptually lossless" quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.

Watson, Andrew B.↗
NASA NTRS1997

Visibility of wavelet quantization noise

The discrete wavelet transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that we call DWT uniform quantization noise; it is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2-lambda, where r is display visual resolution in pixels/degree, and lambda is the wavelet level. Thresholds increase rapidly with wavelet spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from lowpass to horizontal/vertical to diagonal. We construct a mathematical model for DWT noise detection thresholds that is a function of level, orientation, and display visual resolution. This allows calculation of a "perceptually lossless" quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.

NASA Center ARC↗
NASA NTRS2011

Influence of Vibrotactile Feedback on Controlling Tilt Motion After Spaceflight

We hypothesize that adaptive changes in how inertial cues from the vestibular system are integrated with other sensory information leads to perceptual disturbances and impaired manual control following transitions between gravity environments. The primary goals of this ongoing post-flight investigation are to quantify decrements in manual control of tilt motion following short-duration spaceflight and to evaluate vibrotactile feedback of tilt as a sensorimotor countermeasure. METHODS. Data is currently being collected on 9 astronaut subjects during 3 preflight sessions and during the first 8 days after Shuttle landings. Variable radius centrifugation (216 deg/s, <20 cm radius) in a darkened room is utilized to elicit otolith reflexes in the lateral plane without concordant canal or visual cues. A Tilt-Translation Sled (TTS) is capable of synchronizing pitch tilt with fore-aft translation to align the resultant gravitoinertial vector with the longitudinal body axis, thereby eliciting canal reflexes without concordant otolith or visual cues. A simple 4 tactor system was implemented to provide feedback when tilt position exceeded predetermined levels in either device. Closed-loop nulling tasks are performed during random tilt steps or sum-of-sines (TTS only) with and without vibrotactile feedback of chair position. RESULTS. On landing day the manual control performance without vibrotactile feedback was reduced by >30% based on the gain or the amount of tilt disturbance successfully nulled. Manual control performance tended to return to baseline levels within 1-2 days following landing. Root-mean-square position error and tilt velocity were significantly reduced with vibrotactile feedback. CONCLUSIONS. These preliminary results are consistent with our hypothesis that adaptive changes in vestibular processing corresponds to reduced manual control performance following G-transitions. A simple vibrotactile prosthesis improves the ability to null out tilt motion within a limited range of motion disturbances.

Wood, S. J.↗
NASA NTRS1990

A chaotic attractor in timing noise from the Vela pulsar?

Fourteen years of timing residual data from the Vela pulsar have been analyzed in order to determine if a chaotic dynamical process is the origin of timing noise. Using the correlation sum technique, a dimension of about 1.5 is obtained. This low dimension indicates underlying structure in the phase residuals which may be evidence for a chaotic attractor. It is therefore possible that nonlinear dynamics intrinsic to the spin-down may be the cause of the timing noise in the Vela pulsar. However, it has been found that the stimulated random walks in frequency and frequency derivative often used to model pulsar timing noise also have low fractal dimension, using the same analysis technique. Recent work suggesting that random processes with steep power spectra can mimic strange attractors seems to be confirmed in the case of these random walks. It appears that the correlation sum estimator for dimension is unable to distinguish between chaotic and random processes.

Harding, Alice K.↗
NASA NTRS1988

Remote sensing of earth terrain

Two monographs and 85 journal and conference papers on remote sensing of earth terrain have been published, sponsored by NASA Contract NAG5-270. A multivariate K-distribution is proposed to model the statistics of fully polarimetric data from earth terrain with polarizations HH, HV, VH, and VV. In this approach, correlated polarizations of radar signals, as characterized by a covariance matrix, are treated as the sum of N n-dimensional random vectors; N obeys the negative binomial distribution with a parameter alpha and mean bar N. Subsequently, and n-dimensional K-distribution, with either zero or non-zero mean, is developed in the limit of infinite bar N or illuminated area. The probability density function (PDF) of the K-distributed vector normalized by its Euclidean norm is independent of the parameter alpha and is the same as that derived from a zero-mean Gaussian-distributed random vector. The above model is well supported by experimental data provided by MIT Lincoln Laboratory and the Jet Propulsion Laboratory in the form of polarimetric measurements.

Kong, J. A.↗
NASA NTRS1989

K-distribution and polarimetric terrain radar clutter

A multivariate K-distribution is proposed to model the statistics of fully polarimetric radar data from earth terrain with polarizations HH, HV, VH, and VV. In this approach, correlated polarizations of radar signals, as characterized by a covariance matrix, are treated as the sum of N n-dimensional random vectors; N obeys the negative binomial distribution with a parameter alpha and mean N-bar. Subsequently, an n-dimensional K-distribution, with either zero or nonzero mean, is developed in the limit of infinite N-bar or illuminated area. The probability density function (PDF) of the K-distributed vector normalized by its Euclidean norm is independent of the parameter alpha and is the same as that derived from a zero-mean Gaussian-distributed random vector.

Yueh, S. H.↗
NASA NTRS1992

Combustion noise and combustion instabilities in propulsion systems

This paper is concerned with some aspects of non-linear behavior of unsteady motions in combustion chambers. The emphasis is on conditions under which organized oscillations having discrete frequencies may exist in the presence of random motions. In order to treat the two types of motions together, and particularly to investigate coupling between noise and combustion instabilities, the unsteady field is represented as a synthesis of acoustic modes having time-varying amplitudes. Each of the amplitudes are written as the sum of two parts, one associated with the random field and the remainder representing the organized oscillations. After spatial averaging, the general problem is reduced to solution of a set of second-order ordinary differential equations whose structure depends on the sorts of nonlinear processes accounted for. This formulation accommodates any physical process; in particular, terms are included to represent noise sources, although only limited modeling is discussed. Our results suggest that random sources of noise have only small effects on combustion instabilities and seem not to be a cause of unstable motions. However, the coupling between the two sorts of unsteady motions may be important as an essential process in a proposed scheme for noise control. It is now a familiar observation that many nonlinear deterministic systems are capable of exhibiting apparently random motions called 'chaos.' This is a particularly interesting possibility for systems which also executed non-deterministic random motions. In combustion chambers, a nonlinear deterministic system (acoustical motions) exists in the presence of noise produced by flow separation, turbulent motions, and energy released by combustion processes. The last part of the paper is directed to the matter of discovering whether or not chaotic motions exist in combustion systems. Analysis has not progressed sufficiently far to answer the question. We report here recent results of processing data taken in one combustor to determine the dimensions of any attractors in the motions. No evidence has been found for chaos in the strict sense, but the method seems to be an important means of investigating the nonlinear behavior of combustion systems.

F. E. C. Culick↗
NASA NTRS1974

A design method for minimizing sensitivity to plant parameter variations

A method is described for minimizing the sensitivity of multivariable systems to parameter variations. The variable parameters are considered as random variables and their effect is included in a quadratic performance index. The performance index is a weighted sum of the state and control covariances that stem from both the random system disturbances and the parameter uncertainties. The numerical solution of the problem is described and application of the method to several initially sensitive tracking systems is discussed. The sensitivity factor of reduction was typically 2 or 3 over a system based on random system noise only, and yet resulted in state RMS increases of only about a factor of two.

Hadass, Z.↗
NASA NTRS1976

Behavior of queues at signalized intersections in heavy traffic

This paper derives the asymptotic behavior of traffic queues at signalized intersections when the excess of departure capacity over arrivals approaches zero from above. The most interesting result is that the distribution of queue length approaches a negative exponential, with fewer restrictive assumptions than hitherto known. The main improvement results from more precise use of a combinatorial lemma of Spitzer, giving the maximum of the partial sums of a sequence of independent identically distributed random variables, plus some specific constructive probability calculations, many of them involving the Fourier transform. New results are presented on the probability that the queue be below a fixed bound and/or on the probability that the queue be empty. Applications to on-line estimators for real-time traffic control are suggested.

Posner, E. C.↗
NASA NTRS1981

Role of the doubly stochastic Neyman type-A and Thomas counting distributions in photon detection

The sums of Meyman type-A and Thomas random variables are shown to retain their form under the constant multiplication parameter constraint. The conditions under which the two random variables converge in distribution to the fixed multiplicative Poisson, and to the Gaussian, are presented. It is shown that the latter result is important, in that it provides a solution to likelihood-ratio detection, estimation and discrimination problems in the presence of many kinds of signal and noise. Among the explicit applications presented are: (1) the photon-counter scintillation detection of nuclear particles when particle flux is low, (2) the photon-counting detection of weak optical signals in the presence of ionizing radiation, and (3) the design of a star-scanner spacecraft guidance system adequate for hostile space environments.

Teich, M. C.↗
NASA NTRS1985

A class of optimum digital phase locked loops for the DSN advanced receiver

A class of optimum digital filters for digital phase locked loop of the deep space network advanced receiver is discussed. The filter minimizes a weighted combination of the variance of the random component of the phase error and the sum square of the deterministic dynamic component of phase error at the output of the numerically controlled oscillator (NCO). By varying the weighting coefficient over a suitable range of values, a wide set of filters are obtained such that, for any specified value of the equivalent loop-noise bandwidth, there corresponds a unique filter in this class. This filter thus has the property of having the best transient response over all possible filters of the same bandwidth and type. The optimum filters are also evaluated in terms of their gain margin for stability and their steady-state error performance.

Hurd, W. J.↗
NASA NTRS1982

A high speed implementation of the random decrement algorithm

The algorithm is useful for measuring net system damping levels in stochastic processes and for the development of equivalent linearized system response models. The algorithm works by summing together all subrecords which occur after predefined threshold level is crossed. The random decrement signature is normally developed by scanning stored data and adding subrecords together. The high speed implementation of the random decrement algorithm exploits the digital character of sampled data and uses fixed record lengths of 2(n) samples to greatly speed up the process. The contributions to the random decrement signature of each data point was calculated only once and in the same sequence as the data were taken. A hardware implementation of the algorithm using random logic is diagrammed and the process is shown to be limited only by the record size and the threshold crossing frequency of the sampled data. With a hardware cycle time of 200 ns and 1024 point signature, a threshold crossing frequency of 5000 Hertz can be processed and a stably averaged signature presented in real time.

Kiraly, L. J.↗
NASA NTRS1983

A high-speed implementation of the random decrement algorithm

The algorithm is useful for measuring net system damping levels in stochastic processes and for the development of equivalent linearized system response models. The algorithm works by summing together all subrecords which occur after predefined threshold level is crossed. The random decrement signature is normally developed by scanning stored data and adding subrecords together. The high speed implementation of the random decrement algorithm exploits the digital character of sampled data and uses fixed record lengths of 2(n) samples to greatly speed up the process. The contributions to the random decrement signature of each data point was calculated only once and in the same sequence as the data were taken. A hardware implementation of the algorithm using random logic is diagrammed and the process is shown to be limited only by the record size and the threshold crossing frequency of the sampled data. With a hardware cycle time of 200 ns and 1024 point signature, a threshold crossing frequency of 5000 Hertz can be processed and a stably averaged signature presented in real time.

Kiraly, L. J.↗
NASA NTRSDate not supplied

Characterizing Spatiotemporal Uncertainty in Interpolated Meteorological Data

Interpolated meteorological data invariably contain errors. These errors have structure in time and space, particularly autocorrelation, which can cause the effects of errors to compound when model outputs are aggregated temporally or spatially. One way to account for this uncertainty is with a probabilistic model from which samples can be drawn that are coherent with respect to underlying spatial and temporal covariance structure. This work describes a probabilistic method for spatial interpolation of point-wise meteorological time series. Observational data from weather stations are generally sparse in space and dense in time (but sometimes missing). The method works by projecting time series onto orthogonal basis vectors and spatially interpolating each resulting component independently. Under suitable assumptions, and data transformations to better satisfy those assumptions, Gaussian process regression provides a complete description of the joint predictive distribution over a Gaussian random field. Spatiotemporally coherent realizations are generated as the sum of conditional (spatial) simulations of each orthogonal (temporal) component. Data-derived and generic orthogonal bases are considered. In addition to spatial interpolation, imputation of missing observational data is examined. The method is applied using near-surface air temperature over the Western United States and validated by comparing theoretical versus actual coverage of predictive distributions and analyzing the degree to which spatial and temporal covariance structure is reproduced. Computational considerations, relating to conditional simulation of random fields, are also addressed.

Conor T Doherty↗