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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1981

Predictability in a solvable stochastic climate model

A highly idealized atmospheric model is presented for the purpose of examining the limits of predictability for the large scales of the temperature field. The model is of the semiempirical type introduced by Budyko (1968, 1969) and Sellers (1969), but forced by a white noise heating term. The advantage of the considered model is its simplicity and the fact that analytical methods can be used throughout so that each assumption and simplification can be examined explicitly. On the other hand, the model lacks many features expected to be important in the real geophysical system. The predictability problem is illustrated by considering first a simple model for the global temperature. The characteristic time for the decay of a global temperature anomaly is determined by the ratio of the associated heat storage to the radiative loss rate.

North, G. R.↗
NASA NTRS1981

Functional methods for waves in random media

Some basic ideas in functional methods for waves in random media are illustrated through a simple random differential equation. These methods are then generalized to solve certain random parabolic equations via an exponential representation given by the Feynman-Kac formula. It is shown that these functional methods are applicable to a number of problems in random wave propagation. They include the forward-scattering approximation in Gaussian white-noise media; the solution of the optical beam propagation problem by a phase-integral method; the high-frequency scattering by bounded random media, and a derivation of approximate moment equations from the functional integral representation.

Chow, P. L.↗
NASA NTRS1981

Functional methods for waves in random media

Some basic ideas in functional methods for waves in random media are illustrated through a simple random differential equation. These methods are then generalized to solve certain random parabolic equations via an exponential representation given by the Feynman-Kac formula. It is shown that these functional methods are applicable to a number of problems in random wave propagation. They include the forward-scattering approximation in Gaussian white-noise media; the solution of the optical beam propagation problem by a phase-integral method; the high-frequency scattering by bounded random media; and a derivation of approximate moment equations from the functional integral representation.

Chow, P. L.↗
NASA NTRS1982

Signal analysis and error analysis studies for a Geopotential Research Mission (GRM)

The signal characteristics and the geopotential parameter recovery capability of the SST Doppler sensor flown on the geopotential research mission (GRM) are discussed. Simulation studies of the velocity profiles resulting from the perturbation produced by a 1 deg/w/1 deg, 1 mgal anomaly as sensed by two GRM spacecraft orbiting altitudes of 160 km and 200 km respectively are described. It was found that the amplitude of the gravity signal drops off by a factor of 1.5 when going from an altitude of 160 km to 200 km. By extrapolation the signal amplitude is further decreased by a factor of 3 when the orbital altitude is increased to 250 km. Thus the amplitude of the measurement drops off as the altitude is increased to the point where it is insignificant at the 1 mgal level for altitudes above 200 km. Spectral analysis results show that for a GRM mission altitude of 160 km and a system precision of 1 micrometer/sec, gravity field information can be sensed up to 230 cycles per orbital revolution - beyond that frequency the gravity signal is characterized by white noise. It follows that at the GRM mission altitude of 160 km and a satellite to satellite Doppler system precision of 1 micrometer per second, 1/1 deg gravity and geoid anomalies can be determined to an accuracy of 3.4 mgals and 8.6 cm respectively.

Kahn, W. D.↗
NASA NTRS1981

Singular perturbation, state aggregation and nonlinear filtering

Consideration is given to a state process evolving in R(n), whose motion is that of a pure jump process in R(n) in the 0(1) time scale, upon which is superimposed a continuous motion along the orbits of a gradient-like vector field g in R(n) in the 0(1/epsilon) time scale. The infinitesimal generator of the state process is, in other words, of the form L + (1/epsilon)g. It follows from the main results presented that the projected filters converge to the finite state Wonham filter corresponding to the problem of estimating the finite state process in the presence of additive white noise.

Hijab, O.↗
NASA NTRS1983

A stochastic-dynamic model for the spatial structure of forecast error statistics

The present investigation is concerned with the presentation of a simplified model of the spatial structure of forecast error statistics, a comparison of the model with actual numerical weather prediction results, and the extent to which simplifying assumptions made in the model are justified. A stochastic-dynamic model is derived for the spatial structure of the global atmospheric mass-field forecast error. The model states that the relative potential vorticity of the forecast error is random. The covariance function of the model's solutions is found to be governed by a simple deterministic equation. The agreement between the stochastic model and actual mass-field forecast errors fields for 12-36 h periods validates the assumptions on which the model is derived. Within this period, the difference between the potential voriticity fields of the atmosphere and of the numerical forecasts used in the comparison is well represented by white noise.

Balgovind, R.↗
NASA NTRS1984

First Results of GPS Time Transfer to Australia

A global positioning system (GPS) time transfer unit was installed at Tidbinbilla Deep Space Communications Complex of the DSN in June 1983. It was used to estimate the relationship to UTC(USNO MC) of the Tidbinbilla frequency and time system TID(FTS) based on a hydrogen maser, and to estimate the performance of the Australian free-running time scale UTC(AUS). Data from the first 3 months were analyzed three ways: by two-hop common view using JPL as intermediary; by long-arc interpolation of measurements against space vehicle clocks; and by long arc interpolation of GPS-Time results. Residuals from a single quadratic fit through 3 months of UTC(USNO MC) -TID(FTS) results were white noise with standard error 15 ns, and a flying clock measurement gave 70 ns agreement. A straight line fit through results UTC(USNO MC) - UTC(AUS) gave 90 ns standard error and 120 ns agreement. It is proposed to use the GPS measurements to steer UTC(AUS) to UTC(BIH), and to rename the existing time scale TA(AUS).

Mck.luck, J.↗
NASA NTRS1984

A note on the temporal behavior of bucket hydrologies

The use of a "canopy' bucket to more accurately represent evapotranspiration over land surfaces is explained. The temporal behavior of the traditional bucket model is compared with one that mimics the effects of interception loss. Results are presented in terms of the spectral response of the parameterization to a hypothetical white noise forcing.

Suarez, M. J.↗
NASA NTRS1984

Forecasts of the 500 mb height using a dynamically oriented statistical model

The forecast skill of a simple dynamically inspired statistical model of the Northern Hemisphere 500 mb height field is evaluated in spectral and physical space for a variety of forecast lead times (1-32 days) and predictand averaging times (1-32 days). The model includes viscous damping, wave propagation, climatology and implicit stochastic forcing. The largest model skill was found for forecasts of the zonal flow and the largest waves. In general, the largest forecast skills were also associated with the largest forecast error, there being a slight geographic phase shift of the skill with respect to the error. Model skills for climate (time-averaged) forecasts are greater when using instantaneous rather than time averages to forecast time averages. Analysis of model errors suggests areas for improvement in representing forcing terms and model physics. However, the model error fields are largely 'white noise' which suggests that global forecast skills substantially larger than those obtained here are unlikely to be achieved by more sophisticated models.

Roads, J. O.↗
NASA NTRS1984

Non-Gaussian approach for parametric random vibration of non-linear structures

The dynamic response of a nonlinear, single degree of freedom structural system subjected to a physically white noise parametric excitation is investigated. The Ito stochastic calculus is employed to derive a general differential equation for the moments of the response coordinates. The differential equations of moments of any order are found to be coupled with higher order moments. A non-Gaussian closure scheme is developed to truncate the moment equations up to fourth order. The statistical of the stationary response are computed numerically and compared with analytical solutions predicted by a Gaussian closure scheme and the stochastic averaging method. It is found that the computed results exhibit the jump phenomenon which is typical of the characteristics of deterministic nonlinear systems. In addition, the numerical algorithm leads to multiple solutions all of which give positive mean squares. However, two of these solutions are found to violate the properties of high order moments. One solution preserves the moments properties and demonstrates that the system achieves a stationary response.

Ibrahim, R. A.↗
NASA NTRS1985

First results of GPS time transfer to Australia

A Global Positioning System time transfer unit built by NBS under contract to JPL was installed at Tidbinbilla Deep Space Communications Complex of the NASA Deep Space Network in June 1983. It has been used to estimate the relationship to UTC(USNO MC) of the Tidbinbilla frequency and time system TID(FTS) based on a hydrogen maser, and thence to estimate the performance of the Australian free-running time scale UTC(AUS). Data from the first three months has been analyzed three ways: by two-hop common view using JPL as intermediary; by long-arc interpolation of measurements against space vehicle clocks; and by long-arc interpolation of GPS-Time results. Residuals from a single quadratic fit through three months of UTC(USNO MC) - TID (FTS) results were white noise with standard error 15 ns, and a flying clock measurement gave 70 ns agreement. A straight line fit through results UTC(USNO MC) - UTC (AUS) gave 90 ns standard error and 120 bns agreement. It is proposed to use the GPS measurements to steer UTS(AUS) to UTC(BIH), and to rename the existing time scale TA(AUS).

Luck, J. M.↗
NASA NTRS1984

Kalman filter modeling

The formulation of appropriate state-space models for Kalman filtering applications is studied. The so-called model is completely specified by four matrix parameters and the initial conditions of the recursive equations. Once these are determined, the die is cast, and the way in which the measurements are weighted is determined foreverafter. Thus, finding a model that fits the physical situation at hand is all important. Also, it is often the most difficult aspect of designing a Kalman filter. Formulation of discrete state models from the spectral density and ARMA random process descriptions is discussed. Finally, it is pointed out that many common processes encountered in applied work (such as band-limited white noise) simply do not lend themselves very well to Kalman filter modeling.

Brown, R. G.↗
NASA NTRS1984

Analog simulation of stochastic satellite response

A numerical study was performed on the effects of stochastic geometry and random environmental torques on the pointing accuracy of spinning and three-axis stabilized satellites. The Euler equations for the motions of satellites yielded the stochastic principal moments and a Fokker-Planck analog simulation was employed to model the response vector of a rigid satellite. White noise inputs were obtained from a random number generator. Attention was given to both fast and slow spin satellites. Responses grew with time in all cases. The growth was initially exponential and eventually reached stable values. In comparison with other theoretical techniques, the Fokker-Planck model detailed the most responses and showed that spin-stabilization is preferable for satellites with low inertial noise levels.

Huang, T. C.↗
NASA NTRS1986

Space infrared telescope pointing control system. Infrared telescope tracking in the presence of target motion

The use of charge-coupled-devices, or CCD's, has been documented by a number of sources as an effective means of providing a measurement of spacecraft attitude with respect to the stars. A method exists of defocussing and interpolation of the resulting shape of a star image over a small subsection of a large CCD array. This yields an increase in the accuracy of the device by better than an order of magnitude over the case when the star image is focussed upon a single CCD pixel. This research examines the effect that image motion has upon the overall precision of this star sensor when applied to an orbiting infrared observatory. While CCD's collect energy within the visible spectrum of light, the targets of scientific interest may well have no appreciable visible emissions. Image motion has the effect of smearing the image of the star in the direction of motion during a particular sampling interval. The presence of image motion is incorporated into a Kalman filter for the system, and it is shown that the addition of a gyro command term is adequate to compensate for the effect of image motion in the measurement. The updated gyro model is included in this analysis, but has natural frequencies faster than the projected star tracker sample rate for dim stars. The system state equations are reduced by modelling gyro drift as a white noise process. There exists a tradeoff in selected star tracker sample time between the CCD, which has improved noise characteristics as sample time increases, and the gyro, which will potentially drift further between long attitude updates. A sample time which minimizes pointing estimation error exists for the random drift gyro model as well as for a random walk gyro model.

Powell, J. D.↗
NASA NTRS1986

On realizations of least-squares estimation and Kalman filtering by systolic arrays

Least-squares (LS) estimation is a basic operation in many signal processing problems. Given y = Ax + v, where A is a m x n coefficient matrix, y is a m x 1 observation vector, and v is a m x 1 zero mean white noise vector, a simple least-squares solution is finding the estimated vector x which minimizes the norm of /Ax-y/. It is well known that for an ill-conditioned matrix A, solving least-squares problems by orthogonal triangular (QR) decomposition and back substitution has robust numerical properties under finite word length effect since 2-norm is preserved. Many fast algorithms have been proposed and applied to systolic arrays. Gentleman-Kung (1981) first presented the trianglular systolic array for a basic Givens reduction. McWhirter (1983) used this array structure to find the least-squares estimation errors. Then by geometric approach, several different systolic array realizations of the recursive least-squares estimation algorithms of Lee et al (1981) were derived by Kalson-Yao (1985). Basic QR decomposition algorithms are considered in this paper and it is found that under a one-row time updating situation, the Householder transformation degenerates to a simple Givens reduction. Next, an improved least-squares estimation algorithm is derived by considering a modified version of fast Givens reduction. From this approach, the basic relationship between Givens reduction and Modified-Gram-Schmidt transformation can easily be understood. This improved algorithm also has simpler computational and inter-cell connection complexities while compared with other known least-squares algorithms and is more realistic for systolic array implementation.

Chen, M. J.↗
NASA NTRS1986

Analytical comparison of transient and steady state visual evoked cortical potentials

To better describe the linear-dynamic properties of the human visual-cortical response system, transient and steady state Visual Evoked Response Potentials (VERP) were observed. The stimulus presentation device provided both the evoking stimulus (flickering or pulsing lights) and a video task display. The steady state stimulus was modulated by a complex, ten frequency, sum-of-sines, wave. The transient VERP was the time-locked average of the EEG to a series of narrow light pulses (pulse width of 10 msec). The Fourier transform of the averaged pulses had properties that approximate band limited white noise, i.e., a flat spectrum over the frequency region spanned by the 10 summed sines. The Fourier transform of both the steady state and the transient evoked potentials resulted in transfer that are equivalent and therefore comparable. To investigate the effects of task loading on evoked potentials, a grammatical reasoning task was provided. Results support the relevancy of continued application of a systems engineering approach for describing neurosensory functioning.

Junker, A. M.↗
NASA NTRS1984

The spatial structure of terrain - A process signal in satellite digital images

Pattern recognition procedures applied to Landsat imagery carry an implicit assumption that the digital data are independently distributed. That assumption is incorrect over virtually any terrain. Deviations from independence occur because slopes follow a systematic pattern of variation arising from the slope-forming processes. That pattern can be identified using the stochastic process methodology of Box and Jenkins.Angles of adjacent slopes are autocorrelated and the bidirectional reflectance function transfers these systematic slope changes to the sensor. Imagery becomes autocorrelated through this transfer. Autocorrelation in the imagery can be removed through direct calculation from a digital elevation model or by use of stochastic process methodology. The latter has the advantage that the residuals are white noise; and it is applicable in any area, even where a D.E.M. is unavailable. The stochastic process signal can be used to study terrain processes.

Craig, R. G.↗
NASA NTRS1986

Modeling, estimation and identification methods for static shape determination of flexible structures

This paper outlines methods for modeling, identification and estimation for static determination of flexible structures. The shape estimation schemes are based on structural models specified by (possibly interconnected) elliptic partial differential equations. The identification techniques provide approximate knowledge of parameters in elliptic systems. The techniques are based on the method of maximum-likelihood that finds parameter values such that the likelihood functional associated with the system model is maximized. The estimation methods are obtained by means of a function-space approach that seeks to obtain the conditional mean of the state given the data and a white noise characterization of model errors. The solutions are obtained in a batch-processing mode in which all the data is processed simultaneously. After methods for computing the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the related estimation error is conducted. In addition to outlining the above theoretical results, the paper presents typical flexible structure simulations illustrating performance of the shape determination methods.

Rodriguez, G.↗