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NASA NTRS1993

The limit of frequency estimation

In phase and frequency measurements, the measured phase and frequency are not the true phase and frequency but the ones which are disturbed by noises, due to the effects of the noise processes. The effects of three noise processes, i.e., White PM, White FM, and Random Walk FM, on the estimations of phase and frequency is discussed. It is indicated that the properties of these two estimations are very different. In phase estimation, the error can be reduced by properly selecting suitable smoothing length NT and smaple interval T. But in frequency estimation, the error cannot be reduced arbitrarily by means of improving estimator or measurement equipment. The precision of frequency is limited by the intrinsic noises in the clock.

Guo, Wei↗
NASA NTRS1993

Investigation for improving Global Positioning System (GPS) orbits using a discrete sequential estimator and stochastic models of selected physical processes

GEODYNII is a conventional batch least-squares differential corrector computer program with deterministic models of the physical environment. Conventional algorithms were used to process differenced phase and pseudorange data to determine eight-day Global Positioning system (GPS) orbits with several meter accuracy. However, random physical processes drive the errors whose magnitudes prevent improving the GPS orbit accuracy. To improve the orbit accuracy, these random processes should be modeled stochastically. The conventional batch least-squares algorithm cannot accommodate stochastic models, only a stochastic estimation algorithm is suitable, such as a sequential filter/smoother. Also, GEODYNII cannot currently model the correlation among data values. Differenced pseudorange, and especially differenced phase, are precise data types that can be used to improve the GPS orbit precision. To overcome these limitations and improve the accuracy of GPS orbits computed using GEODYNII, we proposed to develop a sequential stochastic filter/smoother processor by using GEODYNII as a type of trajectory preprocessor. Our proposed processor is now completed. It contains a correlated double difference range processing capability, first order Gauss Markov models for the solar radiation pressure scale coefficient and y-bias acceleration, and a random walk model for the tropospheric refraction correction. The development approach was to interface the standard GEODYNII output files (measurement partials and variationals) with software modules containing the stochastic estimator, the stochastic models, and a double differenced phase range processing routine. Thus, no modifications to the original GEODYNII software were required. A schematic of the development is shown. The observational data are edited in the preprocessor and the data are passed to GEODYNII as one of its standard data types. A reference orbit is determined using GEODYNII as a batch least-squares processor and the GEODYNII measurement partial (FTN90) and variational (FTN80, V-matrix) files are generated. These two files along with a control statement file and a satellite identification and mass file are passed to the filter/smoother to estimate time-varying parameter states at each epoch, improved satellite initial elements, and improved estimates of constant parameters.

Goad, Clyde C.↗
NASA NTRS1991

Basic research in solar physics

This grant, dating back more than 20 years has supported a variety of investigations of the chromospheres and coronae of the Sun and related cool stars by the Principal Investigator, his postdocs and graduate students, and colleagues at other institutions. This work involved studies of radiative transfer and spectral line formation theory, and the application of these techniques to the analysis of spectra obtained from space and ground-based observatories in the optical, ultraviolet, x-ray and radio portions of the spectrum. Space observations have included the analysis of spectra from OSO-7, Skylab, SMM, and the HRTS rocket experiments. Recent work has concentrated on the interaction of magnetic fields, plasma and radiation in the outer atmospheres of the Sun and other magnetically active stars with different fundamental parameters. Our study of phenomena common to the Sun and stars, the 'solar-stellar connection', can elucidate the fundamental physics, because spatially-resolved observations of the Sun provide us with the 'groundtruth,' while interpretation of stellar data permit us to isolate those parameters critical to stellar activity. Recently, we have studied the differences in physical properties between solar regions of high magnetic flux density and the surrounding plasma. High-resolution CN and CO spectroheliograms have been used to model the thermal inhomogeneities driven by unstable CO cooling, and we have analyzed spatially resolved UV spectra from HRTS to model the thermal structure and energy balance of small-scale structures. The study of nonlinear relations between atmospheric radiative losses and the photospheric magnetic flux density has been continued. We have also proposed a new model for the decay of plages by random walk diffusion of magnetic flux. Our analysis of phenomena common to the Sun and stars included the application of available spectroscopic diagnostics, establishing evidence that the atmospheres of the least active stars are heated at a 'basal' rate that is also found in the centers of solar supergranules, and using the Doppler-imaging technique to measure the position, size, and brightness of stellar active regions. We are computing multi-component models for solar and stellar atmospheres, and models for coronal loops and for the transition-region down flows. The study of solar and stellar flares permits us to assess the role of turbulent energy transport, to pinpoint the mechanism behind Type I radio bursts, to determine whether plasma radiation or cyclotron maser is responsible for microwave flares on M dwarfs, and to extend our knowledge of the basic physics pertinent to cyclotron-maser processes operating on the Sun.

Linsky, Jeffrey L.↗
NASA NTRS1994

Numerical and experimental analyses of the radiant heat flux produced by quartz heating systems

A method is developed for predicting the radiant heat flux distribution produced by tungsten filament, tubular fused-quartz envelope heating systems with reflectors. The method is an application of Monte Carlo simulation, which takes the form of a random walk or ray tracing scheme. The method is applied to four systems of increasing complexity, including a single lamp without a reflector, a single lamp with a Hat reflector, a single lamp with a parabolic reflector, and up to six lamps in a six-lamp contoured-reflector heating unit. The application of the Monte Carlo method to the simulation of the thermal radiation generated by these systems is discussed. The procedures for numerical implementation are also presented. Experiments were conducted to study these quartz heating systems and to acquire measurements of the corresponding empirical heat flux distributions for correlation with analysis. The experiments were conducted such that several complicating factors could be isolated and studied sequentially. Comparisons of the experimental results with analysis are presented and discussed. Good agreement between the experimental and simulated results was obtained in all cases. This study shows that this method can be used to analyze very complicated quartz heating systems and can account for factors such as spectral properties, specular reflection from curved surfaces, source enhancement due to reflectors and/or adjacent sources, and interaction with a participating medium in a straightforward manner.

Turner, Travis L.↗
NASA NTRS1994

Accuracy metrics for judging time scale algorithms

Time scales have been constructed in different ways to meet the many demands placed upon them for time accuracy, frequency accuracy, long-term stability, and robustness. Usually, no single time scale is optimum for all purposes. In the context of the impending availability of high-accuracy intermittently-operated cesium fountains, we reconsider the question of evaluating the accuracy of time scales which use an algorithm to span interruptions of the primary standard. We consider a broad class of calibration algorithms that can be evaluated and compared quantitatively for their accuracy in the presence of frequency drift and a full noise model (a mixture of white PM, flicker PM, white FM, flicker FM, and random walk FM noise). We present the analytic techniques for computing the standard uncertainty for the full noise model and this class of calibration algorithms. The simplest algorithm is evaluated to find the average-frequency uncertainty arising from the noise of the cesium fountain's local oscillator and from the noise of a hydrogen maser transfer-standard. This algorithm and known noise sources are shown to permit interlaboratory frequency transfer with a standard uncertainty of less than 10(exp -15) for periods of 30-100 days.

Douglas, R. J.↗
NASA NTRS1994

Hydrogen masers and cesium fountains at NRC

The NRC masers H-3 and H-4 have been operating since June 1993 with cavity servo control. These low-flux active H masers are showing stabilities of about 10(exp -15) from 1 hour to several days. Stability results are presented, and the current and planned uses of the masers are discussed. A cesium fountain primary frequency standard project has been started at NRC. Trapping and launching experiments with the goal of 7 m/s launches are beginning. We discuss our plans for a local oscillator and servo that exploit the pulsed aspect of cesium fountain standards, and meet the challenge of 10(exp -14) tau(exp -1/2) stability without requiring masers. At best, we expect to run this frequency standard initially for periods of hours each working day rather than continuously for years, and so frequency transfer to outside laboratories has been carefully considered. We conclude that masers (or other even better secondary clocks) are required to exploit this potential accuracy of the cesium fountain. We present and discuss our conclusion that it is feasible to transfer frequency in this way with a transfer-induced uncertainty of less than 10(exp -15), even in the presence of maser frequency drift and random walk noise.

Boulanger, J.-S.↗
NASA NTRS1993

A petabyte size electronic library using the N-Gram memory engine

A model library containing petabytes of data is proposed by Triada, Ltd., Ann Arbor, Michigan. The library uses the newly patented N-Gram Memory Engine (Neurex), for storage, compression, and retrieval. Neurex splits data into two parts: a hierarchical network of associative memories that store 'information' from data and a permutation operator that preserves sequence. Neurex is expected to offer four advantages in mass storage systems. Neurex representations are dense, fully reversible, hence less expensive to store. Neurex becomes exponentially more stable with increasing data flow; thus its contents and the inverting algorithm may be mass produced for low cost distribution. Only a small permutation operator would be recalled from the library to recover data. Neurex may be enhanced to recall patterns using a partial pattern. Neurex nodes are measures of their pattern. Researchers might use nodes in statistical models to avoid costly sorting and counting procedures. Neurex subsumes a theory of learning and memory that the author believes extends information theory. Its first axiom is a symmetry principle: learning creates memory and memory evidences learning. The theory treats an information store that evolves from a null state to stationarity. A Neurex extracts information data without a priori knowledge; i.e., unlike neural networks, neither feedback nor training is required. The model consists of an energetically conservative field of uniformly distributed events with variable spatial and temporal scale, and an observer walking randomly through this field. A bank of band limited transducers (an 'eye'), each transducer in a bank being tuned to a sub-band, outputs signals upon registering events. Output signals are 'observed' by another transducer bank (a mid-brain), except the band limit of the second bank is narrower than the band limit of the first bank. The banks are arrayed as n 'levels' or 'time domains, td.' The banks are the hierarchical network (a cortex) and transducers are (associative) memories. A model Neurex was built and studied. Data were 50 MB to 10 GB samples of text, data base, and images: black/white, grey scale, and high resolution in several spectral bands. Memories at td, S(m(sub td)), were plotted against outputs of memories at td-1. S(m(sub td)) was Boltzman distributed, and memory frequencies exhibited self-organized criticality (SOC); i.e., 'l/f(sup beta)' after long exposures to data. Whereas output signals from level n may be encoded with B(sub output) = O(-log(2)f(sup beta)) bits, and input data encoded with B(sub input) = O((S(td)/S(td-1))(sup n)), B(sup output)/B(sub input) is much less than 1 always, the Neurex determines a canonical code for data and it is a lossless data compressor. Further tests are underway to confirm these results with more data types and larger samples.

Bugajski, Joseph M.↗
NASA NTRS1992

Unsteady flow past an airfoil pitched at constant rate

The unsteady flow past a NACA 0012 airfoil that is undertaking a constant-rate pitching up motion is investigated experimentally by the PIDV technique in a water towing tank. The Reynolds number is 5000, based upon the airfoil's chord and the free-stream velocity. The airfoil is pitching impulsively from 0 to 30 deg. with a dimensionless pitch rate alpha of 0.131. Instantaneous velocity and associated vorticity data have been acquired over the entire flow field. The primary vortex dominates the flow behavior after it separates from the leading edge of the airfoil. Complete stall emerges after this vortex detaches from the airfoil and triggers the shedding of a counter-rotating vortex near the trailing edge. A parallel computational study using the discrete vortex, random walk approximation has also been conducted. In general, the computational results agree very well with the experiment.

Lourenco, L.↗
NASA NTRS1994

Investigation of Allan variance for determining noise spectral forms with application to microwave radiometry

An investigation of the Allan variance method as a possible means for characterizing fluctuations in radiometric noise diodes has been performed. The goal is to separate fluctuation components into white noise, flicker noise, and random-walk noise. The primary means is by discrete-time processing, and the study focused primarily on the digital processes involved. Noise satisfying the requirements was generated by direct convolution, fast Fourier transformation (FFT) processing in the time domain, and FFT processing in the frequency domain. Some of the numerous results obtained are presented along with the programs used in the study.

Stanley, William D.↗
NASA NTRS1995

Estimation of attitude sensor timetag biases

This paper presents an extended Kalman filter for estimating attitude sensor timing errors. Spacecraft attitude is determined by finding the mean rotation from a set of reference vectors in inertial space to the corresponding observed vectors in the body frame. Any timing errors in the observations can lead to attitude errors if either the spacecraft is rotating or the reference vectors themselves vary with time. The state vector here consists of the attitude quaternion, timetag biases, and, optionally, gyro drift rate biases. The filter models the timetags as random walk processes: their expectation values propagate as constants and white noise contributes to their covariance. Thus, this filter is applicable to cases where the true timing errors are constant or slowly varying. The observability of the state vector is studied first through an examination of the algebraic observability condition and then through several examples with simulated star tracker timing errors. The examples use both simulated and actual flight data from the Extreme Ultraviolet Explorer (EUVE). The flight data come from times when EUVE had a constant rotation rate, while the simulated data feature large angle attitude maneuvers. The tests include cases with timetag errors on one or two sensors, both constant and time-varying, and with and without gyro bias errors. Due to EUVE's sensor geometry, the observability of the state vector is severely limited when the spacecraft rotation rate is constant. In the absence of attitude maneuvers, the state elements are highly correlated, and the state estimate is unreliable. The estimates are particularly sensitive to filter mistuning in this case. The EUVE geometry, though, is a degenerate case having coplanar sensors and rotation vector. Observability is much improved and the filter performs well when the rate is either varying or noncoplanar with the sensors, as during a slew. Even with bad geometry and constant rates, if gyro biases are independently known, the timetag error for a single sensor can be accurately estimated as long as its boresight is not too close to the spacecraft rotation axis.

Sedlak, J.↗
NASA NTRS1995

A digital boxcar integrator for IMS spectra

When trying to detect or quantify a signal at or near the limit of detectability, it is invariably embeded in the noise. This statement is true for nearly all detectors of any physical phenomena and the limit of detectability, hopefully, occurs at very low signal-to-noise levels. This is particularly true of IMS (Ion Mobility Spectrometers) spectra due to the low vapor pressure of several chemical compounds of great interest and the small currents associated with the ionic detection process. Gated Integrators and Boxcar Integrators or Averagers are designed to recover fast, repetitive analog signals. In a typical application, a time 'Gate' or 'Window' is generated, characterized by a set delay from a trigger or gate pulse and a certain width. A Gated Integrator amplifies and integrates the signal that is present during the time the gate is open, ignoring noise and interference that may be present at other times. Boxcar Integration refers to the practice of averaging the output of the Gated Integrator over many sweeps of the detector. Since any signal present during the gate will add linearly, while noise will add in a 'random walk' fashion as the square root of the number of sweeps, averaging N sweeps will improve the 'Signal-to-Noise Ratio' by a factor of the square root of N.

Cohen, Martin J.↗
NASA NTRS1994

Charged-particle motion in multidimensional magnetic-field turbulence

We present a new analysis of the fundamental physics of charged-particle motion in a turbulent magnetic field using a numerical simulation. The magnetic field fluctuations are taken to be static and to have a power spectrum which is Kolmogorov. The charged particles are treated as test particles. It is shown that when the field turbulence is independent of one coordinate (i.e., k lies in a plane), the motion of these particles across the magnetic field is essentially zero, as required by theory. Consequently, the only motion across the average magnetic field direction that is allowed is that due to field-line random walk. On the other hand, when a fully three-dimensional realization of the turbulence is considered, the particles readily cross the field. Transport coefficients both along and across the ambient magnetic field are computed. This scheme provides a direct computation of the Fokker-Planck coefficients based on the motions of individual particles, and allows for comparison with analytic theory.

Giacalone, J.↗
NASA NTRS1993

A diffusion-limited aggregation model for the evolution of drainage networks

We propose a modified diffusion-limited aggregation (DLA) model for the evolution of fluvial drainage networks. Random walkers are introduced randomly on a grid, and each two-dimensional random walk proceeds until the walker finds a drainage network on which to accrete. This model for headward growth of drainage networks generates drainage patterns remarkably similar to actual drainages. The model also predicts statistical features which agree with actual networks, including the frequency-order (bifurcation) ratio (R(sub b) = 3.98) and the stream length-order (R(sub r) = 2.09). Using the definition of network fractal dimension D = log R(sub b)/log R(sub r), we find that our DLA model gives D = 1.87, near the observed range of D approximately equal to 1.80 - 1.85.

Masek, Jeffrey G.↗
NASA NTRS1994

The short-term prediction of universal time and length of day using atmospheric angular momentum

The ability to predict short-term variations in the Earth's rotation has gained importance in recent years owing to more precise spacecraft tracking requirements. Universal time (UT1), that component of the Earth's orientation corresponding to the rotation angle, can be measured by number of high-precision space geodetic techniques. A Kalman filter developed at the Jet Propulsion Laboratory (JPL) optimally combines these different data sets and generates a smoothed times series and a set of predictions for UT1, as well as for additional Earth orientation components. These UT1 predictions utilize an empirically derived random walk stochastic model for the length of the day (LOD) and require frequent and up-to-date measurements of either UT1 or LOD to keep errors from quickly accumulating. Recent studies have shown that LOD variations are correlated with changes in the Earth's axial atmospheric angular momentum (AAM) over timescales of several years down to as little as 8 days. AAM estimates and forecasts out to 10 days are routinely available from meteorological analysis centers; these data can supplement geodetic measurements to improve the short-term prediction of LOD and have therefore been incorporated as independent data types in the JPL Kalman filter. We find that AAM and, to a lesser extent, AAM forecast data are extremely helpful in generating accurate near-real-time estimates of UT1 and LOD and in improving short-term predictions of these quantities out to about 10 days.

Freedman, A. P.↗
NASA NTRS1995

A count probability cookbok: Spurious effects and the scaling model

We study the errors brought by finite volume effects and dilution effects on the practical determination of the count probability distribution function P(sub N)(n,l), which is the probability of having N objects in a cell of volume l cubed for a set of average number density n. Dilution effects are particularly revelant to the so-called sparse sampling strategy. This work is mainly done in the framework of the Bailan & Schaeffer scaling model, which assumes that the Q-body correlation functions obey the scaling relation Xi(sub Q)(lambda r(sub l),....lambda r(sub Q) = lambda(exp -(Q-1)gamma) Xi(sub Q)(r(sub 1),....r(sub Q)). We use three synthetic samples as references to perform our analysis: a fractal generated by a Rayleigh-Levy random walk with approximately 3 x 10(exp 4) objects, a sample dominated by a spherical power-law cluster with approximately 3 x 10(exp 4) objects and a cold dark matter (CDM) universe involving approximately 3 x 10(exp 5) matter particles.

Colombi, S.↗
NASA NTRS1994

On the effects of a weak magnetic field on turbulent transport

We discuss the effects of a weak large-scale magnetic field on turbulent transport. We show by means of a series of two-dimensional numerical experiments that turbulent diffusion can be effectively suppressed by a (large scale) magnetic field whose energy is small compared to equipartition. The suppression mechanism is associated with a subtle modification of the Lagrangian energy spectrum, and it does not require any substantial reduction of the turbulent amplitude. We exploit the relation between diffusion and random walking to emphasize that the effect of a large-scale magnetic field is to induce a long-term memory in the field of turbulence. The implications of the general case of three-dimensional transport are briefly discussed.

Cattaneo, F.↗
NASA NTRS1995

Solar wind eddies and the heliospheric current sheet

Ulysses has collected data between 1 and 5 AU during, and just following solar maximum, when the heliospheric current sheet (HCS) can be thought of as reaching its maximum tilt and being subject to the maximum amount of turbulence in the solar wind. The Ulysses solar wind plasma instrument measures the vector velocity and can be used to estimate the flow speed and direction in turbulent 'eddies' in the solar wind that are a fraction of an astronomical unit in size and last (have either a turnover or dynamical interaction time of) several hours to more than a day. Here, in a simple exercise, these solar wind eddies at the HCS are characterized using Ulysses data. This character is then used to define a model flow field with eddies that is imposed on an ideal HCS to estimate how the HCS will be deformed by the flow. This model inherently results in the complexity of the HCS increasing with heliocentric distance, but the result is a measure of the degree to which the observed change in complexity is a measure of the importance of solar wind flows in deforming the HCS. By comparison with randomly selected intervals not located on the HCS, it appears that eddies on the HCS are similar to those elsewhere at this time during the solar cycle, as is the resultant deformation of the interplanetary magnetic field (IMF). The IMF deformation is analogous to what is often termed the 'random walk' of interplanetary magnetic field lines.

Suess, S. T.↗
NASA NTRS1995

Large-scale magnetic variances near the South Solar Pole

We summarize recent Ulysses observations of the variances over large temporal scales in the interplanetary magnetic field components and their increase as Ulysses approached the South Solar Pole. A model of these fluctuations is shown to provide a very good fit to the observed amplitude and temporal variation of the fluctuations. In addition, the model predicts that the transport of cosmic rays in the heliosphere will be significantly altered by this level of fluctuations. In addition to altering the inward diffusion and drift access of cosmic rays over the solar poles, we find that the magnetic fluctuations also imply a large latitudinal diffusion, caused primarily by the associated field-line random walk.

Jokipii, J. R.↗