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NASA NTRS1984

Boolean difference equations. I - Formulation and dynamic behavior

In many biological and physical systems, feedback mechanisms depend on a set of thresholds associated with the state variables. Each feedback has a characteristic time scale. It is suggested that delay-difference equations for Boolean-valued variables are an appropriate mathematical framework for such situations: the feedback thresholds result in the discrete, on-off character of the variables, and the interaction time scales of the feedbacks are expressed as delays. The initial-value problem for Boolean delay equations (B-Delta-Es) is formulated, and shown to have unique solutions for all times. Examples of periodic and aperiodic solutions are given. Aperiodic solutions have increasing complexity which depends on time t roughly as t to the l-1 power, l being the number of delays. Stability of solutions is defined, and some examples of stability analysis are given; additional stability questions are raised. The present formulation of (B-Delta-Es) is compared with related work and generalizations are suggested.

Dee, D.↗

NASA NTRS1985

Ignition of mixtures of SiH sub 4, CH sub 4, O sub 2, and Ar or N sub 2 behind reflected shock waves

Ignition delay times in mixtures of methane, silane, and oxygen diluted with argon and nitrogen were measured behind reflected shock waves generated in the chemical kinetic shock tube at Langley Research Center. The delay times were inferred from the rapid increase in pressure that occurs at ignition, and the ignition of methane was verified from the emission of infrared radiation from carbon dioxide. Pressures of 1.25 atm and temperatures from 1100 K to 1300 K were generated behind the reflected shocks; these levels are representative of those occurring within a supersonic Ramjet combustor. Expressions for the ignition delay time as a function of temperature were obtained from least squares curve fits to the data for overall equivalence ratios of 0.7 and 1.0. The ignition delay times with argon as the diluent were longer than those with nitrogen as the diluent. The infrared wavelength observations at 4.38 microns for carbon dioxide indicated that silane and methane ignited simultaneously (i.e., within the time resolution of the measurement). A combined chemical kinetic mechanism for mixtures of silane, methane, oxygen, and argon or nitrogen was assembled from one mechanism that accurately predicted the ignition of methane and a second mechanism that accurately predicted silane hydrogen ignition. Comparisons between this combined mechanism and experiment indicated that additional reactions, possibly between silyl and methyl fragments, are needed to develop a good silane methane mechanism.

Mclain, A. G.↗

NASA NTRS1984

Sidelobe reduction of Barker codes, part 7.1C

Barker codes can be realized as simple digital preprocessors, or with the use of a delay line, can be realized as an analogue device. Assuming the process observed has an autocorrelation time that is long compared to the code length, a gain in signal to noise, G = N where N is the number of elements in the code, may be realized. Typically Barker codes are implemented by shifting the phase of the transmitted signal by 0 or 180 degrees according to the code pattern. A typical detection scheme is shown where the output of the radar receiver is delayed by an analogue delay line or a shift register. The signal in each element of the delay line or shift register is continuously multiplied by the code and all elements are summed. A principal disadvantage was the sidelobe response. In the case of MST or ST radar echoes where there is a dynamic range as large as 60 dB, these unwanted sidelobes cause an increase in the apparent width of atmospheric layers, or some narrow layer to appear at several altitudes. The sidelobes of a Barker code may be reduced by tapering the response of the decoder. Optimum tapers, are shown. It is found that the sidelobe response is greatly reduced with very little loss in G.

Green, J. L.↗

NASA NTRS1984

Pilot differences and motion cuing effects on simulated helicopter hover

The effects that cues of aircraft motion, delays in visual scene, and movement of a ship model have on pilots' ability to hover a simulated helicopter near a destroyer-class ship were examined. Twelve pilots were tested in a within-subject factorial combination of fixed-base, moving-base, and G-seat conditions in which delays of 66 or 128 ms existed in the simulator's visual display and the pilots had to hover near a moving or stationary ship. Best control performance was seen under the moving-base conditions, whereas poorest control was associated with the fixed-base simulation. An intermediate level of performance was produced by the G-seat. In addition, visual delay affected control of the roll axis of the simulation, and interactions between pilots and motion cuing and visual delay were seen. Movement of the ship model had little effect.

Ricard, G. L.↗

NASA NTRS1985

Geodesy by radio interferometry - Effects of atmospheric modeling errors on estimates of baseline length

Analysis of very long baseline interferometry data indicates that systematic errors in prior estimates of baseline length, of order 5 cm for approximately 8000-km baselines, were due primarily to mismodeling of the electrical path length of the troposphere and mesosphere ('atmospheric delay'). Here observational evidence for the existence of such errors in the previously used models for the atmospheric delay is discussed, and a new 'mapping' function for the elevation angle dependence of this delay is developed. The delay predicted by this new mapping function differs from ray trace results by less than approximately 5 mm, at all elevations down to 5 deg elevation, and introduces errors into the estimates of baseline length of less than about 1 cm, for the multistation intercontinental experiment analyzed here.

Davis, J. L.↗

NASA NTRS1986

Atmospheric contributions to the column variance in direct-detection dial

One of the most important parameters of a Differential Absorption Lidar (DIAL) system is the delay time between the on and off resonant pulses. It is important that this delay time is sufficiently small to ensure that the atmosphere is effectively frozen between the pulses. Therefore, most Dial systems were designed with two lasers firing alternately less than 1 msec apart. Despite the importance of this parameter in the design of DIAL systems and its contribution to the overall error of a column measurement, very little is known about the size of the error for the case of a direct-detection system using atmospheric backscatter. The ultraviolet DIAL system uses two independent YAG/dye lasers and is therefore suitable for measuring the effects of different pulse delays on the variance of column measurements for a variety of atmospheric conditions. A set of DIAL returns were acquired with the two lasers tuned to the same wavelength and with a range of pulse delay times between 250 microseconds and several minutes. This data set was recorded in full on a computer and was used both to test different averaging techniques and also to evaluate atmospheric contributions to DIAL columns.

Milton, M. J. T.↗

NASA NTRS1986

A synchronization technique for optical PPM signals

A technique for maintaining synchronization between optical PPM (pulse-position modulation) pulses and a receiver clock by means of a delay-tracking loop is described and analyzed. The tracking loop is driven by a doubly stochastic Poisson process that contains information about the location of the desired slot boundaries. The slot boundaries are subject to slowly varying random delays that are ultimately tracked by the loop. The concept of fractional rms delay error is introduced to quantify the effects of signal and background induced shot noise on the performance of the delay-tracking loop.

Vilnrotter, V. A.↗

NASA NTRS1987

The effect of the dynamic wet troposphere on radio interferometric measurements

A statistical model of water vapor fluctuations is used to describe the effect of the dynamic wet troposphere on radio interferometric measurements. It is assumed that the spatial structure of refractivity is approximated by Kolmogorov turbulence theory, and that the temporal fluctuations are caused by spatial patterns moved over a site by the wind, and these assumptions are examined for the VLBI delay and delay rate observables. The results suggest that the delay rate measurement error is usually dominated by water vapor fluctuations, and water vapor induced VLBI parameter errors and correlations are determined as a function of the delay observable errors. A method is proposed for including the water vapor fluctuations in the parameter estimation method to obtain improved parameter estimates and parameter covariances.

Treuhaft, R. N.↗

NASA NTRS1986

A synchronization technique for optical PPM signals

Vilnrotter, V. A.↗

NASA NTRS1987

Time-dependent approximation schemes for some problems of parameter estimation in distributed systems

A parameter estimation method that can be used to estimate functional parameters in delay differential equations and moving boundary problems is discussed. In either problem, the original model equation (which is infinite-dimensional) is approximated by a system of ordinary differential equations that can be solved numerically in an efficient way. The approximation scheme is based on time-dependent spline elements. For the delay equation with time-varying delay, convergence results are presented that indicate the estimates obtained using the approximating system. Numerical test examples converge in some sense to a best-fit parameter for the original system are included by means of which time-varying and state-dependent delays and a time-varying diffusion coefficient in a one-phase, one-dimensional Stefan problem are estimated.

Murphy, K. A.↗

NASA NTRS1988

Phase connection for geodesy - Results from a 245-km baseline

In an effort to greatly improve the measurement precision of VLBI observables used to determine geodetic baselines, the potential of utilizing fringe phase has been investigated. The 245-km baseline between Mojave and Owens Valley in CA has been most thoroughly studied for this purpose. In trying several different experimental designs, it appears that source scheduling is not the critical factor in determining when phase connection can be established. Normally, instrumental instabilities are also not limiting (although nominal functioning of the instrumentation is essential). The most serious factor in limiting opportunities for phase connection seems to be atmospheric variability. However, when the observation SNR is made large (greater than 50) to give very precise group delays (and hence enhance the chance of resolving phase ambiguities), the improvement in baseline uncertainty obtained using phase delays is only marginal compared with the corresponding group delay solution. For this case, the baseline error budget is dominated by stochastic variations in clock and atmospheric delay contributions rather than by observation noise.

Ray, J. R.↗

NASA NTRS1988

Effects of source structure on astrometry and geodesy

VLBI hybrid maps of a number of radio sources have been used to make calculations of the effects of source structure on group delay and phase delay for baselines of different lengths. The effects on the two types of delay are of comparable magnitude and have a slightly stronger than linear dependence on baseline length. For sources selected to have only modest structure, the rms delay error caused by structure at 8.4 GHz is on the order of 30 to 50 picoseconds for intercontinental baselines.

Ulvestad, James S.↗

NASA NTRS1989

Long period pseudo random number sequence generator

A circuit for generating a sequence of pseudo random numbers, (A sub K). There is an exponentiator in GF(2 sup m) for the normal basis representation of elements in a finite field GF(2 sup m) each represented by m binary digits and having two inputs and an output from which the sequence (A sub K). Of pseudo random numbers is taken. One of the two inputs is connected to receive the outputs (E sub K) of maximal length shift register of n stages. There is a switch having a pair of inputs and an output. The switch outputs is connected to the other of the two inputs of the exponentiator. One of the switch inputs is connected for initially receiving a primitive element (A sub O) in GF(2 sup m). Finally, there is a delay circuit having an input and an output. The delay circuit output is connected to the other of the switch inputs and the delay circuit input is connected to the output of the exponentiator. Whereby after the exponentiator initially receives the primitive element (A sub O) in GF(2 sup m) through the switch, the switch can be switched to cause the exponentiator to receive as its input a delayed output A(K-1) from the exponentiator thereby generating (A sub K) continuously at the output of the exponentiator. The exponentiator in GF(2 sup m) is novel and comprises a cyclic-shift circuit; a Massey-Omura multiplier; and, a control logic circuit all operably connected together to perform the function U(sub i) = 92(sup i) (for n(sub i) = 1 or 1 (for n(subi) = 0).

Wang, Charles C.↗

NASA NTRS1990

Goldstone intracomplex connected element interferometry

Interferometric observations of the radio source pair 3C 84 and OE 400 were made on the 21 km baseline between Deep Space Station (DSS) 13 and DSS 15 to explore the angular navigation potential of intracomplex connected element interferometry (CEI). The differential phase-delay observable formed from pairs of 3 minute scans exhibited a precision of 1 psec, while the actual scatter of the phase-delay residuals for eleven scans over the 90 minute observing session was about 10 psec, consistent with the expected few millimeter fluctuations in the wet tropospheric path delay. Fitting for the position of OE 400 relative to 3C 84 yielded an error ellipse with a semi-minor axis of 60 nrad. Given the short data arc in this experiment, the orthogonal direction in the plane of the sky is not well determined; however, a second baseline or a data arc spanning a larger fraction of the source mutual visibility window could provide simultaneous determination of both right ascension and declination. Examination of the phase-delay residuals supports the accuracy of the cycle ambiguity resolution. However, reliable phase ambiguity resolution will pose the most significant challenge to routine use of CEI for spacecraft tracking, particularly when the a priori spacecraft source position is not well known. Several approaches for ambiguity resolution are briefly outlined.

Edwards, C. D.↗

NASA NTRS1990

Radio-source structure in astrometric and geodetic very long baseline interferometry

An algorithm to calculate source structure corrections for bandwidth synthesis delays and delay rates is used to refer the position of extragalacitc radio sources to a specific feature of each source's morphology. The delay and delay rate are obtained from VBLI observations. The algorithm and its theoretical basis are described, and simulations for a simple two-component source are discussed. VLBI data for the complex radio source NRAO 140 are analyzed. For this source, structure corrections are calculated with maps from three different VLBI imaging techniques: the hybrid-CLEAN algorithm, the maximum entropy method, and model fitting. The calculated structure corrections are compared with brightness distributions to the actual data. The results are used to map NRAO 140. It is found that the CLEAN map produces the most accurate structure corrections.

Charlot, P.↗

NASA NTRS1990

The relative timing of microwaves and X-rays from solar flares

The delay of microwaves relative to hard X-rays from solar flares is investigated. For short-time scale delays, it was found that for reasonable thick-target model parameters and for injected electron distributions which are separable in time, energy, pitch angle, and position, the observed delay cannot be explained by magnetic trapping of electrons in the corona. It can be accounted for if higher energy microwave producing electrons are accelerated later than lower energy hard X-ray producing electrons. For larger time-scale delays, it is found that the flux during the rising phase of the flares can be explained well in terms of the thick-target model, but during the decay phase this model predicts too little microwave flux. A number of possibilities for this excess microwave flux are explored including spectral hardening, magnetic trapping, and thermal synchrotron and free-free emission.

Lu, Edward T.↗

NASA NTRS1990

Interpreting the handling qualities of aircraft with stability and control augmentation

The general process of designing an aircraft for good flying qualities is first discussed. Lessons learned are pointed out, with piloted evaluation emerging as a crucial element. Two sources of rating variability in performing these evaluations are then discussed. First, the finite endpoints of the Cooper-Harper scale do not bias parametric statistical analyses unduly. Second, the wording of the scale does introduce some scatter. Phase lags generated by augmentation systems, as represented by equivalent time delays, often cause poor flying qualities. An analysis is introduced which allows a designer to relate any level of time delay to a probability of loss of aircraft control. This view of time delays should, it is hoped, allow better visibility of the time delays in the design process.

Hodgkinson, J.↗

NASA NTRS1990

Digital carrier demodulator employing components working beyond normal limits

In a digital device, having an input comprised of a digital sample stream at a frequency F, a method is disclosed for employing a component designed to work at a frequency less than F. The method, in general, is comprised of the following steps: dividing the digital sample stream into odd and even digital samples streams each at a frequency of F/2; passing one of the digital sample streams through the component designed to work at a frequency less than F where the component responds only to the odd or even digital samples in one of the digital sample streams; delaying the other digital sample streams for the time it takes the digital sample stream to pass through the component; and adding the one digital sample stream after passing through the component with the other delayed digital sample streams. In the specific example, the component is a finite impulse response filter of the order ((N + 1)/2) and the delaying step comprised passing the other digital sample streams through a shift register for a time (in sampling periods) of ((N + 1)/2) + r, where r is a pipline delay through the finite impulse response filter.

Hurd, William J.↗