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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 NTRS1987

Inverse solution of Kepler's equation for hyperbolic orbits

An algorithm is presented for efficient inverse solution of Kepler's equation for hyperbolic orbits. It is shown that an expansion of Barker's equation into a bicubic polynomial provides a good approximation to obtain accurate starting values for rapid numerical solution of Kepler's equation. In the approximate equation a cubic in normalized elapsed flight time from pericenter is set equal to a cubic in a function S of eccentricity and true anomaly. The initial estimate of S to use in an iteration formula is obtained by evaluating the cubic in normalized flight time and finding in most cases the single real root of the other cubic. This initial estimate has an accuracy corresponding to values of true anomaly in error by less than 0.5 degrees generally.

Boltz, Frederick W.↗

NASA NTRS1988

A mathematical theory of learning control for linear discrete multivariable systems

When tracking control systems are used in repetitive operations such as robots in various manufacturing processes, the controller will make the same errors repeatedly. Here consideration is given to learning controllers that look at the tracking errors in each repetition of the process and adjust the control to decrease these errors in the next repetition. A general formalism is developed for learning control of discrete-time (time-varying or time-invariant) linear multivariable systems. Methods of specifying a desired trajectory (such that the trajectory can actually be performed by the discrete system) are discussed, and learning controllers are developed. Stability criteria are obtained which are relatively easy to use to insure convergence of the learning process, and proper gain settings are discussed in light of measurement noise and system uncertainties.

Phan, Minh↗

NASA NTRS1989

On the equivalence of Gaussian elimination and Gauss-Jordan reduction in solving linear equations

A novel general approach to round-off error analysis using the error complexity concepts is described. This is applied to the analysis of the Gaussian Elimination and Gauss-Jordan scheme for solving linear equations. The results show that the two algorithms are equivalent in terms of our error complexity measures. Thus the inherently parallel Gauss-Jordan scheme can be implemented with confidence if parallel computers are available.

Tsao, Nai-Kuan↗

NASA NTRS1989

Bandwidth efficient coding for fading channels - Code construction and performance analysis

The authors apply a general method of bounding the event error probability of trellis-coded modulation schemes to fading channels and use the effective length and the minimum-squared-product distance to replace the minimum-free-squared-Euclidean distance as code design parameters for Rayleigh and Rician fading channels with a substantial multipath component. They present 8-PSK trellis codes specifically constructed for fading channels that outperform equivalent codes designed for the additive white Gaussian noise channel when v is greater than or equal to 5. For quasiregular trellis codes there exists an efficient algorithm for evaluating event error probability, and numerical results on Pe which demonstrate the importance of the effective length as a code design parameter for fading channels with or without side information have been obtained. This is consistent with the case for binary signaling, where the Hamming distance remains the best code design parameter for fading channels. The authors show that the use of Reed-Solomon block codes with expanded signal sets becomes interesting only for large values of E(s)/N(0), where they begin to outperform trellis codes.

Schlegel, Christian↗

NASA NTRS1991

Precise automatic differential stellar photometry

The factors limiting the precision of differential stellar photometry are reviewed. Errors due to variable atmospheric extinction can be reduced to below 0.001 mag at good sites by utilizing the speed of robotic telescopes. Existing photometric systems produce aliasing errors, which are several millimagnitudes in general but may be reduced to about a millimagnitude in special circumstances. Conventional differential photometry neglects several other important effects, which are discussed in detail. If all of these are properly handled, it appears possible to do differential photometry of variable stars with an overall precision of 0.001 mag with ground based robotic telescopes.

Young, Andrew T.↗

NASA NTRS1990

Wavefront control of large optical systems

Several levels of wavefront control are necessary for the optimum performance of very large telescopes, especially segmented ones like the Large Deployable Reflector. In general, the major contributors to wavefront error are the segments of the large primary mirror. Wavefront control at the largest optical surface may not be the optimum choice because of the mass and inaccessibility of the elements of this surface that require upgrading. The concept of two-stage optics was developed to permit a poor wavefront from the large optics to be upgraded by means of a wavefront corrector at a small exit pupil of the system.

Meinel, Aden B.↗

NASA NTRS1992

Evaluation of force-torque displays for use with space station telerobotic activities

Recent experiments which addressed Space Station remote manipulation tasks found that tactile force feedback (reflecting forces and torques encountered at the end-effector through the manipulator hand controller) does not improve performance significantly. Subjective response from astronaut and non-astronaut test subjects indicated that force information, provided visually, could be useful. No research exists which specifically investigates methods of presenting force-torque information visually. This experiment was designed to evaluate seven different visual force-torque displays which were found in an informal telephone survey. The displays were prototyped in the HyperCard programming environment. In a within-subjects experiment, 14 subjects nullified forces and torques presented statically, using response buttons located at the bottom of the screen. Dependent measures included questionnaire data, errors, and response time. Subjective data generally demonstrate that subjects rated variations of pseudo-perspective displays consistently better than bar graph and digital displays. Subjects commented that the bar graph and digital displays could be used, but were not compatible with using hand controllers. Quantitative data show similar trends to the subjective data, except that the bar graph and digital displays both provided good performance, perhaps do to the mapping of response buttons to display elements. Results indicate that for this set of displays, the pseudo-perspective displays generally represent a more intuitive format for presenting force-torque information.

Hendrich, Robert C.↗

NASA NTRS1992

Separation distance and static transmission error of involute spur gears

The effects of separation distance and deflection of gear teeth on the static transmission error of involute spur gears are investigated. In this paper, only low-contact-ratio gears with true involute profile are studied. Gear ratio and tooth addendum are varied to examine their effects on the separation distance and static transmission error. Results obtained from the investigation shows that the contact ratio and static transmission error are affected significantly if considering the separation distance. In general, the magnitude of contact ratio has been increased and the variation of static transmission error has been smoothed. The most significant change occurs for a gear pair with a theoretical contact ratio close to 1.95.

Tse, David K.↗

NASA NTRS1992

Diffraction analysis and evaluation of several focus- and track-error detection schemes for magneto-optical disk systems

A commonly used tracking method on pre-grooved magneto-optical (MO) media is the push-pull technique, and the astigmatic method is a popular focus-error detection approach. These two methods are analyzed using DIFFRACT, a general-purpose scalar diffraction modeling program, to observe the effects on the error signals due to focusing lens misalignment, Seidel aberrations, and optical crosstalk (feedthrough) between the focusing and tracking servos. Using the results of the astigmatic/push-pull system as a basis for comparison, a novel focus/track-error detection technique that utilizes a ring toric lens is evaluated as well as the obscuration method (focus error detection only).

Bernacki, Bruce E.↗

NASA NTRS1992

Linear regression in astronomy. II

A wide variety of least-squares linear regression procedures used in observational astronomy, particularly investigations of the cosmic distance scale, are presented and discussed. The classes of linear models considered are (1) unweighted regression lines, with bootstrap and jackknife resampling; (2) regression solutions when measurement error, in one or both variables, dominates the scatter; (3) methods to apply a calibration line to new data; (4) truncated regression models, which apply to flux-limited data sets; and (5) censored regression models, which apply when nondetections are present. For the calibration problem we develop two new procedures: a formula for the intercept offset between two parallel data sets, which propagates slope errors from one regression to the other; and a generalization of the Working-Hotelling confidence bands to nonstandard least-squares lines. They can provide improved error analysis for Faber-Jackson, Tully-Fisher, and similar cosmic distance scale relations.

Feigelson, Eric D.↗

NASA NTRS1996

Elevation correction factor for absolute pressure measurements

With the arrival of highly accurate multi-port pressure measurement systems, conditions that previously did not affect overall system accuracy must now be scrutinized closely. Errors caused by elevation differences between pressure sensing elements and model pressure taps can be quantified and corrected. With multi-port pressure measurement systems, the sensing elements are connected to pressure taps that may be many feet away. The measurement system may be at a different elevation than the pressure taps due to laboratory space or test article constraints. This difference produces a pressure gradient that is inversely proportional to height within the interface tube. The pressure at the bottom of the tube will be higher than the pressure at the top due to the weight of the tube's column of air. Tubes with higher pressures will exhibit larger absolute errors due to the higher air density. The above effect is well documented but has generally been taken into account with large elevations only. With error analysis techniques, the loss in accuracy from elevation can be easily quantified. Correction factors can be applied to maintain the high accuracies of new pressure measurement systems.

Panek, Joseph W.↗

NASA NTRS2000

Verification and Validation of Autonomy Software at NASA

Autonomous software holds the promise of new operation possibilities, easier design and development, and lower operating costs. However, as those system close control loops and arbitrate resources on-board with specialized reasoning, the range of possible situations becomes very large and uncontrollable from the outside, making conventional scenario-based testing very inefficient. Analytic verification and validation (V&V) techniques, and model checking in particular, can provide significant help for designing autonomous systems in a more efficient and reliable manner, by providing a better coverage and allowing early error detection. This article discusses the general issue of V&V of autonomy software, with an emphasis towards model-based autonomy, model-checking techniques, and concrete experiments at NASA.

Pecheur, Charles↗

NASA NTRS2000

Verification and Validation of Autonomy Software at NASA

Autonomous software holds the promise of new operation possibilities, easier design and development and lower operating costs. However, as those system close control loops and arbitrate resources on board with specialized reasoning, the range of possible situations becomes very large and uncontrollable from the outside, making conventional scenario-based testing very inefficient. Analytic verification and validation (V&V) techniques, and model checking in particular, can provide significant help for designing autonomous systems in a more efficient and reliable manner, by providing a better coverage and allowing early error detection. This article discusses the general issue of V&V of autonomy software, with an emphasis towards model-based autonomy, model-checking techniques and concrete experiments at NASA.

Pecheur, Charles↗

NASA NTRS2002

Equivalent Linearization Analysis of Geometrically Nonlinear Random Vibrations Using Commercial Finite Element Codes

Two new equivalent linearization implementations for geometrically nonlinear random vibrations are presented. Both implementations are based upon a novel approach for evaluating the nonlinear stiffness within commercial finite element codes and are suitable for use with any finite element code having geometrically nonlinear static analysis capabilities. The formulation includes a traditional force-error minimization approach and a relatively new version of a potential energy-error minimization approach, which has been generalized for multiple degree-of-freedom systems. Results for a simply supported plate under random acoustic excitation are presented and comparisons of the displacement root-mean-square values and power spectral densities are made with results from a nonlinear time domain numerical simulation.

Rizzi, Stephen A.↗

NASA NTRS2013

RF Reference Switch for Spaceflight Radiometer Calibration

The goal of this technology is to provide improved calibration and measurement sensitivity to the Soil Moisture Active Passive Mission (SMAP) radiometer. While RF switches have been used in the past to calibrate microwave radiometers, the switch used on SMAP employs several techniques uniquely tailored to the instrument requirements and passive remote-sensing in general to improve radiometer performance. Measurement error and sensitivity are improved by employing techniques to reduce thermal gradients within the device, reduce insertion loss during antenna observations, increase insertion loss temporal stability, and increase rejection of radar and RFI (radio-frequency interference) signals during calibration. The two legs of the single-pole double-throw reference switch employ three PIN diodes per leg in a parallel-shunt configuration to minimize insertion loss and increase stability while exceeding rejection requirements at 1,413 MHz. The high-speed packaged diodes are selected to minimize junction capacitance and resistance while ensuring the parallel devices have very similar I-V curves. Switch rejection is improved by adding high-impedance quarter-wave tapers before and after the diodes, along with replacing the ground via of one diode per leg with an open circuit stub. Errors due to thermal gradients in the switch are reduced by embedding the 50-ohm reference load within the switch, along with using a 0.25-in. (approximately equal to 0.6-cm) aluminum prebacked substrate. Previous spaceflight microwave radiometers did not embed the reference load and thermocouple directly within the calibration switch. In doing so, the SMAP switch reduces error caused by thermal gradients between the load and switch. Thermal issues are further reduced by moving the custom, highspeed regulated driver circuit to a physically separate PWB (printed wiring board). Regarding RF performance, previous spaceflight reference switches have not employed high-impedance tapers to improve rejection. The use of open-circuit stubs instead of a via to provide an improved RF short is unique to this design. The stubs are easily tunable to provide high rejection at specific frequencies while maintaining very low insertion loss in-band.

Knuble, Joseph↗

NASA NTRS2020

Underlying Fundamentals of Kalman Filtering for River Network Modeling

The grand challenge of producing hydrometeorological estimates every time and everywhere has motivated the fusion of sparse observations with dense numerical models, with a particular interest on discharge in river modeling. Ensemble methods are largely preferred as they enable the estimation of error properties, but at the expense of computational load and generally with underestimations. These imperfect stochastic estimates motivate the use of correction methods, that is, error localization and inflation, although the physical justifications for their optimality are limited. The purpose of this study is to use one of the simplest forms of data assimilation when applied to river modeling and reveal the underlying mechanisms impacting its performance. Our framework based on assimilating daily averaged in situ discharge measurements to correct daily averaged runoff was tested over a 4-yr case study of two rivers in Texas. Results show that under optimal conditions of inflation and localization, discharge simulations are consistently improved such that the mean values of Nash–Sutcliffe efficiency are enhanced from211.32 to 0.55 at observed gauges and from212.24 to21.10 at validation gauges. Yet, parameters controlling the inflation and the localization have a large impact on the performance. Further investigations of these sensitivities showed that optimal inflation occurs when compensating exactly for discrepancies in the magnitude of errors while optimal localization matches the distance traveled during one assimilation window. These results may be applicable to more advanced data assimilation methods as well as for larger applications motivated by upcoming river-observing satellite missions, such as NASA’s Surface Water and Ocean Topography mission.

Streamflow↗

NASA NTRS2024

Summarizing Multiple Aspects of Triple Collocation Analysis in a Single Diagram

With the ongoing expansion of global observation networks, it is expected that we shall routinely analyze records of geophysical variables such as temperature from multiple collocated instruments. Validating datasets in this situation is not a trivial task because every observing system has its own bias and noise. Triple collocation is a general statistical framework to estimate the error characteristics in three or more observational-based datasets. In a triple colocation analysis, several metrics are routinely reported but traditional multiple-panel plots are not the most effective way to display information. A new formula of error variance is derived for connecting the key terms in the triple collocation theory. A diagram based on this formula is devised to facilitate triple collocation analysis of any data from observations, as illustrated using three aerosol optical depth datasets from the recent Aerosol Cloud meTeorology Interactions oVer the western ATlantic Experiment (ACTIVATE). An observational-based skill score is also derived to evaluate the quality of three datasets by taking into account both error variance and correlation coefficient. Several applications are discussed and sample plotting routines are provided.

triple collocation↗

NASA NTRS2000

Retrieving the Vertical Structure of the Effective Aerosol Complex Index of Refraction from a Combination of Aerosol in Situ and Remote Sensing Measurements During TARFOX

The largest uncertainty in estimates of the effects of atmospheric aerosols on climate stems from uncertainties in the determination of their microphysical properties, including the aerosol complex index of refraction, which in turn determines their optical properties. A novel technique is used to estimate the aerosol complex index of refraction in distinct vertical layers from a combination of aerosol in situ size distribution and remote sensing measurements during the Tropospheric Aerosol Radiative Forcing Observational Experiment (TARFOX). In particular, aerosol backscatter measurements using the NASA Langley LASE (Lidar Atmospheric Sensing Experiment) instrument and in situ aerosol size distribution data are utilized to derive vertical profiles of the "effective" aerosol complex index of refraction at 815 nm (i.e., the refractive index that would provide the same backscatter signal in a forward calculation on the basis of the measured in situ particle size distributions for homogeneous, spherical aerosols). A sensitivity study shows that this method yields small errors in the retrieved aerosol refractive indices, provided the errors in the lidar-derived aerosol backscatter are less than 30% and random in nature. Absolute errors in the estimated aerosol refractive indices are generally less than 0.04 for the real part and can be as much as 0.042 for the imaginary part in the case of a 30% error in the lidar-derived aerosol backscatter. The measurements of aerosol optical depth from the NASA Ames Airborne Tracking Sunphotometer (AATS-6) are successfully incorporated into the new technique and help constrain the retrieved aerosol refractive indices. An application of the technique to two TARFOX case studies yields the occurrence of vertical layers of distinct aerosol refractive indices. Values of the estimated complex aerosol refractive index range from 1.33 to 1.45 for the real part and 0.001 to 0.008 for the imaginary part. The methodology devised in this study provides, for the first time, a complete set of vertically resolved aerosol size distribution and refractive index data. yielding the vertical distribution of aerosol optical properties required for the determination of aerosol-induced radiative flux changes.

Redemann, J.↗