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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Applying integrals of motion to the numerical solution of differential equations

A method is developed for using the integrals of systems of nonlinear, ordinary, differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scalar or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction.

Vezewski, D. J.↗
NASA NTRS2004

Using Redundancy To Reduce Errors in Magnetometer Readings

A method of reducing errors in noisy magnetic-field measurements involves exploitation of redundancy in the readings of multiple magnetometers in a cluster. By "redundancy"is meant that the readings are not entirely independent of each other because the relationships among the magnetic-field components that one seeks to measure are governed by the fundamental laws of electromagnetism as expressed by Maxwell's equations. Assuming that the magnetometers are located outside a magnetic material, that the magnetic field is steady or quasi-steady, and that there are no electric currents flowing in or near the magnetometers, the applicable Maxwell 's equations are delta x B = 0 and delta(raised dot) B = 0, where B is the magnetic-flux-density vector. By suitable algebraic manipulation, these equations can be shown to impose three independent constraints on the values of the components of B at the various magnetometer positions. In general, the problem of reducing the errors in noisy measurements is one of finding a set of corrected values that minimize an error function. In the present method, the error function is formulated as (1) the sum of squares of the differences between the corrected and noisy measurement values plus (2) a sum of three terms, each comprising the product of a Lagrange multiplier and one of the three constraints. The partial derivatives of the error function with respect to the corrected magnetic-field component values and the Lagrange multipliers are set equal to zero, leading to a set of equations that can be put into matrix.vector form. The matrix can be inverted to solve for a vector that comprises the corrected magnetic-field component values and the Lagrange multipliers.

Kulikov, Igor↗
NASA NTRS1989

Probability distribution of wind retrieval error for the NASA scatterometer

The NASA scatterometer (NSCAT) is a spaceborne scatterometer scheduled to be deployed in the mid-1990s. An analysis of the wind retrieval error distribution for wind estimates based on backscatter measurements made by the NSCAT instrument is presented. The results are based on an end-to-end simulation of the scatterometer instrument and data processing. In general, the distribution of the wind speed error, when normalized, is independent of the true wind speed and direction. The wind speed error can be characterized by a normal distribution. The wind direction error is independent of the true wind speed, but depends on the true wind direction. Details for wind vectors with true wind speeds from 3 m/s to 33 m/s and true wind directions from 0 to 360 deg are presented.

Leotta, Daniel F.↗
NASA NTRS2022

Quantifying Errors in 3D CME Parameters Derived from Synthetic Data Using White-Light Reconstruction Techniques

Current efforts in space weather forecasting of CMEs have been focused on predicting their arrival time and magnetic structure. To make these predictions, methods have been developed to derive the true CME speed, size, position, and mass, among others. Difficulties in determining the input parameters for CME forecasting models arise from the lack of direct measurements of the coronal magnetic fields and uncertainties in estimating the CME 3D geometric and kinematic parameters after eruption. White-light coronagraph images are usually employed by a variety of CME reconstruction techniques that assume more or less complex geometries. This is the first study from our International Space Science Institute (ISSI) team “Understanding Our Capabilities in Observing and Modeling Coronal Mass Ejections”, in which we explore how subjectivity affects the 3D CME parameters that are obtained from the Graduated Cylindrical Shell (GCS) reconstruction technique, which is widely used in CME research. To be able to quantify such uncertainties, the “true” values that are being fitted should be known, which are impossible to derive from observational data. We have designed two different synthetic scenarios where the “true” geometric parameters are known in order to quantify such uncertainties for the first time. We explore this by using two sets of synthetic data: 1) Using the ray-tracing option from the GCS model software itself, and 2) Using 3D magnetohydrodynamic (MHD) simulation data from the Magnetohydrodynamic Algorithm outside a Sphere code. Our experiment includes different viewing configurations using single and multiple viewpoints. CME reconstructions using a single viewpoint had the largest errors and error ranges overall for both synthetic GCS and simulated MHD white-light data. As the number of viewpoints increased from one to two, the errors decreased by approximately 4° in latitude, 22° in longitude, 14° in tilt, and 10° in half-angle. Our results quantitatively show the critical need for at least two viewpoints to be able to reduce the uncertainty in deriving CME parameters. We did not find a significant decrease in errors when going from two to three viewpoints for our specific hypothetical three spacecraft scenario using synthetic GCS white-light data. As we expected, considering all configurations and numbers of viewpoints, the mean absolute errors in the measured CME parameters are generally significantly higher in the case of the simulated MHD white-light data compared to those from the synthetic white-light images generated by the GCS model. We found the following CME parameter error bars as a starting point for quantifying the minimum error in CME parameters from white-light reconstructions: Δθ (latitude)=6° +2° -3° , Δϕ (longitude)=11° +18° -6° , Δγ (tilt)=25° +8° -7° , Δx (half-angle)=10° +12° -6° , Δh (height)=0.6 +1.2 -0.4 R ⨀ , and Δκ (ratio)=0.1 +0.03 -0.02 .

Coronal mass ejections↗
NASA NTRS2022

Quantifying Errors in 3D CME Parameters Derived From Synthetic Data Using White-Light Reconstruction Techniques

Current efforts in space weather forecasting of CMEs have been focused on predicting their arrival time and magnetic structure. To make these predictions, methods have been developed to derive the true CME speed, size, position, and mass, among others. Difficulties in determining the input parameters for CME forecasting models arise from the lack of direct measurements of the coronal magnetic fields and uncertainties in estimating the CME 3D geometric and kinematic parameters after eruption. White-light coronagraph images are usually employed by a variety of CME reconstruction techniques that assume more or less complex geometries. This is the first study from our International Space Science Institute (ISSI) team “Understanding Our Capabilities in Observing and Modeling Coronal Mass Ejections”, in which we explore how subjectivity affects the 3D CME parameters that are obtained from the Graduated Cylindrical Shell (GCS) reconstruction technique, which is widely used in CME research. To be able to quantify such uncertainties, the “true” values that are being fitted should be known, which are impossible to derive from observational data. We have designed two different synthetic scenarios where the “true” geometric parameters are known in order to quantify such uncertainties for the first time. We explore this by using two sets of synthetic data: 1) Using the ray-tracing option from the GCS model software itself, and 2) Using 3D magnetohydrodynamic (MHD) simulation data from the Magnetohydrodynamic Algorithm outside a Sphere code. Our experiment includes different viewing configurations using single and multiple viewpoints. CME reconstructions using a single viewpoint had the largest errors and error ranges overall for both synthetic GCS and simulated MHD white-light data. As the number of viewpoints increased from one to two, the errors decreased by approximately 4° in latitude, 22° in longitude, 14° in tilt, and 10° in half-angle. Our results quantitatively show the critical need for at least two viewpoints to be able to reduce the uncertainty in deriving CME parameters. We did not find a significant decrease in errors when going from two to three viewpoints for our specific hypothetical three spacecraft scenario using synthetic GCS white-light data. As we expected, considering all configurations and numbers of viewpoints, the mean absolute errors in the measured CME parameters are generally significantly higher in the case of the simulated MHD white-light data compared to those from the synthetic white-light images generated by the GCS model. We found the following CME parameter error bars as a starting point for quantifying the minimum error in CME parameters from white-light reconstructions: Δθ (latitude)=6° +2° -3° , Δϕ (longitude)=11° +18° -6° , Δγ (tilt)=25° +8° -7° , Δx (half-angle)=10° +12° -6° , Δh (height)=0.6 +1.2 -0.4 R ⨀ , and Δκ (ratio)=0.1 +0.03 -0.02 .

Coronal mass ejections↗
NASA NTRS1971

Arithmetic error codes - Cost and effectiveness studies for application in digital system design.

The application of error-detecting or error-correcting codes in digital computer design requires studies of cost and effectiveness tradeoffs to supplement the knowledge of their theoretical properties. General criteria for cost and effectiveness studies of error codes are developed, and results are presented for arithmetic error codes with the low-cost check modulus 2 super a - 1. Both separate (residue) and nonseparate (AN) codes are considered. The class of multiple arithmetic error codes is developed as an extension of low-cost single codes.

Avizienis, A.↗
NASA NTRS1987

More on the decoder error probability for Reed-Solomon codes

The decoder error probability for Reed-Solomon codes (more generally, linear maximum distance separable codes) is examined. McEliece and Swanson offered an upper bound on P sub E (u), the decoder error probability given that u symbol errors occurs. This upper bound is slightly greater than Q, the probability that a completely random error pattern will cause decoder error. By using a combinatoric technique, the principle of inclusion and exclusion, an exact formula for P sub E (u) is derived. The P sub e (u) for the (255, 223) Reed-Solomon Code used by NASA, and for the (31,15) Reed-Solomon code (JTIDS code), are calculated using the exact formula, and the P sub E (u)'s are observed to approach the Q's of the codes rapidly as u gets larger. An upper bound for the expression is derived, and is shown to decrease nearly exponentially as u increases. This proves analytically that P sub E (u) indeed approaches Q as u becomes large, and some laws of large numbers come into play.

Cheung, K.-M.↗
NASA NTRS1989

More on the decoder error probability for Reed-Solomon codes

The decoder error probability for Reed-Solomon codes (more generally, linear maximum distance separable codes) is examined. McEliece and Swanson offered an upper bound on P sub E (u), the decoder error probability given that u symbol errors occur. This upper bound is slightly greater than Q, the probability that a completely random error pattern will cause decoder error. By using a combinatoric technique, the principle of inclusion and exclusion, an exact formula for P sub E (u) is derived. The P sub E (u) for the (255,223) Reed-Solomon Code used by NASA, and for the (31,15) Reed-Solomon code (JTIDS code), are calculated using the exact formula, and the P sub E (u)'s are observed to approach the Q's of the codes rapidly as u gets larger. An upper bound for the expression is derived, and is shown to decrease nearly exponentially as u increases. This proves analytically that P sub E (u) indeed approaches Q as u becomes large, and some laws of large numbers come into play.

Cheung, Kar-Ming↗
NASA NTRS1972

Image correlation and sampling study

The development of analytical approaches for solving image correlation and image sampling of multispectral data is discussed. Relevant multispectral image statistics which are applicable to image correlation and sampling are identified. The general image statistics include intensity mean, variance, amplitude histogram, power spectral density function, and autocorrelation function. The translation problem associated with digital image registration and the analytical means for comparing commonly used correlation techniques are considered. General expressions for determining the reconstruction error for specific image sampling strategies are developed.

Popp, D. J.↗
NASA NTRS1974

Decision-directed automatic gain control for MAPSK systems

An automatic gain control (AGC) loop is presented for use with M-ary amplitude and phase shift keying (MAPSK) systems. The gain control amplifier is regulated by an error signal formed by the difference between the estimated amplitude level and the received amplitude level. The AGC performance is thus independent of the short-term average received signal energy. AGC loop analysis and simulation is presented for M-ary amplitude shift keying and quadrature amplitude shift keying. The AGC is shown to have a negligible degradation on the symbol probability of error for most practical cases. A generalized AGC for an arbitrary MAPSK system is presented.

Weber, W. J., III↗
NASA NTRS1978

Potential end-to-end imaging information rate advantages of various alternative communication systems

Various communication systems were considered which are required to transmit both imaging and a typically error sensitive, class of data called general science/engineering (gse) over a Gaussian channel. The approach jointly treats the imaging and gse transmission problems, allowing comparisons of systems which include various channel coding and data compression alternatives. Actual system comparisons include an Advanced Imaging Communication System (AICS) which exhibits the rather significant potential advantages of sophisticated data compression coupled with powerful yet practical channel coding.

Rice, R. F.↗
NASA NTRS1978

Precision orbit computations for Starlette

The Starlette satellite, launched in February 1975 was designed to minimize the effects of nongravitational forces and to obtain the highest possible accuracy for laser range measurements. Analyses of the first four months of laser tracking data from nine stations have confirmed the stability of the orbit and the precision to which the satellite's position can be established. Initial orbit computations using the GSFC GEM - 7 gravity model produced rms fits of about 8 to 10 meters for arc lengths of 5 days. After tailoring a gravity model specifically to Starlette, the rms fits for the 5 day arcs were reduced significantly to the 1 to 2 meter level. An rms fit of 4.3 meters was obtained for a 90 day arc. Five day arcs overlapped by 2.5 days showed rms satellite position differences generally less than 2 meters. Prediction errors at the end of two months were less than 30 milliseconds.

Marsh, J. G.↗
NASA NTRS1982

End-to-end imaging information rate advantages of various alternative communication systems

The efficiency of various deep space communication systems which are required to transmit both imaging and a typically error sensitive class of data called general science and engineering (gse) are compared. The approach jointly treats the imaging and gse transmission problems, allowing comparisons of systems which include various channel coding and data compression alternatives. Actual system comparisons include an advanced imaging communication system (AICS) which exhibits the rather significant advantages of sophisticated data compression coupled with powerful yet practical channel coding. For example, under certain conditions the improved AICS efficiency could provide as much as two orders of magnitude increase in imaging information rate compared to a single channel uncoded, uncompressed system while maintaining the same gse data rate in both systems. Additional details describing AICS compression and coding concepts as well as efforts to apply them are provided in support of the system analysis.

Rice, R. F.↗
NASA NTRS1983

Spiral-bevel geometry and gear train precision

A new aproach to the solution of determination of surface principal curvatures and directions is proposed. Direct relationships between the principal curvatures and directions of the tool surface and those of the principal curvatures and directions of generated gear surface are obtained. The principal curvatures and directions of geartooth surface are obtained without using the complicated equations of these surfaces. A general theory of the train kinematical errors exerted by manufacturing and assembly errors is discussed. Two methods for the determination of the train kinematical errors can be worked out: (1) with aid of a computer, and (2) with a approximate method. Results from noise and vibration measurement conducted on a helicopter transmission are used to illustrate the principals contained in the theory of kinematic errors.

Litvin, F. L.↗
NASA NTRS1983

The impact of satellite soundings and their distribution on forecast accuracy

The impact of satellite data is found to vary considerably from one map to another and from one geographic region to another. However, the impact of satellite data is generally small in comparison with forecast error. On the average, over land areas (where good conventional data permit accurate verification), the impact of satellite data on 48-hr forecasts of 500-mb height is seen to be neutral. Indirect numerical evidence is found, however, that satellite data has a marked positive impact in the lower and middle troposphere in ocean regions, especially those regions where conventional data are sparse. The impact over oceans is found to be especially noticeable in maps depicting the mean differences between the satellite and the conventional-data-only maps averaged over the period of the data set (January 1-14, 1980), both for analyses and for forecasts to 48 hours.

Thomasell, A., Jr.↗
NASA NTRS1982

Performance of staggered quadrature modulations over nonlinear satellite channels with uplink noise and intersymbol interference

In this paper, the performance of staggered quadrature modulations over nonlinear satellite channels is analyzed. The effects of uplink noise and intersymbol interference caused by transmitter filtering are included. The approach taken employs computational techniques based on moments of the interference. The expressions for the system bit error rate are derived for a general transponder model characterized by AM-AM and AM-PM conversion characteristics. Specific numerical results are presented for a hard-limited satellite repeater using staggered quadrature overlapped raised cosine (SQORC) and minimum-shift-keying (MSK) modulations.

Simon, M. K.↗