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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

A simplified procedure for correcting both errors and erasures of a Reed-Solomon code using the Euclidean algorithm

It is well known that the Euclidean algorithm or its equivalent, continued fractions, can be used to find the error locator polynomial and the error evaluator polynomial in Berlekamp's key equation needed to decode a Reed-Solomon (RS) code. A simplified procedure is developed and proved to correct erasures as well as errors by replacing the initial condition of the Euclidean algorithm by the erasure locator polynomial and the Forney syndrome polynomial. By this means, the errata locator polynomial and the errata evaluator polynomial can be obtained, simultaneously and simply, by the Euclidean algorithm only. With this improved technique the complexity of time domain RS decoders for correcting both errors and erasures is reduced substantially from previous approaches. As a consequence, decoders for correcting both errors and erasures of RS codes can be made more modular, regular, simple, and naturally suitable for both VLSI and software implementation. An example illustrating this modified decoding procedure is given for a (15, 9) RS code.

Truong, T. K.↗
NASA NTRS1991

Euclidean black hole vortices

We argue the existence of solutions of the Euclidean Einstein equations that correspond to a vortex sitting at the horizon of a black hole. We find the asymptotic behaviors, at the horizon and at infinity, of vortex solutions for the gauge and scalar fields in an abelian Higgs model on a Euclidean Schwarzschild background and interpolate between them by integrating the equations numerically. Calculating the backreaction shows that the effect of the vortex is to cut a slice out of the Schwarzschild geometry. Consequences of these solutions for black hole thermodynamics are discussed.

Dowker, Fay↗
NASA NTRS1992

Modeling of Euclidean braided fiber architectures to optimize composite properties

Three-dimensional braided fiber reinforcements are a very effective toughening mechanism for composite materials. The integral yarn path inherent to this fiber architecture allows for effective multidirectional dispersion of strain energy and negates delamination problems. In this paper a geometric model of Euclidean braid fiber architectures is presented. This information is used to determine the degree of geometric isotropy in the braids. This information, when combined with candidate material properties, can be used to quickly generate an estimate of the available load-carrying capacity of Euclidean braids at any arbitrary angle.

Armstrong-Carroll, E.↗
NASA NTRS1994

Mimicking within Euclidean space a cosmological time dilation of gamma-ray burst durations

If gamma-ray burst sources are cosmological in origin, then the time dilation at large z can correlate a burst's duration with its peak flux. Detection of this effect is thought by many to be strong evidence for a cosmological burst origin. In this Letter I show that an apparent time distortion--either a dilation or contraction--is generally expected for an ensemble of bursts that is spatially limited within Euclidean space. The appearance of this effect is correlated with the falling away of the log N-log P curve from a -3/2 slope line. An example of this effect is provided by the relativistic bulk motion model, which produces a strong time dilation when spatially limited in Euclidean space. As a consequence, envidence that weak bursts have longer durations than strong bursts is not evidence of a cosmological burst origin.

Brainerd, J. J.↗
NASA NTRS1979

Euclidean controllability of linear delay systems with limited controls

For linear delay systems with limited controls the notion of a proper control system is introduced. If the uncontrolled system x(t) = Ax(t) + Bx(t - h) is uniformly asymptotically stable and the control equation x(t) = Ax(t) + Bx(t-) + Cu(t) is proper, then the control system is Euclidean null-controllable. It is noted that controllability is equivalent to the system being proper for delay systems with unlimited power.

Chukwu, E. N.↗
NASA NTRS1980

Numerical generation of two-dimensional orthogonal curvilinear coordinates in an Euclidean space

A noniterative method for the numerical generation of orthogonal curvilinear coordinates for plane annular regions between two arbitrary smooth closed curves was developed. The basic generating equation is the Gaussian equation for an Euclidean space which is solved analytically. The method is applied in many cases and these test results demonstrate that the proposed method can be readily applied to a wide variety of problems. The method can also be used for simply connected regions only by obtaining the solution of the linear equation under the changed boundary conditions.

Warsi, Z. U. A.↗
NASA NTRS1982

Observer reference triad rotation, magnetic fields, and rotation in Euclidean cosmological models

It is shown that a cosmological model with Euclidean space sections admits fluid flows if a magnetic field is present. Further, if observer reference frames spin in their response to the universe, a vorticity may exist. Limits can be set on any present intergalactic magnetic field of less than 5.38 x 10 to the -10th gauss (for a model with the chosen symmetry and choice of initial field and fluid velocity components).

Fennelly, A. J.↗
NASA NTRS1988

A lower bound on the minimum Euclidean distance of trellis-coded modulation schemes

A lower bound on the minimum free Euclidean distance of trellis-coded modulation (TCM) is derived that guarantees the existence of good TCM codes of any complexity. The bound is used to compare trellis codes combined with phase-shift keying, pulse amplitude modulation, and quadrature amplitude-shift keying modulation. This random coding bound is the first lower bound on the free distance of trellis codes, is tighter than any upper bound for large constraint lengths, and predicts the asymptotic performance of TCM when the complexity of the code becomes large. The bound can be used with any code rate and any modulation scheme and shows that the free distance increases linearly with the constraint length for large values of the constraint length.

Rouanne, Marc↗
NASA NTRS1993

Optimal realizable filters and the minimum Euclidean distance principle

Minimizing a Euclidean distance in the complex plane optimizes a wide class of correlation metrics for filters implemented on realistic devices. The algorithm searches over no more than two real scalars (gain and phase). It unifies a variety of previous solutions for special cases (e.g., a maximum signal-to-noise ratio with colored noise and a real filter and a maximum correlation intensity with no noise and a coupled filter). It extends optimal partial information filter theory to arbitrary spatial light modulators (fully complex, coupled, discrete, finite contrast ratio, and so forth), additive input noise (white or colored), spatially nonuniform filter modulators, and additive correlation detection noise (including signal dependent noise).

Juday, Richard D.↗
NASA NTRS2012

Optimization of the Multi-Spectral Euclidean Distance Calculation for FPGA-based Spaceborne Systems

Due to the high quantity of operations that spaceborne processing systems must carry out in space, new methodologies and techniques are being presented as good alternatives in order to free the main processor from work and improve the overall performance. These include the development of ancillary dedicated hardware circuits that carry out the more redundant and computationally expensive operations in a faster way, leaving the main processor free to carry out other tasks while waiting for the result. One of these devices is SpaceCube, a FPGA-based system designed by NASA. The opportunity to use FPGA reconfigurable architectures in space allows not only the optimization of the mission operations with hardware-level solutions, but also the ability to create new and improved versions of the circuits, including error corrections, once the satellite is already in orbit. In this work, we propose the optimization of a common operation in remote sensing: the Multi-Spectral Euclidean Distance calculation. For that, two different hardware architectures have been designed and implemented in a Xilinx Virtex-5 FPGA, the same model of FPGAs used by SpaceCube. Previous results have shown that the communications between the embedded processor and the circuit create a bottleneck that affects the overall performance in a negative way. In order to avoid this, advanced methods including memory sharing, Native Port Interface (NPI) connections and Data Burst Transfers have been used.

Cristo, Alejandro↗
NASA NTRSDate not supplied

Discriminative Methodology using the Unscented Transform in Special Euclidean Group SE(3) for Autonomous GN&C

Kalman filtering techniques usually compare a known dynamic model with some process noise to an updated, noisy measurement. Both sources of noise are generally assumed to be Gaussian and are filtered to obtain a more accurate estimate of the state of the system of interest. However, these methods assume that a relatively accurate dynamical model already exists. By including discriminative methodology to interpret differences in the predictive model and the measured states over time, an incorrect model can be corrected overtime, allowing a spacecraft to learn about its environment and adapt to changing conditions. In this paper, a discriminative unscented Kalman filter (DUKF) is introduced on the special Euclidean group SE(3) formulation framework. A spacecraft is initialized near a small body with no knowledge of its parameters, and using several consecutive conditional models the environment is studied and the filter is updated. The case study of a spacecraft in a slightly elliptical, inclined, relatively tight orbit around the irregular moon Phobos is simulated and discussed. The accuracy of this approach is quantifying the differences between the true state, the UKF with a poor model, and the DUKF.

GN&C↗
NASA NTRS1984

The Euclidean slope of the X-ray source counts - A 'cosmic conspiracy'

The selection criteria adopted for the Einstein Observatory Medium Sensitivity survey are delineated and the results of an analysis of the source-count relation for extragalactic X ray sources is presented. Only IPC fields at least 20 deg outside of the galactic plane, and then only those images in the center of the fields, were included. A total of 345 objects were sighted in the 0.3-3.5 keV energy interval, and 77 percent were concluded to be extragalactic. Most were associated with active galactic nuclei (AGN), including Seyfert galaxies and quasars, and galactic clusters. A slope of about 1.7 was calculated for the power law of the energy spectra of AGNs and close to 1.0 for clusters.

Gioia, I. M.↗
NASA NTRSDate not supplied

Autonomous Control for Arbitrary Thruster Configurations and Mass Properties in Special Euclidean Group SE(3)

Most current methods for determining maneuvers and thrust firing sequences depend on explicit and predetermined commands generated by a combination of on-board systems and ground-based human-in-the-loop methods. For spacecraft and space structures with changing mass properties and thruster configurations, such as the Deep Space Gateway as it changes configurations throughout its lifetime, determining these commands can be time-consuming and computationally intensive. However, recent work within the Lie GroupSE (3) has offered ways of autonomously determining the location, power, precision, and capabilities of thrusters in any arbitrary position. Furthermore, a method for determining thruster firing sequences based on an arbitrary control input (both translational and rotational in a coupled, 6-element vector) and arbitrary thruster configurations has also recently been developed. When combining these methods, any spacecraft with any mass properties and thruster configurations can be understood in terms of controllability limits and thruster firing sequences can be generated quickly and with low computational load, thus extending the autonomous capabilities of deep space missions. In this work, this method is presented and explored in terms of computational load, robustness in the presence of uncertainty, and overall performance. The capabilities of this method are also examined in the case of the Deep Space Gateway both in fully controllable configurations and uncontrollable configurations.

Control↗
NASA NTRSDate not supplied

Autonomous Control for Arbitrary Thruster Configurations and Mass Properties in Special Euclidean Group SE(3)

Most current methods for determining maneuvers and thrust firing sequences depend on explicit and predetermined commands generated by a combination of on-board systems and ground-based human-in-the-loop methods. For spacecraft and space structures with changing mass properties and thruster configurations, such as the Deep Space Gateway as it changes configurations throughout its lifetime, determining these commands can be time-consuming and computationally intensive. However, recent work within the Lie group SE(3) has offered ways of autonomously determining the location, power, precision, and capabilities of thrusters in any arbitrary position. Furthermore, a method for determining thruster firing sequences based on an arbitrary control input (both translational and rotational in a coupled, 6-element vector) and arbitrary thruster configurations has also recently been developed. When combining these methods, any spacecraft with any mass properties and thruster configurations can be understood in terms of controllability limits and thruster firing sequences can be generated quickly and with low computational load, thus extending the autonomous capabilities of deep space missions. In this work, this method is presented and explored in terms of convergence time to the desired pose. The capabilities of this method are also examined in the case of the Deep Space Gateway both in fully controllable configurations and uncontrollable configurations.

SE(3)↗
NASA NTRS1989

Multi-level bandwidth efficient block modulation codes

The multilevel technique is investigated for combining block coding and modulation. There are four parts. In the first part, a formulation is presented for signal sets on which modulation codes are to be constructed. Distance measures on a signal set are defined and their properties are developed. In the second part, a general formulation is presented for multilevel modulation codes in terms of component codes with appropriate Euclidean distances. The distance properties, Euclidean weight distribution and linear structure of multilevel modulation codes are investigated. In the third part, several specific methods for constructing multilevel block modulation codes with interdependency among component codes are proposed. Given a multilevel block modulation code C with no interdependency among the binary component codes, the proposed methods give a multilevel block modulation code C which has the same rate as C, a minimum squared Euclidean distance not less than that of code C, a trellis diagram with the same number of states as that of C and a smaller number of nearest neighbor codewords than that of C. In the last part, error performance of block modulation codes is analyzed for an AWGN channel based on soft-decision maximum likelihood decoding. Error probabilities of some specific codes are evaluated based on their Euclidean weight distributions and simulation results.

Lin, Shu↗
NASA NTRS1999

Can A "Hyperspace" Really Exist?

The idea of "hyperspace" is suggested as a possible approach to faster-than-light (FTL) motion. A brief summary of a 1986 study on the Euclidean representation of space-time by the author is presented. Some new calculations on the relativistic momentum and energy of a free particle in Euclidean "hyperspace" are now added and discussed. The superimposed Energy-Momentum curves for subluminal particles, tachyons, and particles in Euclidean "hyperspace" are presented. It is shown that in Euclidean "hyperspace", instead of a relativistic time dilation there is a time "compression" effect. Some fundamental questions are presented,

Zampino, Edward J.↗
NASA NTRS1989

Extension to Eulers's theorem to n-dimensional spaces

Euler's theorem states that any sequence of finite rotations of a rigid body can be described as a single rotation of the body about a fixed axis in three-dimensional Euclidean space. The usual statement of the theorem in the literature cannot be extended to Euclidean spaces of other dimensions. Equivalent formulations of the theorem are given in this paper and proven in a way which does not limit them to the three-dimensional Euclidean space. Thus, the equivalent theorems hold in other dimensions. The proof of one formulation presents an algorithm which shows how to compute an angular-difference matrix that represents a single rotation which is equivalent to the sequence of rotations that have generated the final n-D orientation. This algorithm results also in a constant angular-velocity which, when applied to the initial orientation, yields eventually the final orientation regardless of what angular velocity generated the latter. Finally, the extension of the theorem is demonstrated in a four-dimensional numerical example.

Bar-Itzhack, Itzhack Y.↗