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At least 469 records · Page 26

Communication-Aware Orbit Design for Small Spacecraft Swarms around Small Bodies

Exploration of small Solar System bodies has traditionally been performed by single monolithic spacecraft carrying a number of science instruments. However, science instruments typically cannot be operated simultaneously due to the instrument requirements including optimal viewing angle, surface illumination, altitude and ground resolution, power, and data constraints. This observation has motivated interest in multi-spacecraft architectures where a swarm of small spacecraft, each carrying a single science instrument, studies a small body after being deployed by a carrier spacecraft, which then collects data from the vehicles and relays it to Earth. Such architectures hold promise to yield significant improvements in mission efficiency, increases in data quality, and shorter mission duration. A key difficulty in the design of such missions is the selection of orbits for the small spacecraft, which must satisfy not only instrument requirements, but also strict inter-spacecraft communication and on-board storage constraints. To address this, in this paper, we present a novel computationally-efficient optimization algorithm for \emph{communication-aware design} of the orbits of a small spacecraft swarm orbiting a small body. The proposed approach captures constraints including instrument requirements, inter-spacecraft communication bandwidths, and on-board memory usage, and it can accommodate highly irregular gravity field models and surface geometries. We propose an efficient algorithm for optimization of instrument observations and inter-spacecraft communications; we then leverage the differentiable nature of the proposed algorithm to accelerate a gradient-based global search algorithm. Numerical simulations of a six-spacecraft swarm studying 433 Eros show that the proposed approach successfully identifies high-quality orbits, and significantly outperform communication-agnostic optimization techniques, resulting in a 10% increase in scientific returns and a 30% increase in the quality of the collected data.

Rahmani, Amir↗

Evaluation, Analysis, and Application of Internal Strain-Gage Balance Data

Experimental processes, analytical methods, and numerical algorithms are described that may be used to predict the forces and moments of an internal strain–gage balance during a wind tunnel test. First, the control volume model of a strain–gage balance and the concepts of load state, load space, and output space are introduced. These important abstractions provide a better understanding of fundamental characteristics of different balance load prediction approaches. Then, the description of strain–gage balance data and the definition of the primary bridge sensitivity are discussed. Afterwards, basic elements of the calibration of a typical six–component balance are reviewed. Two fundamentally different balance load prediction methods, the processing of check loads, and related topics are also discussed. Three real–world balance data examples are reviewed in great detail to illustrate typical analysis results for a variety of strain–gage balance designs. Finally, important observations are summarized and recommendations are provided. – Additional information and detailed mathematical derivations can be found in the appendices of the document. They include the following topics: balance terminology, definitions of important statistical metrics, balance axis system conventions, balance load transformations, the combined load diagram, electrical output format options, bi–directional output characteristics, determination of the natural zeros, derivation of two balance load prediction methods, description of two tare load iteration algorithms, modeling of balance temperature effects, basics of three–component moment balances, definition of the percent contribution, detection of linear and near–linear dependencies in balance calibration data, a regression model search algorithm, balance interactions, and other related information.

strain-gage balance↗

Numerical arc segmentation algorithm for a radio conference - A software tool for communication satellite systems planning

A detailed description of a Numerical Arc Segmentation Algorithm for a Radio Conference (NASARC) software package for communication satellite systems planning is presented. This software provides a method of generating predetermined arc segments for use in the development of an allotment planning procedure to be carried out at the 1988 World Administrative Radio Conference (WARC - 88) on the use of the GEO and the planning of space services utilizing GEO. The features of the NASARC software package are described, and detailed information is given about the function of each of the four NASARC program modules. The results of a sample world scenario are presented and discussed.

Whyte, W. A.↗

Predictive Lateral Logic for Numerical Entry Guidance Algorithms

Recent entry guidance algorithm development123 has tended to focus on numerical integration of trajectories onboard in order to evaluate candidate bank profiles. Such methods enjoy benefits such as flexibility to varying mission profiles and improved robustness to large dispersions. A common element across many of these modern entry guidance algorithms is a reliance upon the concept of Apollo heritage lateral error (or azimuth error) deadbands in which the number of bank reversals to be performed is non-deterministic. This paper presents a closed-loop bank reversal method that operates with a fixed number of bank reversals defined prior to flight. However, this number of bank reversals can be modified at any point, including in flight, based on contingencies such as fuel leaks where propellant usage must be minimized.

Smith, Kelly M.↗

Numerical Arc Segmentation Algorithm for a Radio Conference-NASARC (version 4.0) technical manual

The information contained in the NASARC (Version 4.0) Technical Manual and NASARC (Version 4.0) User's Manual relates to the Numerical Arc Segmentation Algorithm for a Radio Conference (NASARC) software development through November 1, 1988. The Technical Manual describes the NASARC concept and the algorithms used to implement the concept. The User's Manual provides information on computer system considerations, installation instructions, description of input files, and program operation instructions. Significant revisions were incorporated in the Version 4.0 software over prior versions. These revisions have further enhanced the modeling capabilities of the NASARC procedure and provide improved arrangements of predetermined arcs within the geostationary orbits. Array dimensions within the software were structured to fit within the currently available 12 megabyte memory capacity of the International Frequency Registration Board (IFRB) computer facility. A piecewise approach to predetermined arc generation in NASARC (Version 4.0) allows worldwide planning problem scenarios to be accommodated within computer run time and memory constraints with enhanced likelihood and ease of solution.

Whyte, Wayne A., Jr.↗

Numerical Arc Segmentation Algorithm for a Radio Conference (NASARC), version 4.0: User's manual

The information in the NASARC (Version 4.0) Technical Manual (NASA-TM-101453) and NASARC (Version 4.0) User's Manual (NASA-TM-101454) relates to the state of Numerical Arc Segmentation Algorithm for a Radio Conference (NASARC) software development through November 1, 1988. The Technical Manual describes the NASARC concept and the algorithms used to implement the concept. The User's Manual provides information on computer system considerations, installation instructions, description of input files, and program operation instructions. Significant revisions were incorporated in the Version 4.0 software over prior versions. These revisions have further enhanced the modeling capabilities of the NASARC procedure and provide improved arrangements of predetermined arcs within the geostationary orbit. Array dimensions within the software were structured to fit within the currently available 12-megabyte memory capacity of the International Frequency Registration Board (IFRB) computer facility. A piecewise approach to predetermined arc generation in NASARC (Version 4.) allows worldwide planning problem scenarios to be accommodated within computer run time and memory constraints with enhanced likelihood and ease of solution.

Whyte, Wayne A., Jr.↗

Numerical Arc Segmentation Algorithm for a Radio Conference-NASARC, Version 2.0: User's Manual

The information contained in the NASARC (Version 2.0) Technical Manual (NASA TM-100160) and the NASARC (Version 2.0) User's Manual (NASA TM-100161) relates to the state of the Numerical Arc Segmentation Algorithm for a Radio Conference (NASARC) software development through October 16, 1987. The technical manual describes the NASARC concept and the algorithms which are used to implement it. The User's Manual provides information on computer system considerations, installation instructions, description of input files, and program operation instructions. Significant revisions have been incorporated in the Version 2.0 software over prior versions. These revisions have enhanced the modeling capabilities of the NASARC procedure while greatly reducing the computer run time and memory requirements. Array dimensions within the software have been structured to fit into the currently available 6-megabyte memory capacity of the International Frequency Registration Board (IFRB) computer facility. A piecewise approach to predetermined arc generation in NASARC (Version 2.0) allows worldwide scenarios to be accommodated within these memory constraints while at the same time reducing computer run time.

Whyte, Wayne A., Jr.↗

Numerical arc segmentation algorithm for a radio conference-NASARC (version 2.0) technical manual

The information contained in the NASARC (Version 2.0) Technical Manual (NASA TM-100160) and NASARC (Version 2.0) User's Manual (NASA TM-100161) relates to the state of NASARC software development through October 16, 1987. The Technical Manual describes the Numerical Arc Segmentation Algorithm for a Radio Conference (NASARC) concept and the algorithms used to implement the concept. The User's Manual provides information on computer system considerations, installation instructions, description of input files, and program operating instructions. Significant revisions have been incorporated in the Version 2.0 software. These revisions have enhanced the modeling capabilities of the NASARC procedure while greatly reducing the computer run time and memory requirements. Array dimensions within the software have been structured to fit within the currently available 6-megabyte memory capacity of the International Frequency Registration Board (IFRB) computer facility. A piecewise approach to predetermined arc generation in NASARC (Version 2.0) allows worldwide scenarios to be accommodated within these memory constraints while at the same time effecting an overall reduction in computer run time.

Whyte, Wayne A., Jr.↗

Analysis of the distribution of pitch angles in model galactic disks - Numerical methods and algorithms

An automated mathematical method capable of successfully isolating the many different features in prototype and observed spiral galaxies and of accurately measuring the pitch angles and lengths of these individual features is developed. The method is applied to analyze the evolution of specific features in a prototype galaxy exhibiting flocculent spiral structure. The mathematical-computational method was separated into two components. Initially, the galaxy was partitioned into dense regions constituting features using two different methods. The results obtained using these two partitioning algorithms were very similar, from which it is inferred that no numerical biasing was evident and that capturing of the features was consistent. Standard least-squares methods underestimated the true slope of the cloud distribution and were incapable of approximating an orientation of 45 deg. The problems were overcome by introducing a superior fit least-squares method, developed with the intention of calculating true orientation rather than a regression line.

Russell, William S.↗

Bringing randomized algorithms to mainstream numerical linear algebra

Numerical linear algebra (NLA) underpins huge swaths of computational science and engineering. For scientists and engineers to make the most of the DOE’s computing resources, it is essential that they have access to high-performance implementations of algorithms with best-in-class scalability and reliability. Despite this, prevailing NLA libraries have little to no support for breakthrough algorithms from the field of randomized numerical linear algebra (RandNLA) that have been developed over the past twenty years. The goal of this LDRD was to break a log-jam that had prevented broad adoption of RandNLA. Our work had two thrusts. The first was to develop RandBLAS: a trustworthy and high-performance C++ library for randomized dimension reduction (an operation widely known as sketching). The second was the development of a novel randomized algorithm for computing a challenging type of matrix decomposition known as Householder QR with column pivoting (Householder QRCP). In this one-year late-start LDRD we successfully delivered RandBLAS 1.0 and new CPU and GPU codes for Householder QRCP. RandBLAS has extensive documentation at https://randblas.readthedocs.io/en/stable/. Papers on RandBLAS and and our high-performance QRCP codes are forthcoming.

97 MATHEMATICS AND COMPUTING↗

Numerical comparison of Kalman filter algorithms - Orbit determination case study

Numerical characteristics of various Kalman filter algorithms are illustrated with a realistic orbit determination study. The case study of this paper highlights the numerical deficiencies of the conventional and stabilized Kalman algorithms. Computational errors associated with these algorithms are found to be so large as to obscure important mismodeling effects and thus cause misleading estimates of filter accuracy. The positive result of this study is that the U-D covariance factorization algorithm has excellent numerical properties and is computationally efficient, having CPU costs that differ negligibly from the conventional Kalman costs. Accuracies of the U-D filter using single precision arithmetic consistently match the double precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity to variations in the a priori statistics.

Bierman, G. J.↗

A numerical comparison of discrete Kalman filtering algorithms: An orbit determination case study

The numerical stability and accuracy of various Kalman filter algorithms are thoroughly studied. Numerical results and conclusions are based on a realistic planetary approach orbit determination study. The case study results of this report highlight the numerical instability of the conventional and stabilized Kalman algorithms. Numerical errors associated with these algorithms can be so large as to obscure important mismodeling effects and thus give misleading estimates of filter accuracy. The positive result of this study is that the Bierman-Thornton U-D covariance factorization algorithm is computationally efficient, with CPU costs that differ negligibly from the conventional Kalman costs. In addition, accuracy of the U-D filter using single-precision arithmetic consistently matches the double-precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity of variations in the a priori statistics.

Thornton, C. L.↗

Middle atmosphere project: A radiative heating and cooling algorithm for a numerical model of the large scale stratospheric circulation

A Curtis matrix is used to compute cooling by the 15 micron and 10 micron bands of carbon dioxide. Escape of radiation to space and exchange the lower boundary are used for the 9.6 micron band of ozone. Voigt line shape, vibrational relaxation, line overlap, and the temperature dependence of line strength distributions and transmission functions are incorporated into the Curtis matrices. The distributions of the atmospheric constituents included in the algorithm, and the method used to compute the Curtis matrices are discussed as well as cooling or heating by the 9.6 micron band of ozone. The FORTRAN programs and subroutines that were developed are described and listed.

Wehrbein, W. M.↗

On the numeric integration of dynamic attitude equations

We describe new types of numerical integration algorithms developed by the authors. The main aim of the algorithms is to numerically integrate differential equations which evolve on geometric objects, such as the rotation group. The algorithms provide iterates which lie on the prescribed geometric object, either exactly, or to some prescribed accuracy, independent of the order of the algorithm. This paper describes applications of these algorithms to the evolution of the attitude of a rigid body.

Crouch, P. E.↗

On the utility of finite element theory for computational fluid dynamics

An implicit finite element numerical solution algorithm is derived for the compressible Navier-Stokes equations expressed in generalized coordinates. The theoretical basis utilizes a Galerkin-Weighted Residuals formulation, and extremization of approximation error within the context of a multipole expansion. A von Neumann analysis for a simplified form indicates the algorithm fourth- to sixth-order phase accurate, with third-order dissipation for the elementary linear element construction. Performance is improved for the algorithm constructed using quadratic interpolation. Numerical experiments for shocked duct flows are employed to optimize the several algorithm parameters. Additional numerical solutions validate algorithm accuracy and utility for aerodynamics applications.

Baker, A. J.↗

A Polynomial Time, Numerically Stable Integer Relation Algorithm

Let x = (x1, x2...,xn be a vector of real numbers. X is said to possess an integer relation if there exist integers a(sub i) not all zero such that a1x1 + a2x2 + ... a(sub n)Xn = 0. Beginning in 1977 several algorithms (with proofs) have been discovered to recover the a(sub i) given x. The most efficient of these existing integer relation algorithms (in terms of run time and the precision required of the input) has the drawback of being very unstable numerically. It often requires a numeric precision level in the thousands of digits to reliably recover relations in modest-sized test problems. We present here a new algorithm for finding integer relations, which we have named the "PSLQ" algorithm. It is proved in this paper that the PSLQ algorithm terminates with a relation in a number of iterations that is bounded by a polynomial in it. Because this algorithm employs a numerically stable matrix reduction procedure, it is free from the numerical difficulties, that plague other integer relation algorithms. Furthermore, its stability admits an efficient implementation with lower run times oil average than other algorithms currently in Use. Finally, this stability can be used to prove that relation bounds obtained from computer runs using this algorithm are numerically accurate.

Ferguson, Helaman R. P.↗