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NASA NTRS1989

Operator induced multigrid algorithms using semirefinement

A variant of multigrid, based on zebra relaxation, and a new family of restriction/prolongation operators is described. Using zebra relaxation in combination with an operator-induced prolongation leads to fast convergence, since the coarse grid can correct all error components. The resulting algorithms are not only fast, but are also robust, in the sense that the convergence rate is insensitive to the mesh aspect ratio. This is true even though line relaxation is performed in only one direction. Multigrid becomes a direct method if an operator-induced prolongation is used, together with the induced coarse grid operators. Unfortunately, this approach leads to stencils which double in size on each coarser grid. The use of an implicit three point restriction can be used to factor these large stencils, in order to retain the usual five or nine point stencils, while still achieving fast convergence. This algorithm achieves a V-cycle convergence rate of 0.03 on Poisson's equation, using 1.5 zebra sweeps per level, while the convergence rate improves to 0.003 if optimal nine point stencils are used. Numerical results for two- and three-dimensional model problems are presented, together with a two level analysis explaining these results.

Decker, Naomi Henderson↗

NASA NTRS1995

Selecting a general-purpose data compression algorithm

The National Space Science Data Center's Common Data Formate (CDF) is capable of storing many types of data such as scalar data items, vectors, and multidimensional arrays of bytes, integers, or floating point values. However, regardless of the dimensionality and data type, the data break down into a sequence of bytes that can be fed into a data compression function to reduce the amount of data without losing data integrity and thus remaining fully reconstructible. Because of the diversity of data types and high performance speed requirements, a general-purpose, fast, simple data compression algorithm is required to incorporate data compression into CDF. The questions to ask are how to evaluate and compare compression algorithms, and what compression algorithm meets all requirements. The object of this paper is to address these questions and determine the most appropriate compression algorithm to use within the CDF data management package that would be applicable to other software packages with similar data compression needs.

Mathews, Gary Jason↗

NASA NTRS1993

Computational Controls Workstation: Algorithms and hardware

The Computational Controls Workstation provides an integrated environment for the modeling, simulation, and analysis of Space Station dynamics and control. Using highly efficient computational algorithms combined with a fast parallel processing architecture, the workstation makes real-time simulation of flexible body models of the Space Station possible. A consistent, user-friendly interface and state-of-the-art post-processing options are combined with powerful analysis tools and model databases to provide users with a complete environment for Space Station dynamics and control analysis. The software tools available include a solid modeler, graphical data entry tool, O(n) algorithm-based multi-flexible body simulation, and 2D/3D post-processors. This paper describes the architecture of the workstation while a companion paper describes performance and user perspectives.

Venugopal, R.↗

NASA NTRS1988

A high-performance FFT algorithm for vector supercomputers

Many traditional algorithms for computing the fast Fourier transform (FFT) on conventional computers are unacceptable for advanced vector and parallel computers because they involve nonunit, power-of-two memory strides. A practical technique for computing the FFT that avoids all such strides and appears to be near-optimal for a variety of current vector and parallel computers is presented. Performance results of a program based on this technique are given. Notable among these results is that a FORTRAN implementation of this algorithm on the CRAY-2 runs up to 77-percent faster than Cray's assembly-coded library routine.

Bailey, David H.↗

NASA NTRS1990

A diagnosis system using object-oriented fault tree models

Spaceborne computing systems must provide reliable, continuous operation for extended periods. Due to weight, power, and volume constraints, these systems must manage resources very effectively. A fault diagnosis algorithm is described which enables fast and flexible diagnoses in the dynamic distributed computing environments planned for future space missions. The algorithm uses a knowledge base that is easily changed and updated to reflect current system status. Augmented fault trees represented in an object-oriented form provide deep system knowledge that is easy to access and revise as a system changes. Given such a fault tree, a set of failure events that have occurred, and a set of failure events that have not occurred, this diagnosis system uses forward and backward chaining to propagate causal and temporal information about other failure events in the system being diagnosed. Once the system has established temporal and causal constraints, it reasons backward from heuristically selected failure events to find a set of basic failure events which are a likely cause of the occurrence of the top failure event in the fault tree. The diagnosis system has been implemented in common LISP using Flavors.

Iverson, David L.↗

NASA NTRS1998

Segmentation and tracking in echocardiographic sequences: active contours guided by optical flow estimates

This paper presents a method for segmentation and tracking of cardiac structures in ultrasound image sequences. The developed algorithm is based on the active contour framework. This approach requires initial placement of the contour close to the desired position in the image, usually an object outline. Best contour shape and position are then calculated, assuming that at this configuration a global energy function, associated with a contour, attains its minimum. Active contours can be used for tracking by selecting a solution from a previous frame as an initial position in a present frame. Such an approach, however, fails for large displacements of the object of interest. This paper presents a technique that incorporates the information on pixel velocities (optical flow) into the estimate of initial contour to enable tracking of fast-moving objects. The algorithm was tested on several ultrasound image sequences, each covering one complete cardiac cycle. The contour successfully tracked boundaries of mitral valve leaflets, aortic root and endocardial borders of the left ventricle. The algorithm-generated outlines were compared against manual tracings by expert physicians. The automated method resulted in contours that were within the boundaries of intraobserver variability.

Non-NASA Center↗

NASA NTRS1990

Real-time adaptive aircraft scheduling

One of the most important functions of any air traffic management system is the assignment of ground-holding times to flights, i.e., the determination of whether and by how much the take-off of a particular aircraft headed for a congested part of the air traffic control (ATC) system should be postponed in order to reduce the likelihood and extent of airborne delays. An analysis is presented for the fundamental case in which flights from many destinations must be scheduled for arrival at a single congested airport; the formulation is also useful in scheduling the landing of airborne flights within the extended terminal area. A set of approaches is described for addressing a deterministic and a probabilistic version of this problem. For the deterministic case, where airport capacities are known and fixed, several models were developed with associated low-order polynomial-time algorithms. For general delay cost functions, these algorithms find an optimal solution. Under a particular natural assumption regarding the delay cost function, an extremely fast (O(n ln n)) algorithm was developed. For the probabilistic case, using an estimated probability distribution of airport capacities, a model was developed with an associated low-order polynomial-time heuristic algorithm with useful properties.

Kolitz, Stephan E.↗

NASA NTRS2003

Phasor algorithms of the SIM fringe estimation

The Space Interferometry Mission (SIM) will provide unprecedented micro-arcsecond (pas) precision to search for extra-solar planets and possible life in the universe. SIM will also revolutionize our understanding of the dynamics and evolutions of the local universe through hundred-fold improvements of inertial astrometry measurements. SIM has two so-called guide interferometers to provide stable inertial orientation knowledge of the baseline, and a science interferometer to measure target fringes. The guide and science measurements are based on the fringe phase measurements using a CCD detector. One of the key issues with SIM is to develop a new algorithm for calculation of fringe parameters. Not only astrometric results need that new algorithm, but also real-time fringe tracking requires a new method to calculate phase and visibility fast and accurately. The formulas for the phasor algorithms for fringe estimation are presented. The signal-noise ratio performances of the fringe quadratures are demonstrated. The advantages of phasor algorithms for application of fast fringe tracking and on-board data compression are discussed.

interferometry↗

NASA NTRS2019

Modeling Deicing Operations in Departure Scheduling Using Fast Time Simulation

In winter snow conditions, aircraft need inspection for deicing service before takeoff. Deicing service is a procedure to remove frost, ice, slush, or snow from aircraft for safe operation. Deicing operations vary by airport in many ways. Some airports have designated deicing zones, whereas some use a closed runway or terminal area to perform the procedure. Nonetheless, deicing operations add extra workloads to controllers, and cause increased taxi traffic on the ground. NASA and Korea Aerospace Research Institute (KARI) have been collaborating to model deicing operations at Incheon International Airport (ICN). This paper describes the deicing model and the study of deicing operations in departure scheduling using fast time simulations. The deicing model uses a heuristic algorithm for deicing zone assignment. In the fast time simulations, the model uses probability distributions derived from actual operation data to model deicing request and deicing zone time. It is envisioned that such a deicing model can be useful in airport surface scheduling to provide decision support and improve traffic management performance in winter snow operations.

modeling and simulation↗

NASA NTRS2019

Modeling Deicing Operations in Departure Scheduling using Fast Time Simulation

surface operation↗

NASA NTRS1972

The k-space formulation of the n-dimensional scattering problem

The n-dimensional scattering problem is solved by means of a k-space formulation of the field equations, thereby replacing the conventional integral equation formulation by a set of two algebraic equations in two unknowns in two spaces (the constitutive equation being an algebraic equation in x-space). These equations are solved by an iterative method with the aid of the fast Fourier transform (FFT) algorithm connecting the two spaces, requiring very simple initial approximations. Since algebraic and FFT equations are used, the number of arithmetic multiple-add operations and storage allocations required for a numerical solution are reduced from the order of N sq (for solving the matrix equations resulting from the conventional integral equations) to the order of N(log base 2 of N) and N, respectively (where N is the number of data points required for the specification of the problem). The advantage gained in speed and storage is thus of the order of N/log base 2 of N and N, respectively. This method is thus considerably more efficient than the conventional matrix method, and permits exact numerical solutions for much larger problems. Arguments are presented toward the view that the field equations are more fundamental in k-space. The details and some numerical results of the application of this method to the three-dimensional electromagnetic scattering problems are presented as an example.

Bojarski, N. N.↗

NASA NTRS1975

The application of image processing to satellite navigation

Given the locations of several landmarks on a satellite acquired image and their true geographic coordinates, the position and orientation of the satellite can be determined. Two methods for automatically locating the image coordinates of specified landmarks are described. The first, a particularly fast sequential similarity detection algorithm for template matching was originally described by Nagel and Rosenfeld. The second method involves iteratively resampling the picture function in the vicinity of the anticipated landmark. A variety of other speedup methods is also described. An application to SMS imagery is envisioned.

Hord, R. M.↗

NASA NTRS1976

The fast decoding of Reed-Solomon codes using number theoretic transforms

It is shown that Reed-Solomon (RS) codes can be encoded and decoded by using a fast Fourier transform (FFT) algorithm over finite fields. The arithmetic utilized to perform these transforms requires only integer additions, circular shifts and a minimum number of integer multiplications. The computing time of this transform encoder-decoder for RS codes is less than the time of the standard method for RS codes. More generally, the field GF(q) is also considered, where q is a prime of the form K x 2 to the nth power + 1 and K and n are integers. GF(q) can be used to decode very long RS codes by an efficient FFT algorithm with an improvement in the number of symbols. It is shown that a radix-8 FFT algorithm over GF(q squared) can be utilized to encode and decode very long RS codes with a large number of symbols. For eight symbols in GF(q squared), this transform over GF(q squared) can be made simpler than any other known number theoretic transform with a similar capability. Of special interest is the decoding of a 16-tuple RS code with four errors.

Reed, I. S.↗

NASA NTRS1976

The fast decoding of Reed-Solomon codes using high-radix fermat theoretic transforms

Fourier-like transforms over GF(F sub n), where F sub n = 2(2n) + 1 is a Fermat prime, are applied in decoding Reed-Solomon codes. It is shown that such transforms can be computed using high-radix fast Fourier transform (FFT) algorithms requiring considerably fewer multiplications than the more usual radix 2 FFT algorithm. A special 256-symbol, 16-symbol-error-correcting, Reed-Solomon (RS) code for space communication-link applications can be encoded and decoded using this high-radix FFT algorithm over GF(F sub 3).

Liu, K. Y.↗

NASA NTRS1976

Dynamic analysis of a class of mixed lumped-distributed parameter systems via numerical techniques

The modeling via transfer matrices of mixed lumped-distributed parameter systems with feedback control is discussed and novel methods of obtaining information on the controlled system's dynamic response via numerical methods is presented. These methods utilize numerical searches in the complex plane for the roots of the transcendental characteristic equation to determine the closed loop system eigenvalues. The fast Fourier transform (FFT) algorithm is utilized but in the inverse fashion (from frequency domain to time domain). The information obtained is identical to that contained in a model in modal coordinates, and can be used to construct such a model. An interactive computer program to do the required calculation is described, as well as its application to a manipulator arm design problem.

Book, W. J.↗

NASA NTRS1977

Range validation using Kalman filter techniques

Range pseudo-residuals may be improved to the level required for data validation by a measurement updating process which utilizes Bierman's adaptation of the Kalman filter measurement updating algorithms together with process noise compensation to account for model errors. This algorithm involves combining the currently available range predictions and measurements to produce an updated range residual measurement whose accuracy is constrained by the range data quality and by the estimated error in the prediction. The algorithm is compact and fast, and is thus suitable for on-line applications in network control or at the station.

Madrid, G. A.↗

NASA NTRS1978

The fast decoding of Reed-Solomon codes using Fermat theoretic transforms and continued fractions

It is shown that Reed-Solomon (RS) codes can be decoded by using a fast Fourier transform (FFT) algorithm over finite fields GF(F sub n), where F sub n is a Fermat prime, and continued fractions. This new transform decoding method is simpler than the standard method for RS codes. The computing time of this new decoding algorithm in software can be faster than the standard decoding method for RS codes.

Reed, I. S.↗

NASA NTRS1981

Fast polynomial transform and its implementation by computer

A fast polynomial transform (FPT) algorithm for computing two-dimensional cyclic convolutions on a general-purpose computer is demonstrated and compared with the FFT approach. An FPT program for two-dimensional convolutions written in FORTRAN is shown to be 20% faster than the conventional FFT algorithm. This higher speed advantage makes the FPT algorithm a candidate for many two-dimensional digital image filtering applications.

Reed, I. S.↗