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NASA NTRS1989

Black light - How sensors filter spectral variation of the illuminant

Visual sensor responses may be used to classify objects on the basis of their surface reflectance functions. In a color image, the image data are represented as a vector of sensor responses at each point in the image. This vector depends both on the surface reflectance functions and on the spectral power distribution of the ambient illumination. Algorithms designed to classify objects on the basis of their surface reflectance functions typically attempt to overcome the dependence of the sensor responses on the illuminant by integrating sensor data collected from multiple surfaces. In machine vision applications, it is shown that it is often possible to design the sensor spectral responsivities so that the vector direction of the sensor responses does not depend upon the illuminant. The conditions under which this is possible are given and an illustrative calculation is performed. In biological systems, where the sensor responsivities are fixed, it is shown that some changes in the illumination cause no change in the sensor responses. Such changes in illuminant are called black illuminants. It is possible to express any illuminant as the sum of two unique components. One component is a black illuminant. The second component is called the visible component. The visible component of an illuminant completely characterizes the effect of the illuminant on the vector of sensor responses.

Brainard, David H.↗

NASA NTRS1988

Storage and computationally efficient permutations of factorized covariance and square-root information matrices

A unified method to permute vector-stored upper-triangular diagonal factorized covariance (UD) and vector stored upper-triangular square-root information filter (SRIF) arrays is presented. The method involves cyclical permutation of the rows and columns of the arrays and retriangularization with appropriate square-root-free fast Givens rotations or elementary slow Givens reflections. A minimal amount of computation is performed and only one scratch vector of size N is required, where N is the column dimension of the arrays. To make the method efficient for large SRIF arrays on a virtual memory machine, three additional scratch vectors each of size N are used to avoid expensive paging faults. The method discussed is compared with the methods and routines of Bierman's Estimation Subroutine Library (ESL).

Muellerschoen, R. J.↗

NASA NTRS1989

A static investigation of several STOVL exhaust system concepts

A static cold flow scale model test was performed in order to determine the internal performance characteristics of various STOVL exhaust systems. All of the concepts considered included a vectorable cruise nozzle and a separate vectorable vertical thrust ventral nozzle mounted on the tailpipe. The two ventral nozzle configurations tested featured vectorable constant thickness cascade vanes for area control and improved performance during transition and vertical lift flight. The best transition performance was achieved using a butterfly door type ventral nozzle and a pitch vectoring 2DCD or axisymmetric cruise nozzle. The clamshell blocker type of ventral nozzle had reduced transition performance due to the choking of the tailpipe flow upstream of the cruise nozzle.

Romine, B. M., Jr.↗

NASA NTRS1989

A technique for representinbg three-dimensional vertical circulation in baroclinic disturbances

A method is presented for producing three-dimensional representations of vertical circulations in frontal zones in cases where the circulations are not confined to the cross-front vertical plane. Various approaches for representing vertical circulations are reviewed. The numerical aspects of the channel-model simulation are summarized. A vector streamfunction, the psi vector, that describes the vertical velocity and the horizontal irrotational flow, is defined. The technique for determining the psi vector for a channel geometry is outlined. Results are presented from applying the psi vector method to four frontal systems in an f-plane primitive equation channel model of a finite-amplitude baroclinic wave.

Keyser, Daniel↗

NASA NTRS1990

Low-g payload placement constraints for space station

Payloads onboard the Space Station will be subjected to a steady state acceleration level dominated by gravity gradient and aerodynamic drag forces. The g-level due to gravity gradient forces depends on the payload location relative to the center of mass, whereas the g-level due to aerodynamic drag may be assumed nearly constant throughout the Space Station. The vector of acceleration due to aerodynamic drag can always be broken down into three orthogonal components, in the direction opposite to the velocity vector, along the local vertical, and perpendicular to the orbit plane. It will be shown that the gravity gradient term has two components, which are orthogonal to one another. One component is along the local vertical and the other is perpendicular to the orbit plane. Thus, the combination of all components form an orthogonal triad of vectors. Addressed here are the payload location constraints to satisfy the requirements of 1 micro-g. The permissible locations are within an open-ended tube having an elliptical cross section, which is aligned with the velocity vector and centered on the system center of mass.

Carpenter, Anita S.↗

NASA NTRS1990

The nondeterministic divide

The nondeterministic divide partitions a vector into two non-empty slices by allowing the point of division to be chosen nondeterministically. Support for high-level divide-and-conquer programming provided by the nondeterministic divide is investigated. A diva algorithm is a recursive divide-and-conquer sequential algorithm on one or more vectors of the same range, whose division point for a new pair of recursive calls is chosen nondeterministically before any computation is performed and whose recursive calls are made immediately after the choice of division point; also, access to vector components is only permitted during activations in which the vector parameters have unit length. The notion of diva algorithm is formulated precisely as a diva call, a restricted call on a sequential procedure. Diva calls are proven to be intimately related to associativity. Numerous applications of diva calls are given and strategies are described for translating a diva call into code for a variety of parallel computers. Thus diva algorithms separate logical correctness concerns from implementation concerns.

Charlesworth, Arthur↗

NASA NTRS1991

Analysis of structural response data using discrete modal filters

The application of reciprocal modal vectors to the analysis of structural response data is described. Reciprocal modal vectors are constructed using an existing experimental modal model and an existing frequency response matrix of a structure, and can be assembled into a matrix that effectively transforms the data from the physical space to a modal space within a particular frequency range. In other words, the weighting matrix necessary for modal vector orthogonality (typically the mass matrix) is contained within the reciprocal model matrix. The underlying goal of this work is mostly directed toward observing the modal state responses in the presence of unknown, possibly closed loop forcing functions, thus having an impact on both operating data analysis techniques and independent modal space control techniques. This study investigates the behavior of reciprocol modal vectors as modal filters with respect to certain calculation parameters and their performance with perturbed system frequency response data.

Freudinger, Lawrence C.↗

NASA NTRS1991

Development of iterative techniques for the solution of unsteady compressible viscous flows

Efficient iterative solution methods are being developed for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. Thus, the extra work required by iterative schemes can also be designed to perform efficiently on current and future generation scalable, missively parallel machines. An obvious candidate for iteratively solving the system of coupled nonlinear algebraic equations arising in CFD applications is the Newton method. Newton's method was implemented in existing finite difference and finite volume methods. Depending on the complexity of the problem, the number of Newton iterations needed per step to solve the discretized system of equations can, however, vary dramatically from a few to several hundred. Another popular approach based on the classical conjugate gradient method, known as the GMRES (Generalized Minimum Residual) algorithm is investigated. The GMRES algorithm was used in the past by a number of researchers for solving steady viscous and inviscid flow problems with considerable success. Here, the suitability of this algorithm is investigated for solving the system of nonlinear equations that arise in unsteady Navier-Stokes solvers at each time step. Unlike the Newton method which attempts to drive the error in the solution at each and every node down to zero, the GMRES algorithm only seeks to minimize the L2 norm of the error. In the GMRES algorithm the changes in the flow properties from one time step to the next are assumed to be the sum of a set of orthogonal vectors. By choosing the number of vectors to a reasonably small value N (between 5 and 20) the work required for advancing the solution from one time step to the next may be kept to (N+1) times that of a noniterative scheme. Many of the operations required by the GMRES algorithm such as matrix-vector multiplies, matrix additions and subtractions can all be vectorized and parallelized efficiently.

Sankar, Lakshmi N.↗

NASA NTRS1990

Spacecraft preliminary orbit determination using tracking measurements obtained from the Tracking and Data Relay Satellite System (TDRSS) and the Ground Spaceflight Tracking and Data Network (GSTDN)

In order to validate the operational and computational capabilities of the Preliminary Orbit Determination System (PODS), tests were performed using tracking measurements for several systems including the ERB satellite, the SMM, the STS and Landsat-4. POD procedures are utilized to generate a state vector following an unplanned orbital perturbation or spacecraft maneuver, when an estimation process such as a differential correction orbit determination cannot obtain a solution. Results are presented to demonstrate POD for several situations involving different qualities of a priori target state vectors, data type combinations, data arc lengths, and mixtures of single-TDRS, dual-TDRS, and GSTDN measurements. The system's ability to determine accurately the state vector for the spacecraft and the effectiveness of the solution screening process are discussed. It is shown that PODS is capable of determining a spacecraft vector when differential correction orbit determination processes fail.

Kirschner, S. M.↗

NASA NTRS1989

An alternative design for a sparse distributed memory

A new design for a Sparse Distributed Memory, called the selected-coordinate design, is described. As in the original design, there are a large number of memory locations, each of which may be activated by many different addresses (binary vectors) in a very large address space. Each memory location is defined by specifying ten selected coordinates (bit positions in the address vectors) and a set of corresponding assigned values, consisting of one bit for each selected coordinate. A memory location is activated by an address if, for all ten of the locations's selected coordinates, the corresponding bits in the address vector match the respective assigned value bits, regardless of the other bits in the address vector. Some comparative memory capacity and signal-to-noise ratio estimates for the both the new and original designs are given. A few possible hardware embodiments of the new design are described.

Jaeckel, Louis A.↗

NASA NTRS1991

Analog VLSI neural network integrated circuits

Two analog very large scale integration (VLSI) vector matrix multiplier integrated circuit chips were designed, fabricated, and partially tested. They can perform both vector-matrix and matrix-matrix multiplication operations at high speeds. The 32 by 32 vector-matrix multiplier chip and the 128 by 64 vector-matrix multiplier chip were designed to perform 300 million and 3 billion multiplications per second, respectively. An additional circuit that has been developed is a continuous-time adaptive learning circuit. The performance achieved thus far for this circuit is an adaptivity of 28 dB at 300 KHz and 11 dB at 15 MHz. This circuit has demonstrated greater than two orders of magnitude higher frequency of operation than any previous adaptive learning circuit.

Kub, F. J.↗

NASA NTRS1991

Improved geometric calibration of the SIR-C data

Errors in the determination of the platform state vector (position and velocity) limit the accuracy with which individual pixels in a SAR (synthetic aperture radar) image can be located. A method of updating the state vector based on the SAR data is described. The algorithm combines reference targets at known locations with the estimates available from the mission control center, utilizing a maximum likelihood estimator. The targets can be located at calibration sites or be easily recognizable targets of opportunity. The accuracy of the update depends on the number of targets, their geometry, and the accuracy of their position determination. The algorithm is tested using Seasat SAR data. High-accuracy state vectors were perturbed by Gaussian distributed errors with standard deviations and cross-correlations based on worst-case expectations for SIR-C (Shuttle Imaging Radar). Tests using ground targets located in topographic maps (1:24,000) showed that state vector position errors on the order of 300-400 m and velocity accuracies of 2-3 m/s are readily achievable.

Madsen, S. N.↗

NASA NTRS1990

Efficient solution of parabolic equations by Krylov approximation methods

Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.

Gallopoulos, E.↗

NASA NTRS1991

Autonomous reconfigurable GPS/INS navigation and pointing system for rendezvous and docking

This paper describes the results of an integrated navigation and pointing system software development effort sponsored by the NASA MSFC through a SBIR Phase 2 Program. The integrated Global Positioning System (GPS)/Inertial Navigation System (INS) implements an autonomous navigation filter that is reconfigurable in real-time to accommodate mission contingencies. An onboard expert system monitors the spacecraft status and reconfigures the navigation filter accordingly, to optimize the system performance. The navigation filter is a multi-mode Kalman filter to estimate the spacecraft position, velocity, and attitude. Three different GPS-based attitude determination techniques, namely, velocity vector matching, attitude vector matching, and interferometric processing, are implemented to encompass different mission contingencies. The integrated GPS/INS navigation filter will use any of these techniques depending on the mission phase and the state of the sensors. The first technique, velocity vector matching, uses the GPS velocity measurement to estimate the INS velocity errors and exploits the correlation between INS velocity and attitude errors to estimate the attitude. The second technique, attitude vector matching, uses INS gyro measurements and GPS carrier phase (integrated Doppler) measurements during a spacecraft rotation maneuver to determine the attitude. Both of these techniques require only one GPS antenna onboard to determine the spacecraft attitude. The third technique, interferometric processing, requires use of multiple GPS antennae. In order to determine 3-axis body attitude, three GPS antennae (2 no-coplanor baselines) are required.

Upadhyay, Triveni N.↗

NASA NTRS1990

Using a multifrontal sparse solver in a high performance, finite element code

We consider the performance of the finite element method on a vector supercomputer. The computationally intensive parts of the finite element method are typically the individual element forms and the solution of the global stiffness matrix both of which are vectorized in high performance codes. To further increase throughput, new algorithms are needed. We compare a multifrontal sparse solver to a traditional skyline solver in a finite element code on a vector supercomputer. The multifrontal solver uses the Multiple-Minimum Degree reordering heuristic to reduce the number of operations required to factor a sparse matrix and full matrix computational kernels (e.g., BLAS3) to enhance vector performance. The net result in an order-of-magnitude reduction in run time for a finite element application on one processor of a Cray X-MP.

King, Scott D.↗

NASA NTRS1992

Efficient use of high performance computers for integrated controls and structures design

Simply transporting design codes from sequential-scalar computers to parallel-vector computers does not fully utilize the computational benefits offered by high performance computers. By performing integrated controls and structures design on an experimental truss platform with both sequential-scalar and parallel-vector design codes, conclusive results are presented to substantiate this claim. The efficiency of a Cholesky factorization scheme in conjunction with a variable-band row data structure is presented. In addition, the Lanczos eigensolution algorithm has been incorporated in the design code for both parallel and vector computations. Comparisons of computational efficiency between the initial design code and the parallel-vector design code are presented. It is shown that the Lanczos algorithm with the Cholesky factorization scheme is far superior to the sub-space iteration method of eigensolution when substantial numbers of eigenvectors are required for control design and/or performance optimization. Integrated design results show the need for continued efficiency studies in the area of element computations and matrix assembly.

Belvin, W. K.↗

NASA NTRS1993

A Lanczos algorithm for vibration, suckling and termal analysis

This paper reviews an eigensolver algorithm based on the Lanczos Method for vibration, buckling and thermal analysis. The original code was written for inclusion in the Computational Mechanics Testbed (COMET), a general purpose finite element code. A portable version of the Lanczos code that is optimized for high-performance supercomputers has been developed. Special features of the algorithm include the capability to compute rigid body modes, thermal modes and Lanczos vectors that are derived from the applied load vector. The latter is necessary when using the Lanczos vectors as reduced-basis vectors in transient structural response and transient heat conduction calculations. The modularity of the code allows the user the option of including the most up-to-date utilities, such as the equation solver best suited for the application. The algorithm is discussed in detail and results of several applications are presented. Timing results for a vibration application indicate that the Lanczos algorithm is twenty times faster than the subspace iteration method which has been extensively used in the past.

Bostic, Susan W.↗

NASA NTRS1994

Recent Developments In Theory Of Balanced Linear Systems

Report presents theoretical study of some issues of controllability and observability of system represented by linear, time-invariant mathematical model of the form. x = Ax + Bu, y = Cx + Du, x(0) = xo where x is n-dimensional vector representing state of system; u is p-dimensional vector representing control input to system; y is q-dimensional vector representing output of system; n,p, and q are integers; x(0) is intial (zero-time) state vector; and set of matrices (A,B,C,D) said to constitute state-space representation of system.

Gawronski, Wodek↗