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At least 181 records · Page 10

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NASA NTRS1976

Regions of constrained maximum likelihood parameter identifiability

This short paper considers the parameter-identification problem of general discrete-time, nonlinear, multiple input-multiple output dynamic systems with Gaussian white distributed measurement errors. Knowledge of the system parameterization is assumed to be available. Regions of constrained maximum likelihood (CML) parameter identifiability are established. A computation procedure employing interval arithmetic is proposed for finding explicit regions of parameter identifiability for the case of linear systems.

Lee, C.-H.↗

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

A variant of nested dissection for solving n by n grid problems

Nested dissection orderings are known to be very effective for solving the sparse positive definite linear systems which arise from n by n grid problems. In this paper nested dissection is shown to be the final step of incomplete nested dissection, an ordering which corresponds to the premature termination of dissection. Analyses of the arithmetic and storage requirements for incomplete nested dissection are given, and the ordering is shown to be competitive with nested dissection under certain conditions.

George, A.↗

NASA NTRS1977

Exact solution of some linear matrix equations using algebraic methods

A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.

Djaferis, T. E.↗

NASA NTRS1977

Matrix computations in MACSYMA

Facilities built into MACSYMA for manipulating matrices with numeric or symbolic entries are described. Computations will be done exactly, keeping symbols as symbols. Topics discussed include how to form a matrix and create other matrices by transforming existing matrices within MACSYMA; arithmetic and other computation with matrices; and user control of computational processes through the use of optional variables. Two algorithms designed for sparse matrices are given. The computing times of several different ways to compute the determinant of a matrix are compared.

Wang, P. S.↗

NASA NTRS1975

Gram-Schmidt algorithms for covariance propagation

This paper addresses the time propagation of triangular covariance factors. Attention is focused on the square-root free factorization, P = UDU/T/, where U is unit upper triangular and D is diagonal. An efficient and reliable algorithm for U-D propagation is derived which employs Gram-Schmidt orthogonalization. Partitioning the state vector to distinguish bias and colored process noise parameters increases mapping efficiency. Cost comparisons of the U-D, Schmidt square-root covariance and conventional covariance propagation methods are made using weighted arithmetic operation counts. The U-D time update is shown to be less costly than the Schmidt method; and, except in unusual circumstances, it is within 20% of the cost of conventional propagation.

Thornton, C. L.↗

NASA NTRS1975

Regions of constrained maximum likelihood parameter identifiability

This paper considers the parameter identification problem of general discrete-time, nonlinear, multiple-input/multiple-output dynamic systems with Gaussian-white distributed measurement errors. Knowledge of the system parameterization is assumed to be known. Regions of constrained maximum likelihood (CML) parameter identifiability are established. A computation procedure employing interval arithmetic is proposed for finding explicit regions of parameter identifiability for the case of linear systems. It is shown that if the vector of true parameters is locally CML identifiable, then with probability one, the vector of true parameters is a unique maximal point of the maximum likelihood function in the region of parameter identifiability and the CML estimation sequence will converge to the true parameters.

Lee, C.-H.↗

NASA NTRS1977

Gram-Schmidt algorithms for covariance propagation

This paper addresses the time propagation of triangular covariance factors. Attention is focused on the square-root free factorization, P = UD(transpose of U), where U is unit upper triangular and D is diagonal. An efficient and reliable algorithm for U-D propagation is derived which employs Gram-Schmidt orthogonalization. Partitioning the state vector to distinguish bias and coloured process noise parameters increase mapping efficiency. Cost comparisons of the U-D, Schmidt square-root covariance and conventional covariance propagation methods are made using weighted arithmetic operation counts. The U-D time update is shown to be less costly than the Schmidt method; and, except in unusual circumstances, it is within 20% of the cost of conventional propagation.

Thornton, C. L.↗

NASA NTRS1977

A mini/microcomputer-based land use information system

The paper describes the Multipurpose Interactive NASA Information System (MINIS), a data management system for land-use applications. MINIS is written nearly entirely in FORTRAN IV, and has a full range of conditional, Boolean and arithmetic commands, as well as extensive format control and the capability of interactive file creation and updating. It requires a mini or microcomputer with at least 64 K of core or semiconductor memory. MINIS has its own equation-oriented query language for retrieval from different kinds of data bases. It features a graphics output which permits output of overlay maps. Some experience of the U.S. Department of Agriculture and the Tennessee State Planning Office with MINIS is discussed.

Seitz, R. N.↗

NASA NTRS1977

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.↗

NASA NTRS1976

Numerical comparison of discrete Kalman filter algorithms - Orbit determination case study

Bierman, G. J.↗

NASA NTRS1976

Laser velocimeter measurements in a large transonic wind tunnel

A two-component fringe type laser velocimeter operated in the backscatter mode was used to measure the free-stream velocity in an undisturbed flow field in a wind-tunnel test section from Mach 0.2 to Mach 1.0 and to measure the velocity along the stagnating streamline of a hemisphere model from Mach 0.2 to Mach 0.8. Burst signals from the laser velocimeter were processed by high-speed burst counters, and histograms of the number of occurrences of a particular counter output were collected by means of a pulse height analyzer. Arithmetic means of the histograms were calculated, and the results were compared with predicted local gas velocities with allowance for the lag of the scattering particles with respect to the gas flow. The free-stream measurements were accurate to within 2% of the calibration measurements. The stagnation streamline measurements show trends similar to theoretical predictions.

Meyers, J. F.↗

NASA NTRS1977

The roles of body mass and gravity in determining the energy requirements of homoiotherms

Studies by Kleiber and by Brody in the 1930's established the 3/4 power of body weight as the unit of metabolic size for homoiotherms. Later Kleiber conceived of the energy requirement as a composite function, with a thermoregulatory component that is proportional to heat loss, and an antigravity component that is directly proportional to body weight. Maintenance feed requirements (F) have been measured with groups of small animals chronically exposed to several acceleration fields (G). Analysis of the results leads to an arithmetic relationship between the maintenance requirement and acceleration field strength: F sub G = F sub 0 + kG. When the equations are compared for groups of different body size, F sub 0 tends to vary between the 0.4 and 0.5 power of body mass - and k tends to be the same, irrespective of body mass. These findings tend to confirm the Kleiber concept of a composite nature of homoiotherm maintenance requirements.

Smith, A. H.↗

NASA NTRS1977

NASTRAN finite element idealization study

The investigation of the effects of variations of mesh refinement and mesh pattern were conducted using a basic rectangular mesh pattern. When employing the constant strain TRMEM element, the basic rectangular pattern was subdivided into triangles. This subdivision employs two different triangular patterns and allows results to be obtained which demonstrate the effect of modelling bias. Errors in tip deflection, direct stress, and shearing stress as a function of mesh size and element aspect ratio were obtained as well as mid-span stress distributions. All problems were solved on an IBM 360/95 computer using MacNeal-Schwendler Version MSC-38 Rigid Format-1 of the NASTRAN computer program. While NASTRAN uses double precision arithmetic for the solution of the global equations for displacements, subsequent computations to obtain element stresses are carried out in single precision. This suggests that some improvement in stress recovery might be expected when using the higher precision DCD machines.

Case, W. R.↗

NASA NTRS1978

A decoding procedure for the Reed-Solomon codes

A decoding procedure is described for the (n,k) t-error-correcting Reed-Solomon (RS) code, and an implementation of the (31,15) RS code for the I4-TENEX central system. This code can be used for error correction in large archival memory systems. The principal features of the decoder are a Galois field arithmetic unit implemented by microprogramming a microprocessor, and syndrome calculation by using the g(x) encoding shift register. Complete decoding of the (31,15) code is expected to take less than 500 microsecs. The syndrome calculation is performed by hardware using the encoding shift register and a modified Chien search. The error location polynomial is computed by using Lin's table, which is an interpretation of Berlekamp's iterative algorithm. The error location numbers are calculated by using the Chien search. Finally, the error values are computed by using Forney's method.

Lim, R. S.↗

NASA NTRS1978

Preamplifier Noise in VLF Receivers

Noise specifications for junction field-effect transistors are presented in different ways depending on the particular semiconductor manufacturer. Arithmetic involved in converting these specifications to equivalent RMS noise in microvolts developed at the preamplifier input terminal is reviewed. These methods were useful for estimating the noise performance of high input impedance preamplifiers used with E-field antennas operating in the range of 1 KHz to 10 MHz. Both the JFET MPF-102 transistor and the COS/MOS CA3600 transistor array provided amplification for VLF receivers where the internally generated noise was well below the atmospheric noise level. The CA3600 transistor array provided better performance because of the more symmetrical complementary MOS transistor transfer characteristics than a single N-type biased JFET transistor. The CMOS amplifier resulted in self-compensating gain characteristics over a very wide temperature range from -55 to +125 C.

Burhans, R. W.↗

NASA NTRS1978

Vision-based guidance for an automated roving vehicle

A controller designed to guide an automated vehicle to a specified target without external intervention is described. The intended application is to the requirements of planetary exploration, where substantial autonomy is required because of the prohibitive time lags associated with closed-loop ground control. The guidance algorithm consists of a set of piecewise-linear control laws for velocity and steering commands, and is executable in real time with fixed-point arithmetic. The use of a previously-reported object tracking algorithm for the vision system to provide position feedback data is described. Test results of the control system on a breadboard rover at the Jet Propulsion Laboratory are included.

Griffin, M. D.↗

NASA NTRS1980

Real-time digital integrator

Field programmable logic array (FPLA) is used to make 3-bit arithmetic logic unit (ALU) for large integrator that can be read and cleared while new data is added to begin new integral. Arrangement of device can provide for full carry/lookahead capability with minimum gate delays.

Rubin, A. L.↗