On minimal partial realizations of a linear input/output map
Minimal partial realizations of linear input/output map, discussing significance in regard to adaptive dynamics identification procedures
Kalman, R. E.↗
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DAA realizations of attitude algorithms
The attitude algorithms applied to strapdown inertial platforms are discussed. A review of six attitude transformation algorithms and the realizations of these algorithms by digital differential analyzers are presented. The number of digital differential analyzers for each algorithm is either smaller than or equal to that obtained by others.
Hung, J. C.↗
DDA realizations of attitude algorithms.
Digital differential analyzer (DDA) realization of the direction cosine, Euler angle, and quaternion algorithms. It is shown that, for any one of the three attitude algorithms, 27 DDAs are needed. This number is considerably smaller than those obtained by others for the cases of Euler angle and quaternion algorithms.
Yeh, Y.↗
Digital filter realizations using a special-purpose stored-program computer.
A special-purpose computer is organized to realize a second-order digital filter in a choice of 11 programming forms. Instructions for the forms are stored in a fast-access READ-ONLY memory. Also, a hard-wired multiplier is employed in the Arithmetic Unit to decrease computation time. The multiplier is organized into uniform functional blocks that are suitable for large-scale integration (LSI). A computer-aided design (CAD) program may be used to select the best filter programming form for a given filter transfer function D(z). The CAD program also aids in the location of the binary point in the data registers of the computer.
White, R.↗
New hardware realizations of nonrecursive digital filters.
Analysis of the bit-level operations involved in the convolution realizing a nonrecursive digital filter leads to hardware designs of digital filters based on the operation of counting. Two distinct designs are outlined: the first one is capable of very high speed but is rather expensive; the second is quite slow but has the advantages of low cost and high flexibility. The basic designs considered utilize fixed-point representation for the data and filter coefficients. Variants allowing floating-point representation of the coefficients are also described.
Zohar, S.↗
An equal-valued capacitor active RC network realization of a fourth-order low-pass Butterworth characteristic
This letter describes an active RC network which realizes a fourth-order low-pass Butterworth characteristic. It requires one active element and has the practical advantage that all capacitors have the same value. A design chart is included.
Huelsman, L. P.↗
The realization of arithmetic processors for delta modulation encoded signals
The design and realization of digital devices which add or multiply delta modulation (DM) encoded signals are presented. These systems operate directly on the DM bit stream. It is shown that the devices can be constructed using standard digital hardware and that the hardware complexity needed to add or multiply the two DM encoded signals is equivalent to that needed for pulse code modulation (PCM) signals. Experimental results are presented showing the operation of these systems. The results obtained by adding or multiplying DM encoded signals are compared with those obtained using PCM encoded signals on the basis of signal-to-noise ratio (SNR). A spectral-analysis technique applicable to a DM encoded signal is developed to obtain SNR curves.
Locicero, J. L.↗
An algorithm for obtaining the minimal realization of a linear time-invariant system and determining if a system is stabilizable-detectable
A definition of centralized fixed modes of a system, which is an adoption of the definition of fixed modes for a decentralized system is made. It is shown that the centralized fixed modes of a system can be easily and efficiently calculated in terms of the eigenvalues of the system, and that the calculation of such fixed modes enables one to determine, in a numerically efficient way, whether a system is controllable, observable, stabilizable, or detectable. An efficient algorithm for reducing a system to minimal realization form is then given. The algorithms have been effectively used on systems of order up to 100.
Davison, E. J.↗
The geometry of the partial realization problem
It is shown that the space of sequences of length n which have an extrapolation of McMillan degree k, and no extrapolations of lower McMillan degree can be given the structure of a differentiable manifold. This approach makes the proof of certain known results on the partial realization problem quite straightforward and makes it possible to establish some important new results as well. A key tool is the fact, proven here, that the set of n by a real Hankel matrices of rank r is a manifold with r+1 connected components.
Brockett, R. W.↗
Galileo spacecraft modal identification using an eigensystem realization algorithm
A modal parameter identification technique referred to as the Eigensystem Realization Algorithm (ERA) was applied to free-response measurements from the Galileo spacecraft modal survey test. The data were recorded following single-point random excitation of the structure. This work is one phase in a research project coordinated by the Jet Propulsion Laboratory to compare the performance of various contemporary identification techniques using Galileo data. Principal emphasis is placed on estimating the accuracy of the ERA-identified modal parameters. Various accuracy indicators, such as Modal Amplitude Coherence and Modal Phase Collinearity, are discussed. More than 20 modes of the spacecraft were identified, demonstrating the ability of the ERA method to determine the dynamics of such complex structures using only a few seconds of test data.
Pappa, R. S.↗
An Eigensystem Realization Algorithm for Application to Modal Testing
Important features of the Eigensystem Realization Algorithm (ERA) are summarized as follows: (1) from the computational standpoint, the algorithm is attractive, since only simple numerical operations are needed; (2) the computational procedure is numerically stable; (3) the structural dynamics requirements for modal parameter identification and the control design requirements for a reduced-state space model are satisfied; (4) data from more than one test can be used simultaneously to efficiently identify the closely spaced eigenvalues; and (5) no restrictions on number of measurements are imposed.
Juang, J. N.↗
Mathematical correlation of modal parameter identification methods via system realization theory
A unified approach is introduced using system realization theory to derive and correlate modal parameter identification methods for flexible structures. Several different time-domain and frequency-domain methods are analyzed and treated. A basic mathematical foundation is presented which provides insight into the field of modal parameter identification for comparison and evaluation. The relation among various existing methods is established and discussed. This report serves as a starting point to stimulate additional research towards the unification of the many possible approaches for modal parameter identification.
Juang, J. N.↗
On realizations of least-squares estimation and Kalman filtering by systolic arrays
Least-squares (LS) estimation is a basic operation in many signal processing problems. Given y = Ax + v, where A is a m x n coefficient matrix, y is a m x 1 observation vector, and v is a m x 1 zero mean white noise vector, a simple least-squares solution is finding the estimated vector x which minimizes the norm of /Ax-y/. It is well known that for an ill-conditioned matrix A, solving least-squares problems by orthogonal triangular (QR) decomposition and back substitution has robust numerical properties under finite word length effect since 2-norm is preserved. Many fast algorithms have been proposed and applied to systolic arrays. Gentleman-Kung (1981) first presented the trianglular systolic array for a basic Givens reduction. McWhirter (1983) used this array structure to find the least-squares estimation errors. Then by geometric approach, several different systolic array realizations of the recursive least-squares estimation algorithms of Lee et al (1981) were derived by Kalson-Yao (1985). Basic QR decomposition algorithms are considered in this paper and it is found that under a one-row time updating situation, the Householder transformation degenerates to a simple Givens reduction. Next, an improved least-squares estimation algorithm is derived by considering a modified version of fast Givens reduction. From this approach, the basic relationship between Givens reduction and Modified-Gram-Schmidt transformation can easily be understood. This improved algorithm also has simpler computational and inter-cell connection complexities while compared with other known least-squares algorithms and is more realistic for systolic array implementation.
Chen, M. J.↗
Numerical synthesis of tri-variate velocity realizations of turbulence
An approach for synthesizing trivariate turbulence velocity field spatial realizations is presented. Some of the spatial frequency characteristics of the random velocity field are described by the von Karman spectrum. The simulation algorithm is based on an efficient autoregressive-moving average (ARMA) scheme involving coefficient square matrices of order three. The determination of the efficient low order ARMA algorithm is preceded by the determination of a suitable high order autoregressive (AR) simulation algorithm. The numerical results are presented in a dimensionless form. Thus, they are applicable for any scale of turbulence.
Spanos, P.-T. D.↗
Mathematical correlation of modal-parameter-identification methods via system-realization theory
A unified approach is introduced using system-realization theory to derive and correlate modal-parameter-identification methods for flexible structures. Several different time-domain methods are analyzed and treated. A basic mathematical foundation is presented which provides insight into the field of modal-parameter identification for comparison and evaluation. The relation among various existing methods is established and discussed. This report serves as a starting point to stimulate additional research toward the unification of the many possible approaches for modal-parameter identification.
Juang, Jer-Nan↗
Realization of an inertial reference frame from Mark III VLBI
Over 350,000 dual frequency Mark III VLBI observations from several geodetic and astrometric observing programs have been used to realize an inertial reference frame through the positions of 325 compact extragalactic radio sources uniformly distributed over the sky with standard errors typically under 1 milliarcsecond (mas). Internal and external tests indicate that the reference frame defined by the relative positions of these radio sources should be accurate and stable at the 1-2 mas level. Because the conventional precession and nutation models are adjusted in the estimation of the source positions, the positions and relative angles are not degraded over the interval of observations or at epochs away from the reference epoch.
Ma, C.↗
Eigensystem realization algorithm modal identification experiences with mini-mast
This paper summarizes work performed under a collaborative research effort between the National Aeronautics and Space Administration (NASA) and the German Aerospace Research Establishment (DLR, Deutsche Forschungsanstalt fur Luft- und Raumfahrt). The objective is to develop and demonstrate system identification technology for future large space structures. Recent experiences using the Eigensystem Realization Algorithm (ERA), for modal identification of Mini-Mast, are reported. Mini-Mast is a 20 m long deployable space truss used for structural dynamics and active vibration-control research at the Langley Research Center. A comprehensive analysis of 306 frequency response functions (3 excitation forces and 102 displacement responses) was performed. Emphasis is placed on two topics of current research: (1) gaining an improved understanding of ERA performance characteristics (theory vs. practice); and (2) developing reliable techniques to improve identification results for complex experimental data. Because of nonlinearities and numerous local modes, modal identification of Mini-Mast proved to be surprisingly difficult. Methods were available, ERA, for obtaining detailed, high-confidence results.
Pappa, Richard S.↗
Approximate truncated balanced realizations for infinite dimensional systems
This paper presents an approximate method for obtaining truncated balance realizations of systems represented by non-rational transfer functions, that is infinite dimensional systems. It is based on the approximation to the Hankel operator.
Hartley, Tom T.↗