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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 379 records · Page 21
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NASA NTRS1974

Reversal-bounded multipushdown machines

Several representations of the recursively enumerable (r.e.) sets are presented. The first states that every r.e. set is the homomorphic image of the intersection of two linear context-free languages. The second states that every r.e. set is accepted by an on-line Turing acceptor with two pushdown stores such that in every computation, each pushdown store can make at most one reversal (that is, one change from 'pushing' to 'popping'). It is shown that this automata theoretic representation cannot be strengthened by restricting the acceptors to be deterministic multitape, nondeterministic one-tape, or nondeterministic multicounter acceptors. This provides evidence that reversal bounds are not a natural measure of computational complexity for multitape Turing acceptors.

Baker, B. S.↗
NASA NTRS1975

A least mean squares CUBIC algorithm for on-line differential of sampled analog signals

A digital computer algorithm is developed for on-line time differentiation of sampled analog voltage signals. The derivative is obtained by employing a least mean squares technique. The recursive algorithm results in a considerable reduction in computer time compared to a complete new solution of the normal equations each time a new data point is accepted. Implementation of the algorithm on a digital computer is discussed. Examples are simulated on a DEC PDP-8 computer.

Allum, J. H. J.↗
NASA NTRS1975

The treatment of bias in the square-root information filter/smoother

The Dyer-McReynolds square-root information filter (SRIF) is rederived, using recursive least-square arguments. The result is applied to a system composed partly of biases. The filter sensitivity matrix, computed covariance, and consider covariance for this augmented system are reviewed. A new computationally attractive representation for the smoothed estimates, in terms of a smoothed sensitivity matrix and a smoothed computed covariance is presented.

Bierman, G. J.↗
NASA NTRS1975

Stability criteria for two-variable polynomials

Recursive algebraic algorithms are developed for testing various stability properties of two-variable polynomials in finite number of steps. Stability is tested with respect to either the half plane or the unit circle applying the equivalent of the Routh or Marden test only two times, regardless of the degree of the polynomial.

Siljak, D. D.↗
NASA NTRS1975

Stability criteria for two-variable polynomials

Recursive algebraic algorithms are developed for testing various stability properties of two-variable polynomials in a finite number of steps. Stability is tested with respect to either the half-plane or the unit circle applying only two times the equivalent of the Routh or Marden test, regardless of the degree of the polynomial.

Siljak, D. D.↗
NASA NTRS1975

Diagrammatic technique for calculating matrix elements of collective operators in superradiance

Adopting the so-called genealogical construction, one can express the eigenstates of collective operators corresponding to a specified mode for an N-atom system in terms of those for an (N-1) atom system. Using these Dicke states as bases and using the Wigner-Eckart theorem, a matrix element of a collective operator of an arbitrary mode can be written as the product of an m-dependent factor and an m-independent reduced matrix element (RME). A set of recursion formulas for the RME is obtained. A graphical representation of the RME on the branching diagram for binary irreducible representations of permutation groups is then introduced. This gives a simple and systematic way of calculating the RME. This method is especially useful when the cooperation number r is close to N/2, where almost exact asymptotic expressions can be obtained easily. The result shows explicity the geometry dependence of superradiance and the relative importance of r-conserving and r-nonconserving processes.

Lee, C. T.↗
NASA NTRS1975

Ground truth applications to orbit refinements

A weighted least-squares recursive estimator program is reported for simulating spacecraft orbital position by analyzing earth and sun sensor data. The program uses constant time adjustment for a set of ephemeris data to eliminate intrack error and to improve attitude determination accuracy.

White, R. L.↗
NASA NTRS1975

A two parameter survey of periodic orbits in the restricted problem of three bodies

Within the context of the restricted problem of three bodies the effects caused by varying the mass ratio of the primaries and the eccentricity of their orbits, upon periodic orbits of the infinitesimal mass which are numerical continuations of circular orbits in the ordinary problem of two bodies are shown. A recursive power series technique is used to numerically integrate the equations of motion as well as the first variational equations in order to generate a two parameter family of perodic orbits and identify the linear stability characteristics. Seven such families are investigated with equally spaced mass ratios from 0.0 to 1.0 and eccentricities of the orbits of the primaries in a range 0.0 to 0.6. Stable orbits are associated with large distances of the infinitesimal mass from the perturbing primary, nearly circular motion of the primaries, and small mass ratios of the primaries. Unstable orbits for the infinitesimal mass are associated with small distances from the perturbing primary, highly elliptic orbits of the primaries and large mass ratios.

Shelus, P. J.↗
NASA NTRS1976

On the role of dimensionality and sample size for unstructured and structured covariance matrix estimation

The experimental observation that a surprisingly small sample size vis-a-vis dimension is needed to achieve good signal-to-interference ratio (SIR) performance with an adaptive predetection filter is explained. The adaptive filter requires estimates as obtained by a recursive stochastic algorithm of the inverse of the filter input data covariance matrix. The SIR performance with sample size is compared for the situations where the covariance matrix estimates are of unstructured (generalized) form and of structured (finite Toeplitz) form; the latter case is consistent with weak stationarity of the input data stochastic process.

Morgera, S. D.↗
NASA NTRS1976

Cubic spline function interpolation in atmosphere models for the software development laboratory: Formulation and data

A tabulation of selected altitude-correlated values of pressure, density, speed of sound, and coefficient of viscosity for each of six models of the atmosphere is presented in block data format. Interpolation for the desired atmospheric parameters is performed by using cubic spline functions. The recursive relations necessary to compute the cubic spline function coefficients are derived and implemented in subroutine form. Three companion subprograms, which form the preprocessor and processor, are also presented. These subprograms, together with the data element, compose the spline fit atmosphere package. Detailed FLOWGM flow charts and FORTRAN listings of the atmosphere package are presented in the appendix.

Kirkpatrick, J. C.↗
NASA NTRS1975

On the time-weighted quadratic sum of linear discrete systems

A method is proposed for obtaining the time-weighted quadratic sum for linear discrete systems. The formula of the weighted quadratic sum is obtained from matrix z-transform formulation. In addition, it is shown that this quadratic sum can be derived in a recursive form for several useful weighted functions. The discussion presented parallels that of MacFarlane (1963) for weighted quadratic integral for linear continuous systems.

Jury, E. I.↗
NASA NTRS1976

Optimization of multi-constrained structures based on optimality criteria

A weight-reduction algorithm is developed for the optimal design of structures subject to several multibehavioral inequality constraints. The structural weight is considered to depend linearly on the design variables. The algorithm incorporates a simple recursion formula derived from the Kuhn-Tucker necessary conditions for optimality, associated with a procedure to delete nonactive constraints based on the Gauss-Seidel iterative method for linear systems. A number of example problems is studied, including typical truss structures and simplified wings subject to static loads and with constraints imposed on stresses and displacements. For one of the latter structures, constraints on the fundamental natural frequency and flutter speed are also imposed. The results obtained show that the method is fast, efficient, and general when compared to other competing techniques. Extensions to the generality of the method to include equality constraints and nonlinear merit functions is discussed.

Rizzi, P.↗
NASA NTRS1976

DHARMA - Discriminant hyperplane abstracting residuals minimization algorithm for separating clusters with fuzzy boundaries

Learning of discriminant hyperplanes in imperfectly supervised or unsupervised training sample sets with unreliably labeled samples along the fuzzy joint boundaries between sample clusters is discussed, with the discriminant hyperplane designed to be a least-squares fit to the unreliably labeled data points. (Samples along the fuzzy boundary jump back and forth from one cluster to the other in recursive cluster stabilization and are considered unreliably labeled.) Minimization of the distances of these unreliably labeled samples from the hyperplanes does not sacrifice the ability to discriminate between classes represented by reliably labeled subsets of samples. An equivalent unconstrained linear inequality problem is formulated and algorithms for its solution are indicated. Landsat earth sensing data were used in confirming the validity and computational feasibility of the approach, which should be useful in deriving discriminant hyperplanes separating clusters with fuzzy boundaries, given supervised training sample sets with unreliably labeled boundary samples.

Dasarathy, B. V.↗
NASA NTRS1976

A finite difference method of solving anisotropic scattering problems

A new method of solving radiative transfer problems is described including a comparison of its speed with that of the doubling method, and a discussion of its accuracy and suitability for computations involving variable optical properties. The method uses a discretization in angle to produce a coupled set of first-order differential equations which are integrated between discrete depth points to produce a set of recursion relations for symmetric and anti-symmetric angular sums of the radiation field at alternate depth points. The formulation given here includes depth-dependent anisotropic scattering, absorption, and internal sources, and allows arbitrary combinations of specular and non-Lambertian diffuse reflection at either or both boundaries. Numerical tests of the method show that it can return accurate emergent intensities even for large optical depths. The method is also shown to conserve flux to machine accuracy in conservative atmospheres

Barkstrom, B. R.↗
NASA NTRS1976

Expansion of the gravitational potential with computerized Poisson series

The paper describes a recursive formulation for the expansion of the gravitational potential valid for both the tesseral and zonal harmonics. The expansion is primarily in rectangular coordinates, but the classical orbit elements or equinoctial orbit elements can be easily substituted. The equations of motion for the zonal harmonics in both classical and equinoctial orbital elements are described in a form which will result in closed-form expressions for the first-order perturbations. In order to achieve this result, the true longitude or true anomaly have to be used as independent variables.

Broucke, R.↗
NASA NTRS1975

Some estimation formulae for continuous time-invariant linear systems

In this brief paper we examine a Riccati equation decomposition due to Reid and Lainiotis and apply the result to the continuous time-invariant linear filtering problem. Exploitation of the time-invariant structure leads to integration-free covariance recursions which are of use in covariance analyses and in filter implementations. A super-linearly convergent iterative solution to the algebraic Riccati equation (ARE) is developed. The resulting algorithm, arranged in a square-root form, is thought to be numerically stable and competitive with other ARE solution methods. Certain covariance relations that are relevant to the fixed-point and fixed-lag smoothing problems are also discussed.

Bierman, G. J.↗