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At least 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Empirical State Error Covariance Matrix for Batch Estimation

State estimation techniques effectively provide mean state estimates. However, the theoretical state error covariance matrices provided as part of these techniques often suffer from a lack of confidence in their abilities to describe the true uncertainty in the estimated states. By a reinterpretation of the equations involved in the weighted least squares algorithm, it is possible to directly arrive at an empirical state error covariance matrix. This proposed empirical state error covariance matrix will contain the effect of all error sources, known or unknown. Results are presented for a simple, two observer, measurement error only problem.

Estimation↗
NASA NTRSDate not supplied

Composite Materials Handbook 17 (CMH-17) Volume 5—Ceramic Matrix Composites

The Composite Materials Handbook‐17 (CMH‐17) Volume 5 for Ceramic Matrix Composites (formerly MIL-HANDBOOK-17) provides the information and guidance necessary to design, fabricate, and implement ceramic matrix composite (CMC) components in aviation applications. This presentation provides an overview of the handbook content, and covers the objectives and activities of the Working Groups that are preparing new content and revising existing text for the next revision. The five Working Groups are: 1) Data Review, 2) Testing, 3) Materials & Processes, 4) Design & Analysis, and 5) Engine Applications. The goal is to release Revision B in 2023. While the handbook is focused on the application of SiC/SiC and Ox/Ox CMCs and EBCs (environmental barrier coatings), the methodologies (testing, data analysis, characterization, etc.) are also applicable to other CMC systems, and the intent is to start incorporating information for Carbon/Carbon (C/C) composites.

Environmental barrier coating (EBC)↗
NASA NTRS1969

Estimating reliability by application of matrix representation

Technique based upon matrix representation and matrix collapsing calculates the probability of successfully completing manned missions and of returning the spacecrew safely to earth. This technique provides analytic expressions for each subsystem, making it possible to relate changes in subsystem reliability directly to mission success and crew safety.

Austin, W. L.↗
NASA NTRS1969

Derivation of a matrix identity.

Matrix identity associated with linear digital filtering and recursive estimating determined using matrix projection operators and properties

Hemami, H.↗
NASA NTRS1972

Application of the matrix exponential kernel

A point matrix kernel for radiation transport, developed by the transmission matrix method, has been used to develop buildup factors and energy spectra through slab layers of different materials for a point isotropic source. Combinations of lead-water slabs were chosen for examples because of the extreme differences in shielding properties of these two materials.

Rohach, A. F.↗
NASA NTRS1972

Matrix transformations for spacecraft attitude determination

A common problem for experimental space physicists is the determination of the attitude matrix T which transforms vectors between representations in X and X' coordinate systems according to (vector V sub X) = (T sub XX')(vector V sub X'). A straightforward, simple, and efficient solution for the transformation matrix is a double-cross transformation. It is calculated from any two directions A and B, which are vectors normalized to unit length and are known in both X and X' coordinates. The B direction need be known only well enough to define the plane in which vectors A and B lie. The problem of the intersection of two cones as applicable to attitude solutions is also discussed.

Cauffman, D. P.↗
NASA NTRS1972

Generation of the invariant coefficients of the characteristic polynomial for an nxn matrix

In theories of numerical stability, roots to a characteristic polynomial are sought, which, in the case of the predictor with iterative correction method of numerical integration, are eigenvalues of a matrix whose elements depend on the coefficients used in the integration process. The characteristic polynomial is displayed explicitly in terms of the elements of the characteristic matrix.

Beaudet, P. R.↗
NASA NTRS1972

An efficient algorithm using matrix methods to solve wind tunnel force-balance equations

An iterative procedure applying matrix methods to accomplish an efficient algorithm for automatic computer reduction of wind-tunnel force-balance data has been developed. Balance equations are expressed in a matrix form that is convenient for storing balance sensitivities and interaction coefficient values for online or offline batch data reduction. The convergence of the iterative values to a unique solution of this system of equations is investigated, and it is shown that for balances which satisfy the criteria discussed, this type of solution does occur. Methods for making sensitivity adjustments and initial load effect considerations in wind-tunnel applications are also discussed, and the logic for determining the convergence accuracy limits for the iterative solution is given. This more efficient data reduction program is compared with the technique presently in use at the NASA Langley Research Center, and computational times on the order of one-third or less are demonstrated by use of this new program.

Smith, D. L.↗
NASA NTRS1972

Theorems on symmetrics and flux conservation in radiative transfer using the matrix operator theory

The matrix operator approach to radiative transfer is shown to be a very powerful technique in establishing symmetry relations for multiple scattering in inhomogeneous atmospheres. Symmetries are derived for the reflection and transmission operators using only the symmetry of the phase function. These results will mean large savings in computer time and storage for performing calculations for realistic planetary atmospheres using this method. The results have also been extended to establish a condition on the reflection matrix of a boundary in order to preserve reciprocity. Finally energy conservation is rigorously proven for conservative scattering in inhomogeneous atmospheres.

Kattawar, G. W.↗
NASA NTRS1971

An explicit form of the Mie phase matrix for multiple scattering calculations in the I, Q, U, and V representation

An explicit expression is obtained for the phase matrix in the I, Q, U, and V Stokes vector representation for a system containing a polydispersion of spherical particles. All of the symmetry relations derived by Hovenier using general arguments are established explicitly. Convenient algorithms are given for the computation of the phase matrix for a spherical polydispersion. Since this theory is so vitally important in radiative transfer, many researchers will need to compute these functions for realistic aerosols distributions. Therefore, results are presented for a haze L distribution so that other researchers will have a way of checking their programs which compute these quantities.

Kattawar, G. W.↗
NASA NTRS1972

Significance criteria for variance matrix applications.

A significance criterion is proposed that compares the strength parameter against the parameter expected from a random group of vectors in variance matrix applications. The variance matrix technique for determining preference or avoidance directions in space for a group of vectors gives only the parameter indicating the strength of the preference or avoidance, and the proposed criterion is shown to be of help in the achievement of reliability.

Siscoe, G. L.↗