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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS2015

Coupled Inertial Navigation and Flush Air Data Sensing Algorithm for Atmosphere Estimation

This paper describes an algorithm for atmospheric state estimation that is based on a coupling between inertial navigation and flush air data sensing pressure measurements. In this approach, the full navigation state is used in the atmospheric estimation algorithm along with the pressure measurements and a model of the surface pressure distribution to directly estimate atmospheric winds and density using a nonlinear weighted least-squares algorithm. The approach uses a high fidelity model of atmosphere stored in table-look-up form, along with simplified models of that are propagated along the trajectory within the algorithm to provide prior estimates and covariances to aid the air data state solution. Thus, the method is essentially a reduced-order Kalman filter in which the inertial states are taken from the navigation solution and atmospheric states are estimated in the filter. The algorithm is applied to data from the Mars Science Laboratory entry, descent, and landing from August 2012. Reasonable estimates of the atmosphere and winds are produced by the algorithm. The observability of winds along the trajectory are examined using an index based on the discrete-time observability Gramian and the pressure measurement sensitivity matrix. The results indicate that bank reversals are responsible for adding information content to the system. The algorithm is then applied to the design of the pressure measurement system for the Mars 2020 mission. The pressure port layout is optimized to maximize the observability of atmospheric states along the trajectory. Linear covariance analysis is performed to assess estimator performance for a given pressure measurement uncertainty. The results indicate that the new tightly-coupled estimator can produce enhanced estimates of atmospheric states when compared with existing algorithms.

Karlgaard, Christopher D.↗
NASA NTRS1992

Linear analysis of opto-mechanical systems

A general framework is presented for the matrix-form, linear optical model analysis of controlled optomechanical systems; the models are conjoined with linear models of structures and controls to compute system performance as a function of optics, structures, and control parameters. Covariance analysis, optimization, and estimation/simulation are used. Attention is given to a tolerancing example for the Hubble Space Telescope's Wide Field and Planetary Camera, which involves the creation of a linear model of residual pupil shear.

Redding, David C.↗
NASA NTRS2021

Thermal Inspection of a Composite Fuselage Section Using theMethod of Proper Generalized Decomposition

Proper Generalized Decomposition (PGD) is a reduced order modeling technique for the simulation of physical systems whose governing equations depend on boundary conditions, initial conditions, material properties, and geometric parameters. It uses separated representations of system covariates combined with an iterative approximation method known as successive enrichment in order to compute an accurate parameter-dependent approximation to the full governing equations. PGD can also be used as an alternative to the Singular Value Decomposition (SVD) of a matrix and therefore as an alternative to PCA thermography. In this paper PGD was used to analyze data derived from the inspection of a composite fuselage forward section using flash thermography, and the results were compared against the standard PCA approach.

Nondestructive Evaluation↗
NASA NTRS1988

Observability analysis of inertial navigation systems during in-flight alignment

In this work the observability of an Inertial Navigation System (INS) during In-Flight Alignment (IFA) is investigated. A systematic approach to the observability analysis of a piece-wise constant system is presented and its use is justified mathematically. As a tool for the investigation a Stepped Observability Matrix (SOM) is constructed and a corresponding Stepped Space is defined. The INS error model is transformed into the Stepped Space during a specially chosen IFA trajectory and a full observability is carried out. The results of the mathematical analysis are checked against the results of covariance simulation and a full agreement is found between the two. Finally, the practical implications of this analysis are outlined.

Bar-Itzhack, I. Y.↗
NASA NTRS1973

An Iterative Approach to the Feature Selection Problem

The problem dealt with concerns feature selection or reducing the dimension of the data to be processed from n to k. By reducing the dimension of the data from n to k, classification time is generally reduced. Yet the dimension reduction should not be so great that classification accuracy is impaired. Thus, the general problem is considered of classifying an n-dimensional observation vector x into one of m-distinct classes where each class is normally distributed with mean and covariance. It is shown that the probability of misclassification is minimized if a maximum likelihood classification procedure is used to classify the data. The dimension of each observation vector to be processed is conveniently reduced by performing the transformation y = Bx, where B is a K by n matrix of rank k. Thus, the n-dimensional classification problem transforms into a k-dimensional classification problem.

Decell, H. P., Jr.↗
NASA NTRS1979

Algebraic methods for the solution of some linear matrix equations

The characterization of polynomials whose zeros lie in certain algebraic domains (and the unification of the ideas of Hermite and Lyapunov) is the basis for developing finite algorithms for the solution of linear matrix equations. Particular attention is given to equations PA + A'P = Q (the Lyapunov equation) and P - A'PA = Q the (discrete Lyapunov equation). The Lyapunov equation appears in several areas of control theory such as stability theory, optimal control (evaluation of quadratic integrals), stochastic control (evaluation of covariance matrices) and in the solution of the algebraic Riccati equation using Newton's method.

Djaferis, T. E.↗
NASA NTRS1972

Adaptive filtering with correlated state noise

An adaptive filter which uses a minimum variance criteria to estimate state noise covariance is presented. It is not necessary to assume white state noise in order to implement the filter. Simulation results are given which demonstrate that the filter tracks a satellite in the presence of modeling errors better than a conventional minimum variance filter with state noise. It is also shown that the propagated convariance matrix of the filter is an accurate indicator of the filter's performance.

Argentiero, P.↗
NASA NTRS2006

On the Extraction of Angular Velocity from Attitude Measurements

In this paper we research the extraction of the angular rate vector from attitude information without differentiation, in particular from quaternion measurements. We show that instead of using a Kalman filter of some kind, it is possible to obtain good rate estimates, suitable for spacecraft attitude control loop damping, using simple feedback loops, thereby eliminating the need for recurrent covariance computation performed when a Kalman filter is used. This considerably simplifies the computations required for rate estimation in gyro-less spacecraft. Some interesting qualities of the Kalman filter gain are explored, proven and utilized. We examine two kinds of feedback loops, one with varying gain that is proportional to the well known Q matrix, which is computed using the measured quaternion, and the other type of feedback loop is one with constant coefficients. The latter type includes two kinds; namely, a proportional feedback loop, and a proportional-integral feedback loop. The various schemes are examined through simulations and their performance is compared. It is shown that all schemes are adequate for extracting the angular velocity at an accuracy suitable for control loop damping.

Bar-Itzhack, I. Y.↗
NASA NTRS2006

Rigid Body Rate Inference from Attitude Variation

In this paper we research the extraction of the angular rate vector from attitude information without differentiation, in particular from quaternion measurements. We show that instead of using a Kalman filter of some kind, it is possible to obtain good rate estimates, suitable for spacecraft attitude control loop damping, using simple feedback loops, thereby eliminating the need for recurrent covariance computation performed when a Kalman filter is used. This considerably simplifies the computations required for rate estimation in gyro-less spacecraft. Some interesting qualities of the Kalman filter gain are explored, proven and utilized. We examine two kinds of feedback loops, one with varying gain that is proportional to the well known Q matrix, which is computed using the measured quaternion, and the other type of feedback loop is one with constant coefficients. The latter type includes two kinds; namely, a proportional feedback loop, and a proportional-integral feedback loop. The various schemes are examined through simulations and their performance is compared. It is shown that all schemes are adequate for extracting the angular velocity at an accuracy suitable for control loop damping.

Bar-Itzhack, I. Y.↗
NASA NTRS1989

Bilinear modeling and nonlinear estimation

New methods are illustrated for online nonlinear estimation applied to the lateral deflection of an elastic beam on board measurements of angular rates and angular accelerations. The development of the filter equations, together with practical issues of their numerical solution as developed from global linearization by nonlinear output injection are contrasted with the usual method of the extended Kalman filter (EKF). It is shown how nonlinear estimation due to gyroscopic coupling can be implemented as an adaptive covariance filter using off-the-shelf Kalman filter algorithms. The effect of the global linearization by nonlinear output injection is to introduce a change of coordinates in which only the process noise covariance is to be updated in online implementation. This is in contrast to the computational approach which arises in EKF methods arising by local linearization with respect to the current conditional mean. Processing refinements for nonlinear estimation based on optimal, nonlinear interpolation between observations are also highlighted. In these methods the extrapolation of the process dynamics between measurement updates is obtained by replacing a transition matrix with an operator spline that is optimized off-line from responses to selected test inputs.

Dwyer, Thomas A. W., III↗
NASA NTRS1983

Evaluation of the effect of vibration nonlinearity on convergence behavior of adaptive higher harmonic controllers

Effect of nonlinearity on convergence of the local linear and global linear adaptive controllers is evaluated. A nonlinear helicopter vibration model is selected for the evaluation which has sufficient nonlinearity, including multiple minimum, to assess the vibration reduction capability of the adaptive controllers. The adaptive control algorithms are based upon a linear transfer matrix assumption and the presence of nonlinearity has a significant effect on algorithm behavior. Simulation results are presented which demonstrate the importance of the caution property in the global linear controller. Caution is represented by a time varying rate weighting term in the local linear controller and this improves the algorithm convergence. Nonlinearity in some cases causes Kalman filter divergence. Two forms of the Kalman filter covariance equation are investigated.

Molusis, J. A.↗
NASA NTRS2010

Fast Solution in Sparse LDA for Binary Classification

An algorithm that performs sparse linear discriminant analysis (Sparse-LDA) finds near-optimal solutions in far less time than the prior art when specialized to binary classification (of 2 classes). Sparse-LDA is a type of feature- or variable- selection problem with numerous applications in statistics, machine learning, computer vision, computational finance, operations research, and bio-informatics. Because of its combinatorial nature, feature- or variable-selection problems are NP-hard or computationally intractable in cases involving more than 30 variables or features. Therefore, one typically seeks approximate solutions by means of greedy search algorithms. The prior Sparse-LDA algorithm was a greedy algorithm that considered the best variable or feature to add/ delete to/ from its subsets in order to maximally discriminate between multiple classes of data. The present algorithm is designed for the special but prevalent case of 2-class or binary classification (e.g. 1 vs. 0, functioning vs. malfunctioning, or change versus no change). The present algorithm provides near-optimal solutions on large real-world datasets having hundreds or even thousands of variables or features (e.g. selecting the fewest wavelength bands in a hyperspectral sensor to do terrain classification) and does so in typical computation times of minutes as compared to days or weeks as taken by the prior art. Sparse LDA requires solving generalized eigenvalue problems for a large number of variable subsets (represented by the submatrices of the input within-class and between-class covariance matrices). In the general (fullrank) case, the amount of computation scales at least cubically with the number of variables and thus the size of the problems that can be solved is limited accordingly. However, in binary classification, the principal eigenvalues can be found using a special analytic formula, without resorting to costly iterative techniques. The present algorithm exploits this analytic form along with the inherent sequential nature of greedy search itself. Together this enables the use of highly-efficient partitioned-matrix-inverse techniques that result in large speedups of computation in both the forward-selection and backward-elimination stages of greedy algorithms in general.

Moghaddam, Baback↗
NASA NTRS1988

Attitude determination and parameter estimation using vector observations

Procedures for attitude determination based on Wahba's loss function are generalized to include the estimation of parameters other than the attitude, such as sensor biases. Optimization with respect to the attitude requires either the singular value decomposition of a 3x3 matrix or finding the maximum eigenvalue and corresponding eigenvector of a 4x4 symmetric matrix, but does not require an a priori estimate of the attitude. Optimization with respect to the other parameters employs an iterative approach, which does require an a priori estimate of these parameters. Conventional state estimation methods require a priori estimates of both the parameters and the attitude, while the algorithms presented in this paper always compute the exact optimal attitude for given values of the parameters. The proposed method is shown to give the correct solution of an example problem. An expression for the covariance of the attitude and parameter estimates is derived.

Markley, F. Landis↗
NASA NTRS1977

A finite element technique for non-deterministic thermal deformation analyses including temperature dependent material properties

A technique utilizing the finite element displacement method is developed for the static analysis of structures subjected to non-deterministic thermal loading in which the material properties, assumed isotropic, are temperature dependent. Matrix equations are developed for the first two statistical moments of the displacements using a third order series expansion for the displacements in terms of the random temperatures. Sample problems are included to demonstrate the range of applicability of the third order series solutions. These solutions are compared with results from Monte Carlo analyses and also, for some problems, with solutions obtained by numerically integrating equations for the statistical properties of the displacements. In general, it is shown that the effect of temperature dependent material properties can have a significant effect on the covariances of the displacements.

Case, W. R., Jr.↗
NASA NTRS1992

Orbit-determination performance of Doppler data for interplanetary cruise trajectories. Part 1: Error analysis methodology

An error covariance analysis methodology is used to investigate different weighting schemes for two-way (coherent) Doppler data in the presence of transmission-media and observing-platform calibration errors. The analysis focuses on orbit-determination performance in the interplanetary cruise phase of deep-space missions. Analytical models for the Doppler observable and for transmission-media and observing-platform calibration errors are presented, drawn primarily from previous work. Previously published analytical models were improved upon by the following: (1) considering the effects of errors in the calibration of radio signal propagation through the troposphere and ionosphere as well as station-location errors; (2) modelling the spacecraft state transition matrix using a more accurate piecewise-linear approximation to represent the evolution of the spacecraft trajectory; and (3) incorporating Doppler data weighting functions that are functions of elevation angle, which reduce the sensitivity of the estimated spacecraft trajectory to troposphere and ionosphere calibration errors. The analysis is motivated by the need to develop suitable weighting functions for two-way Doppler data acquired at 8.4 GHz (X-band) and 32 GHz (Ka-band). This weighting is likely to be different from that in the weighting functions currently in use; the current functions were constructed originally for use with 2.3 GHz (S-band) Doppler data, which are affected much more strongly by the ionosphere than are the higher frequency data.

Ulvestad, J. S.↗
NASA NTRS1991

Basic research for the geodynamics program

The mathematical models of space very long base interferometry (VLBI) observables suitable for least squares covariance analysis were derived and estimatability problems inherent in the space VLBI system were explored, including a detailed rank defect analysis and sensitivity analysis. An important aim is to carry out a comparative analysis of the mathematical models of the ground-based VLBI and space VLBI observables in order to describe the background in detail. Computer programs were developed in order to check the relations, assess errors, and analyze sensitivity. In order to investigate the estimatability of different geodetic and geodynamic parameters from the space VLBI observables, the mathematical models for time delay and time delay rate observables of space VLBI were analytically derived along with the partial derivatives with respect to the parameters. Rank defect analysis was carried out both by analytical and numerical testing of linear dependencies between the columns of the normal matrix thus formed. Definite conclusions were formed about the rank defects in the system.

Source record↗
NASA NTRS1996

DCTune Perceptual Optimization of Compressed Dental X-Rays

In current dental practice, x-rays of completed dental work are often sent to the insurer for verification. It is faster and cheaper to transmit instead digital scans of the x-rays. Further economies result if the images are sent in compressed form. DCTune is a technology for optimizing DCT (digital communication technology) quantization matrices to yield maximum perceptual quality for a given bit-rate, or minimum bit-rate for a given perceptual quality. Perceptual optimization of DCT color quantization matrices. In addition, the technology provides a means of setting the perceptual quality of compressed imagery in a systematic way. The purpose of this research was, with respect to dental x-rays, 1) to verify the advantage of DCTune over standard JPEG (Joint Photographic Experts Group), 2) to verify the quality control feature of DCTune, and 3) to discover regularities in the optimized matrices of a set of images. We optimized matrices for a total of 20 images at two resolutions (150 and 300 dpi) and four bit-rates (0.25, 0.5, 0.75, 1.0 bits/pixel), and examined structural regularities in the resulting matrices. We also conducted psychophysical studies (1) to discover the DCTune quality level at which the images became 'visually lossless,' and (2) to rate the relative quality of DCTune and standard JPEG images at various bitrates. Results include: (1) At both resolutions, DCTune quality is a linear function of bit-rate. (2) DCTune quantization matrices for all images at all bitrates and resolutions are modeled well by an inverse Gaussian, with parameters of amplitude and width. (3) As bit-rate is varied, optimal values of both amplitude and width covary in an approximately linear fashion. (4) Both amplitude and width vary in systematic and orderly fashion with either bit-rate or DCTune quality; simple mathematical functions serve to describe these relationships. (5) In going from 150 to 300 dpi, amplitude parameters are substantially lower and widths larger at corresponding bit-rates or qualities. (6) Visually lossless compression occurs at a DCTune quality value of about 1. (7) At 0.25 bits/pixel, comparative ratings give DCTune a substantial advantage over standard JPEG. As visually lossless bit-rates are approached, this advantage of necessity diminishes. We have concluded that DCTune optimized quantization matrices provide better visual quality than standard JPEG. Meaningful quality levels may be specified by means of the DCTune metric. Optimized matrices are very similar across the class of dental x-rays, suggesting the possibility of a 'class-optimal' matrix. DCTune technology appears to provide some value in the context of compressed dental x-rays.

Watson, Andrew B.↗