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At least 217 records · Page 12

All sources NASA NTRS DOE OSTI

DOE OSTI2020

Block Krylov Subspace Methods for Functions of Matrices II: Modified Block FOM

We analyze an expansion of the generalized block Krylov subspace framework of [Electron. Trans. Numer. Anal., 47 (2017), pp. 100--126]. This expansion allows the use of low-rank modifications of the matrix projected onto the block Krylov subspace and contains, as special cases, the block GMRES method and the new block Radau--Arnoldi method. Within this general setting, we present results that extend the interpolation property from the nonblock case to a matrix polynomial interpolation property for the block case, and we relate the eigenvalues of the projected matrix to the latent roots of these matrix polynomials. Some error bounds for these modified block FOM methods for solving linear systems are presented. We then show how cospatial residuals can be preserved in the case of families of shifted linear block systems. This result is used to derive computationally practical restarted algorithms for block Krylov approximations that compute the action of a matrix function on a set of several vectors simultaneously. Finally, we prove some error bounds and present numerical results showing that two modifications of FOM, the block harmonic and the block Radau--Arnoldi methods for matrix functions, can significantly improve the convergence behavior.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1990

Large field-of-view KD*P modulator

This paper describes how FOV errors have affected the polarization measurements of the NASA Marshall vector magnetograph and how a polarimeter has been modified to minimize these errors. The design of a large-FOV (LFOV) KD*P modulator is discussed. The Poincare sphere is used to visualize the function of the different optical elements that make up the LFOV modulator.

West, E. A.↗

NASA NTRS1998

A transition matrix approach to the Davenport gryo calibration scheme

The in-flight gyro calibration scheme commonly used by NASA Goddard Space Flight Center (GSFC) attitude ground support teams closely follows an original version of the Davenport algorithm developed in the late seventies. Its basic idea is to minimize the least-squares differences between attitudes gyro- propagated over the course of a maneuver and those determined using post- maneuver sensor measurements. The paper represents the scheme in a recursive form by combining necessary partials into a rectangular matrix, which is propagated in exactly the same way as a Kalman filters square transition matrix. The nontrivial structure of the propagation matrix arises from the fact that attitude errors are not included in the state vector, and therefore their derivatives with respect to estimated a parameters do not appear in the transition matrix gyro defined in the conventional way. In cases when the required accuracy can be achieved by a single iteration, representation of the Davenport gyro calibration scheme in a recursive form allows one to discard each gyro measurement immediately after it was used to propagate the attitude and state transition matrix. Another advantage of the new approach is that it utilizes the same expression for the error sensitivity matrix as that used by the Kalman filter. As a result the suggested modification of the Davenport algorithm made it possible to reuse software modules implemented in the Kalman filter estimator, where both attitude errors and gyro calibration parameters are included in the state vector. The new approach has been implemented in the ground calibration utilities used to support the Tropical Rainfall Measuring Mission (TRMM). The paper analyzes some preliminary results of gyro calibration performed by the TRMM ground attitude support team. It is demonstrated that an effect of the second iteration on estimated values of calibration parameters is negligibly small, and therefore there is no need to store processed gyro data. This opens a promising opportunity for onboard implementation of the suggested recursive procedure by combining, it with the Kalman filter used to obtain necessary attitude solutions at the beginning and end of each maneuver.

Natanson, G. A.↗

DOE OSTI2024

Taylor-Expansion-Based Robust Power Flow in Unbalanced Distribution Systems: A Hybrid Data-Aided Method

Traditional power flow methods often adopt certain assumptions designed for passive balanced distribution systems, thus lacking practicality for unbalanced operation. moreover, their computation accuracy and efficiency are heavily subject to unknown errors and bad data in measurements or prediction data of distributed energy resources (ders). to address these issues, this paper proposes a hybrid data-aided robust power flow algorithm in unbalanced distribution systems, which combines taylor series expansion knowledge with a data-driven regression technique. the proposed method initiates a linearization power flow model to derive an explicitly analytical solution by modified taylor expansion. to mitigate the approximation loss that surges due to the der integration and bad data, we further develop a data-aided robust support vector regression approach to estimate the errors efficiently. comparative analysis in the 13-bus and 123-bus ieee unbalanced feeders shows that the proposed hybrid algorithm achieves superior computational efficiency, with guaranteed accuracy and robustness against outliers.

data-driven↗

NASA NTRS1990

Masking of errors in transmission of VAPC-coded speech

A subjective evaluation is provided of the bit error sensitivity of the message elements of a Vector Adaptive Predictive (VAPC) speech coder, along with an indication of the amenability of these elements to a popular error masking strategy (cross frame hold over). As expected, a wide range of bit error sensitivity was observed. The most sensitive message components were the short term spectral information and the most significant bits of the pitch and gain indices. The cross frame hold over strategy was found to be useful for pitch and gain information, but it was not beneficial for the spectral information unless severe corruption had occurred.

Cox, Neil B.↗

NASA NTRS1983

A function space approach to state and model error estimation for elliptic systems

An approach is advanced for the concurrent estimation of the state and of the model errors of a system described by elliptic equations. The estimates are obtained by a deterministic least-squares approach that seeks to minimize a quadratic functional of the model errors, or equivalently, to find the vector of smallest norm subject to linear constraints in a suitably defined function space. The minimum norm solution can be obtained by solving either a Fredholm integral equation of the second kind for the case with continuously distributed data or a related matrix equation for the problem with discretely located measurements. Solution of either one of these equations is obtained in a batch-processing mode in which all of the data is processed simultaneously or, in certain restricted geometries, in a spatially scanning mode in which the data is processed recursively. After the methods for computation of the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the corresponding estimation error is conducted. Based on this analysis, explicit expressions for the mean-square estimation error associated with both the state and model error estimates are then developed.

Rodriguez, G.↗

NASA NTRS1983

A function space approach to state and model error estimation for elliptic systems

An approach is advanced for the concurrent estimation of the state and of the model errors of a system described by elliptic equations. The estimates are obtained by a deterministic least-squares approach that seeks to minimize a quadratic functional of the model errors, or equivalently, to find the vector of smallest norm subject to linear constraints in a suitably defined function space. The minimum norm solution can be obtained by solving either a Fredholm integral equation of the second kind for the case with continuously distributed data or a related matrix equation for the problem with discretely located measurements. Solution of either one of these equations is obtained in a batch-processing mode in which all of the data is processed simultaneously or, in certain restricted geometries, in a spatially scanning mode in which the data is processed recursively. After the methods for computation of the optimal esimates are developed, an analysis of the second-order statistics of the estimates and of the corresponding estimation error is conducted. Based on this analysis, explicit expressions for the mean-square estimation error associated with both the state and model error estimates are then developed. While this paper focuses on theoretical developments, applications arising in the area of large structure static shape determination are contained in a closely related paper (Rodriguez and Scheid, 1982).

Rodriguez, G.↗

DOE OSTI2018

Toolpath generation from fiber orientation distribution

We define toolpaths as contours of a level-set function and fit these contours with a given fiber orientation distribution. To define the orientation error, we use the difference between the tangent vectors of these contours and the given fiber orientations. Our fit consist in an optimization problem where we minimize the orientation error subject to manufacturing constraints. Two examples are provided.

42 ENGINEERING↗

NASA NTRS1996

Two Reduced Resolution Filter Approaches to Data Assimilation

In this paper we evaluate the performance of two reduced resolution filter approaches to data assimilation. The main distinction between these approaches is in the manner they propagate error covariances. Both account for error covariances in a space with dimension m smaller than the model's state vector dimension n. In the first approach the m dimensional error covariance matrix is interpolated to the n-dimensional space and propagated with the n-dimensional dynamics. In the second approach the low-dimensional error covariance matrix is propagated by a dynamical operator generated in the m-dimensional space. Our experiments indicate that the first approach provides a more reliable simplified scheme for error covariance propagation than the second approach.

Todling, Ricardo↗

NASA NTRS1986

Optimal control of quaternion propagation errors in spacecraft navigation

Optimal control techniques are used to drive the numerical error (truncation, roundoff, commutation) in computing the quaternion vector to zero. The normalization of the quaternion is carried out by appropriate choice of a performance index, which can be optimized. The error equations are derived from Friedland's (1978) theoretical development, and a matrix Riccati equation results for the computation of the gain matrix. Simulation results show that a high precision of the order of 10 to the -12th can be obtained using this technique in meeting the q(T)q=1 constraint. The performance of the estimator in the presence of the feedback control that maintains the normalization, is studied.

Vathsal, S.↗

DOE OSTI2016

TU-AB-202-06: Quantitative Evaluation of Deformable Image Registration in MRI-Guided Adaptive Radiation Therapy

Purpose: To assess the performance of the deformable image registration algorithm used for MRI-guided adaptive radiation therapy using image feature analysis. Methods: MR images were collected from five patients treated on the MRIdian (ViewRay, Inc., Oakwood Village, OH), a three head Cobalt-60 therapy machine with an 0.35 T MR system. The images were acquired immediately prior to treatment with a uniform 1.5 mm resolution. Treatment sites were as follows: head/neck, lung, breast, stomach, and bladder. Deformable image registration was performed using the ViewRay software between the first fraction MRI and the final fraction MRI, and the DICE similarity coefficient (DSC) for the skin contours was reported. The SIFT and Harris feature detection and matching algorithms identified point features in each image separately, then found matching features in the other image. The target registration error (TRE) was defined as the vector distance between matched features on the two image sets. Each deformation was evaluated based on comparison of average TRE and DSC. Results: Image feature analysis produced between 2000–9500 points for evaluation on the patient images. The average (± standard deviation) TRE for all patients was 3.3 mm (±3.1 mm), and the passing rate of TRE<3 mm was 60% on the images. The head/neck patient had the best average TRE (1.9 mm±2.3 mm) and the best passing rate (80%). The lung patient had the worst average TRE (4.8 mm±3.3 mm) and the worst passing rate (37.2%). DSC was not significantly correlated with either TRE (p=0.63) or passing rate (p=0.55). Conclusions: Feature matching provides a quantitative assessment of deformable image registration, with a large number of data points for analysis. The TRE of matched features can be used to evaluate the registration of many objects throughout the volume, whereas DSC mainly provides a measure of gross overlap. We have a research agreement with ViewRay Inc.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2025

A two-level GPU-accelerated incomplete LU preconditioner for general sparse linear systems

This paper presents a parallel preconditioning approach based on incomplete LU (ILU) factorizations in the framework of Domain Decomposition (DD) for general sparse linear systems. We focus on distributed memory parallel architectures, specifically, those that are equipped with graphic processing units (GPUs). In addition to block-Jacobi, we present general purpose two-level ILU Schur complement-based approaches, where different strategies are presented to solve the coarse-level reduced system. These strategies are combined with modified ILU methods in the construction of the coarse-level operator, in order to effectively remove smooth errors by targeting an algebraically smooth vector. We leverage available GPU-based sparse matrix kernels to accelerate the setup and the solve phases of the proposed ILU preconditioner. We evaluate the efficiency of the proposed methods as a smoother for algebraic multigrid (AMG) and as a preconditioner for Krylov subspace methods on challenging anisotropic diffusion problems and a collection of general sparse matrices.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1972

An adaptive observer for single-input single-output linear systems

It is shown that the full order adaptive observer for single input, single output, observable, continuous, stable, linear differential systems in the absence of a deterministic or random disturbance vector guarantees the vanishing of observation error, regardless of the size of the constant or slowly varying parameter ignorance. The observer parameters are directly changed in a Liapunov adaptive way so as to eventually yield the unknown full order Luenberger observer. The observer poles throughout may be placed freely in the stable region and no derivatives are required in the adaptive law.

Carroll, R. L.↗

NASA NTRS1984

An attitude reorientation algorithm for the Galileo spacecraft

This paper presents an onboard closed loop attitude reorientation algorithm for a dual-spin spacecraft, Galileo. The basic concept for the design uses the despun stator as a reference and fires a sequence of fixed duration thruster pulses to precess the angular momentum vector to its commanded orientation. The error signals used to despin the stator and to perform the turn are derived from the stator error quaternion which is computed using gyro outputs. Constraints considered in the design include gyro rate saturation, plume impingement effects, system parameter variations, as well as software reliability and flexibility. The performance of the algorithm was predicted by analysis and confirmed by computer simulation results. It was concluded that a reorientation accuracy of better than 1 milliradian with a nutation angle of less than 1 degree during the turn can be achieved.

Lin, H.-S.↗

NASA NTRS1988

Identification of terrain cover using the optimum polarimetric classifier

A systematic approach for the identification of terrain media such as vegetation canopy, forest, and snow-covered fields is developed using the optimum polarimetric classifier. The covariance matrices for various terrain cover are computed from theoretical models of random medium by evaluating the scattering matrix elements. The optimal classification scheme makes use of a quadratic distance measure and is applied to classify a vegetation canopy consisting of both trees and grass. Experimentally measured data are used to validate the classification scheme. Analytical and Monte Carlo simulated classification errors using the fully polarimetric feature vector are compared with classification based on single features which include the phase difference between the VV and HH polarization returns. It is shown that the full polarimetric results are optimal and provide better classification performance than single feature measurements.

Kong, J. A.↗

NASA NTRS1994

TDRS orbit determination by radio interferometry

In support of a NASA study on the application of radio interferometry to satellite orbit determination, MITRE developed a simulation tool for assessing interferometry tracking accuracy. The Orbit Determination Accuracy Estimator (ODAE) models the general batch maximum likelihood orbit determination algorithms of the Goddard Trajectory Determination System (GTDS) with the group and phase delay measurements from radio interferometry. ODAE models the statistical properties of tracking error sources, including inherent observable imprecision, atmospheric delays, clock offsets, station location uncertainty, and measurement biases, and through Monte Carlo simulation, ODAE calculates the statistical properties of errors in the predicted satellites state vector. This paper presents results from ODAE application to orbit determination of the Tracking and Data Relay Satellite (TDRS) by radio interferometry. Conclusions about optimal ground station locations for interferometric tracking of TDRS are presented, along with a discussion of operational advantages of radio interferometry.

Pavloff, Michael S.↗

NASA NTRS2013

Orion Exploration Flight Test-1 Contingency Drogue Deploy Velocity Trigger

As a backup to the GPS-aided Kalman filter and the Barometric altimeter, an "adjusted" velocity trigger is used during entry to trigger the chain of events that leads to drogue chute deploy for the Orion Multi-Purpose Crew Vehicle (MPCV) Exploration Flight Test-1 (EFT-1). Even though this scenario is multiple failures deep, the Orion Guidance, Navigation, and Control (GN&C) software makes use of a clever technique that was taken from the Mars Science Laboratory (MSL) program, which recently successfully landing the Curiosity rover on Mars. MSL used this technique to jettison the heat shield at the proper time during descent. Originally, Orion use the un-adjusted navigated velocity, but the removal of the Star Tracker to save costs for EFT-1, increased attitude errors which increased inertial propagation errors to the point where the un-adjusted velocity caused altitude dispersions at drogue deploy to be too large. Thus, to reduce dispersions, the velocity vector is projected onto a "reference" vector that represents the nominal "truth" vector at the desired point in the trajectory. Because the navigation errors are largely perpendicular to the truth vector, this projection significantly reduces dispersions in the velocity magnitude. This paper will detail the evolution of this trigger method for the Orion project and cover the various methods tested to determine the reference "truth" vector; and at what point in the trajectory it should be computed.

Gay, Robert S.↗

NASA NTRS1994

Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres

Although neglecting polarization and replacing the rigorous vector radiative transfer equation by its approximate scalar counterpart has no physical background, it is a widely used simplification when the incident light is unpolarized and only the intensity of the reflected light is to be computed. We employ accurate vector and scalar multiple-scattering calculations to perform a systematic study of the errors induced by the neglect of polarization in radiance calculations for a homogeneous, plane-parallel Rayleigh-scattering atmosphere (with and without depolarization) above a Lambertian surface. Specifically, we calculate percent errors in the reflected intensity for various directions of light incidence and reflection, optical thicknesses of the atmosphere, single-scattering albedos, depolarization factors, and surface albedos. The numerical data displayed can be used to decide whether or not the scalar approximation may be employed depending on the parameters of the problem. We show that the errors decrease with increasing depolarization factor and/or increasing surface albedo. For conservative or nearly conservative scattering and small surface albedos, the errors are maximum at optical thicknesses of about 1. The calculated errors may be too large for some practical applications, and, therefore, rigorous vector calculations should be employed whenever possible. However, if approximate scalar calculations are used, we recommend to avoid geometries involving phase angles equal or close to 0 deg and 90 deg, where the errors are especially significant. We propose a theoretical explanation of the large vector/scalar differences in the case of Rayleigh scattering. According to this explanation, the differences are caused by the particular structure of the Rayleigh scattering matrix and come from lower-order (except first-order) light scattering paths involving right scattering angles and right-angle rotations of the scattering plane.

Mishchenko, M. I.↗