Search NASA⌕ Search

SEARCH · Search NASA

Results for “error vector”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS2009

Ares I Static Tests Design

Probabilistic engineering design enhances safety and reduces costs by incorporating risk assessment directly into the design process. In this paper, we assess the format of the quantitative metrics for the vehicle which will replace the Space Shuttle, the Ares I rocket. Specifically, we address the metrics for in-flight measurement error in the vector position of the motor nozzle, dictated by limits on guidance, navigation, and control systems. Analyses include the propagation of error from measured to derived parameters, the time-series of dwell points for the duty cycle during static tests, and commanded versus achieved yaw angle during tests. Based on these analyses, we recommend a probabilistic template for specifying the maximum error in angular displacement and radial offset for the nozzle-position vector. Criteria for evaluating individual tests and risky decisions also are developed.

Carson, William↗
NASA NTRS2006

Accommodating Sensor Uncertainty in the Cones Method: Polycones and Fuzzycones

The "cones method" is an analytical algorithm to combine a pair of angle observations into a common vector. Two new algorithms have been developed to optimize the "cones method" solutions when more than two observation angles are available and when estimates of measurement uncertainties can be made. The polycones algorithm consists of determining a simple weighted average of the solution vectors over all possible pairs of measurements with the weights determined from the measurement uncertainty. The Fuzzycones method finds the vector of maximum probability. Both of these methods have been implemented and tested and both reduce errors in computed vector positions.

Hashmall, Joseph A.↗
NASA NTRS1979

Navigation and meteorological error equations for some aerodynamic parameters

Mathematical equations for the analysis of the errors that are expected in a set of postflight aerodynamic parameters are presented. The errors are due to inaccuracies in the Shuttle best estimate trajectory and in the meteorological data obtained in support of the flights. The error analysis shows that the parameter vector, Z, and its associated error covariance matrix, C sub Z, is calculated from a given state vector, X, and its associated covariance matrix, C sub X.

Krikorian, M. J.↗
NASA NTRS2017

Automation of POST Cases via External Optimizer and "Artificial p2" Calculation

During conceptual design speed and accuracy are often at odds. Specifically in the realm of launch vehicles, optimizing the ascent trajectory requires a larger pool of analytical power and expertise. Experienced analysts working on familiar vehicles can produce optimal trajectories in a short time frame, however whenever either "experienced" or "familiar " is not applicable the optimization process can become quite lengthy. In order to construct a vehicle agnostic method an established global optimization algorithm is needed. In this work the authors develop an "artificial" error term to map arbitrary control vectors to non-zero error by which a global method can operate. Two global methods are compared alongside Design of Experiments and random sampling and are shown to produce comparable results to analysis done by a human expert.

Dees, Patrick D.↗
NASA NTRS1972

Distribution of error in least-squares solution of an overdetermined system of linear simultaneous equations

Probability density functions were derived for errors in the evaluation of unknowns by the least squares method in system of nonhomogeneous linear equations. Coefficients of the unknowns were assumed correct and computational precision were also assumed. A vector space was used, with number of dimensions equal to the number of equations. An error vector was defined and assumed to have uniform distribution of orientation throughout the vector space. The density functions are shown to be insensitive to the biasing effects of the source of the system of equations.

Miller, C. D.↗
NASA NTRS1980

Level B/C software ground navigation program. Delta-T processor

The Delta-T Processor (DTP) computes the instantaneous downtrack error in a specified orbiter onboard navigation state vector recovered via downlink telemetry. The downtrack error, expressed in units of time, is computed based on current incoming Earth based range and Doppler navigation tracking data and the ground selected onboard navigation state vector. The computed time difference when used to modify the timetag of the vector used for onboard navigation reduces the instantaneous downtrack error in this vector to within the threshold of the DTP, the input data, and the onboard software. This threshold is currently estimated to be approximately 2 to 4 nautical miles. The DTP is not restricted to using only onboard vectors. Any vector, either input via the manual entry device or accessible via the vector administration table, may be used. The DTP does not require that both data types be available.

Source record↗
NASA NTRS1973

On 'Type L' multivariable linear systems.

The purpose of this paper is to summarize results for linear multivariable systems that are analogous to those single input single output systems which are 'type l', i.e., that contain l integrators. Both frequency domain and time-domain properties are given. Appropriate conditions that guarantee zero steady state error in tracking vector polynomial inputs are presented.

Sandell, N., Jr.↗
NASA NTRS1986

Implementation of the Lanczos method for structural vibration analysis on a parallel computer

The use of the Lanczos method in a parallel environment is investigated by implementing the algorithm for structural vibration problems on a parallel computer. It is shown that introducing shifts, assigning each processor a different region in the eigenvalue spectrum, and implementing the Lanczos method in parallel is an effective strategy for speeding up calculations. Test problem results include examples of the 'Lanczos phenomenon' where roundoff error in the vector orthogonalization can result in spurious eigenvalues which must be identified and discarded. The calculation strategy described here permits straightforward determination of these spurious eigenvalues. It is demonstrated that significant speedups in calculation time can be realized over traditional sequential methods.

Bostic, S. W.↗
NASA NTRS2014

CM5, a Pre-Swarm Comprehensive Geomagnetic Field Model Derived from Over 12 Yr of CHAMP, Orsted, SAC-C and Observatory Data

A comprehensive magnetic field model named CM5 has been derived from CHAMP, Ørsted and SAC-C satellite and observatory hourly-means data from 2000 August to 2013 January using the Swarm Level-2 Comprehensive Inversion (CI) algorithm. Swarm is a recently launched constellation of three satellites to map the Earth's magnetic field. The CI technique includes several interesting features such as the bias mitigation scheme known as Selective Infinite Variance Weighting (SIVW), a new treatment for attitude error in satellite vector measurements, and the inclusion of 3-D conductivity for ionospheric induction. SIVW has allowed for a much improved lithospheric field recovery over CM4 by exploiting CHAMP along-track difference data yielding resolution levels up to spherical harmonic degree 107, and has allowed for the successful extraction of the oceanic M2 tidal magnetic field from quiet, nightside data. The 3-D induction now captures anomalous Solar-quiet features in coastal observatory daily records. CM5 provides a satisfactory, continuous description of the major magnetic fields in the near-Earth region over this time span, and its lithospheric, ionospheric and oceanic M2 tidal constituents may be used as validation tools for future Swarm Level-2 products coming from the CI algorithm and other dedicated product algorithms.

modelling and interpretation↗
NASA NTRS1979

Evaluation of the navigation performance of shipboard-VTOL-landing guidance systems

The objective of this study was to explore the performance of a VTOL aircraft landing approach navigation system that receives data (1) from either a microwave scanning beam (MSB) or a radar-transponder (R-T) landing guidance system, and (2) information data-linked from an aviation facility ship. State-of-the-art low-cost-aided inertial techniques and variable gain filters were used in the assumed navigation system. Compensation for ship motion was accomplished by a landing pad deviation vector concept that is a measure of the landing pad's deviation from its calm sea location. The results show that the landing guidance concepts were successful in meeting all of the current Navy navigation error specifications, provided that vector magnitude of the allowable error, rather than the error in each axis, is a permissible interpretation of acceptable performance. The success of these concepts, however, is strongly dependent on the distance measuring equipment bias. In addition, the 'best possible' closed-loop tracking performance achievable with the assumed point-mass VTOL aircraft guidance concept is demonstrated.

Mcgee, L. A.↗
NASA NTRS2014

Background Error Covariance Estimation Using Information from a Single Model Trajectory with Application to Ocean Data Assimilation

An attractive property of ensemble data assimilation methods is that they provide flow dependent background error covariance estimates which can be used to update fields of observed variables as well as fields of unobserved model variables. Two methods to estimate background error covariances are introduced which share the above property with ensemble data assimilation methods but do not involve the integration of multiple model trajectories. Instead, all the necessary covariance information is obtained from a single model integration. The Space Adaptive Forecast error Estimation (SAFE) algorithm estimates error covariances from the spatial distribution of model variables within a single state vector. The Flow Adaptive error Statistics from a Time series (FAST) method constructs an ensemble sampled from a moving window along a model trajectory.SAFE and FAST are applied to the assimilation of Argo temperature profiles into version 4.1 of the Modular Ocean Model (MOM4.1) coupled to the GEOS-5 atmospheric model and to the CICE sea ice model. The results are validated against unassimilated Argo salinity data. They show that SAFE and FAST are competitive with the ensemble optimal interpolation (EnOI) used by the Global Modeling and Assimilation Office (GMAO) to produce its ocean analysis. Because of their reduced cost, SAFE and FAST hold promise for high-resolution data assimilation applications.

Error Covariance↗
NASA NTRS2014

Background Error Covariance Estimation using Information from a Single Model Trajectory with Application to Ocean Data Assimilation into the GEOS-5 Coupled Model

An attractive property of ensemble data assimilation methods is that they provide flow dependent background error covariance estimates which can be used to update fields of observed variables as well as fields of unobserved model variables. Two methods to estimate background error covariances are introduced which share the above property with ensemble data assimilation methods but do not involve the integration of multiple model trajectories. Instead, all the necessary covariance information is obtained from a single model integration. The Space Adaptive Forecast error Estimation (SAFE) algorithm estimates error covariances from the spatial distribution of model variables within a single state vector. The Flow Adaptive error Statistics from a Time series (FAST) method constructs an ensemble sampled from a moving window along a model trajectory. SAFE and FAST are applied to the assimilation of Argo temperature profiles into version 4.1 of the Modular Ocean Model (MOM4.1) coupled to the GEOS-5 atmospheric model and to the CICE sea ice model. The results are validated against unassimilated Argo salinity data. They show that SAFE and FAST are competitive with the ensemble optimal interpolation (EnOI) used by the Global Modeling and Assimilation Office (GMAO) to produce its ocean analysis. Because of their reduced cost, SAFE and FAST hold promise for high-resolution data assimilation applications.

Data Assimilation↗
DOE OSTI2025

Q-Cluster: Quantum Error Mitigation Through Noise-Aware Unsupervised Learning

Quantum error mitigation (QEM) is critical in reducing the impact of noise in the pre-fault-tolerant era, and is expected to complement error correction in fault-tolerant quantum computing (FTQC). In this work, we propose a novel QEM approach, Q-Cluster, that uses unsupervised learning (clustering) to reshape the measured bit-string distribution. Our approach starts with a simplified bit-flip noise model. It first performs clustering on noisy measurement results, i.e., bit-strings, based on the Hamming distance. The centroid of each cluster is calculated using a qubit-wise majority vote. Next, the noisy distribution is adjusted with the clustering outcomes and the bitflip error rates using Bayesian inference. Our simulation results show that Q-Cluster can mitigate high noise rates (up to 40% per qubit) with the simple bit-flip noise model. However, real quantum computers do not fit such a simple noise model. To address the problem, we (a) apply Pauli twirling to tailor the complex noise channels to Pauli errors, and (b) employ a machine learning model, ExtraTrees regressor, to estimate an effective bit-flip error rate using a feature vector consisting of machine calibration data (gate & measurement error rates), circuit features (number of qubits, numbers of different types of gates, etc.) and the shape of the noisy distribution (entropy). Our experimental results show that our proposed Q-Cluster scheme improves the fidelity by a factor of 1.46x, on average, compared to the unmitigated output distribution, for a set of low-entropy benchmarks on five different IBM quantum machines. Our approach outperforms the state-of-art QEM approaches RZNE [28], M3 [24], Hammer [35], and QBEEP [33] by 1.26x,1.29x,1.47x, and 2.65 x, respectively.

42 ENGINEERING↗
NASA NTRS1988

Robust vector quantization for noisy channels

The paper briefly discusses techniques for making vector quantizers more tolerant to tranmsission errors. Two algorithms are presented for obtaining an efficient binary word assignment to the vector quantizer codewords without increasing the transmission rate. It is shown that about 4.5 dB gain over random assignment can be achieved with these algorithms. It is also proposed to reduce the effects of error propagation in vector-predictive quantizers by appropriately constraining the response of the predictive loop. The constrained system is shown to have about 4 dB of SNR gain over an unconstrained system in a noisy channel, with a small loss of clean-channel performance.

Demarca, J. R. B.↗
NASA NTRS1973

A unified development of several techniques for the representation of random vectors and data sets

Linear vector space theory is used to develop a general representation of a set of data vectors or random vectors by linear combinations of orthonormal vectors such that the mean squared error of the representation is minimized. The orthonormal vectors are shown to be the eigenvectors of an operator. The general representation is applied to several specific problems involving the use of the Karhunen-Loeve expansion, principal component analysis, and empirical orthogonal functions; and the common properties of these representations are developed.

Bundick, W. T.↗
NASA NTRSDate not supplied

Is There A Relationship Between Cornered-Hat Methods and A Residual Approach to Estimate System Uncertainty?

Recently a relationship has been established between a now traditional residual diagnostic used to estimate observation, background and analysis error covariances of interest to data assimilation and the three-cornered hat (3CH) method. An existing extension of the traditional residual diagnostic uses residuals from a fixed lag-1 Kalman smoother to retrieve system (model) error covariance. It is thus natural to ask if an additional relationship can be established between this extended residual method and some form of cornered--hat method. The answer might seem straightforward. Unlike in the standard residual estimation case, attempting to estimate model error amounts to estimating the statistics of a residual quantity itself. As shown in this presentation, in such cases the 3CH method becomes trivial: the sought out uncertainty can be derived directly from the covariance of the residual quantity at hand. In the particular case of estimating model error, one of the corners would have to be composed of vectors providing estimates of model error; these are not typically available in practice. Therefore, at first glance the present work finds no relationship between the lag-1 smoother residual diagnostic for system error estimation and cornered--hat methods. However, the work suggests that a two-tiered 3CH might be all that is necessary for system uncertainty to be obtained with 3CH.

Ricardo Todling↗
NASA NTRS2009

A Systematic Approach to Sensor Selection for Aircraft Engine Health Estimation

A systematic approach for selecting an optimal suite of sensors for on-board aircraft gas turbine engine health estimation is presented. The methodology optimally chooses the engine sensor suite and the model tuning parameter vector to minimize the Kalman filter mean squared estimation error in the engine s health parameters or other unmeasured engine outputs. This technique specifically addresses the underdetermined estimation problem where there are more unknown system health parameters representing degradation than available sensor measurements. This paper presents the theoretical estimation error equations, and describes the optimization approach that is applied to select the sensors and model tuning parameters to minimize these errors. Two different model tuning parameter vector selection approaches are evaluated: the conventional approach of selecting a subset of health parameters to serve as the tuning parameters, and an alternative approach that selects tuning parameters as a linear combination of all health parameters. Results from the application of the technique to an aircraft engine simulation are presented, and compared to those from an alternative sensor selection strategy.

Simon, Donald L.↗
NASA NTRS1976

Parametric study of predictor accuracy impact on OFT rendezvous targeting

A parametric study was made to quantitatively define the effects of errors in the state vector predictor used by the Operational Flight Trainer (OFT) rendezvous targeting algorithms. The effect of the predictor accuracy on the OFT rendezvous profile is shown by the sensitivity of various critical rendezvous parameters with respect to downrange and radial predictor error rates. The effect of both inertial (same errors on both vehicles) and relative (differential errors on one vehicle with respect to the other) errors were considered. Relative radial error rates had the largest impact on the rendezvous followed by relative downrange errors, radial inertial errors and downrange inertial errors.

Glenn, S. W.↗