Search NASA⌕ Search

SEARCH · Search NASA

Results for “linear covariance”

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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

A dynamic measure of controllability and observability for the placement of actuators and sensors on large space structures

The degree of controllability of a large space structure is found by a four step procedure: (1) finding the minimum control energy for driving the system from a given initial state to the origin in the prescribed time; (2) finding the region of initial state which can be driven to the origin with constrained control energy and time using optimal control strategy; (3) scaling the axes so that a unit displacement in every direction is equally important to control; and (4) finding the linear measurement of the weighted "volume" of the ellipsoid in the equicontrol space. For observability, the error covariance must be reduced toward zero using measurements optimally, and the criterion must be standardized by the magnitude of tolerable errors. The results obtained using these methods are applied to the vibration modes of a free-free beam.

Vandervelde, W. E.↗
NASA NTRS2006

Convective Weather Forecast Quality Metrics for Air Traffic Management Decision-Making

Since numerical weather prediction models are unable to accurately forecast the severity and the location of the storm cells several hours into the future when compared with observation data, there has been a growing interest in probabilistic description of convective weather. The classical approach for generating uncertainty bounds consists of integrating the state equations and covariance propagation equations forward in time. This step is readily recognized as the process update step of the Kalman Filter algorithm. The second well known method, known as the Monte Carlo method, consists of generating output samples by driving the forecast algorithm with input samples selected from distributions. The statistical properties of the distributions of the output samples are then used for defining the uncertainty bounds of the output variables. This method is computationally expensive for a complex model compared to the covariance propagation method. The main advantage of the Monte Carlo method is that a complex non-linear model can be easily handled. Recently, a few different methods for probabilistic forecasting have appeared in the literature. A method for computing probability of convection in a region using forecast data is described in Ref. 5. Probability at a grid location is computed as the fraction of grid points, within a box of specified dimensions around the grid location, with forecast convection precipitation exceeding a specified threshold. The main limitation of this method is that the results are dependent on the chosen dimensions of the box. The examples presented Ref. 5 show that this process is equivalent to low-pass filtering of the forecast data with a finite support spatial filter. References 6 and 7 describe the technique for computing percentage coverage within a 92 x 92 square-kilometer box and assigning the value to the center 4 x 4 square-kilometer box. This technique is same as that described in Ref. 5. Characterizing the forecast, following the process described in Refs. 5 through 7, in terms of percentage coverage or confidence level is notionally sound compared to characterizing in terms of probabilities because the probability of the forecast being correct can only be determined using actual observations. References 5 through 7 only use the forecast data and not the observations. The method for computing the probability of detection, false alarm ratio and several forecast quality metrics (Skill Scores) using both the forecast and observation data are given in Ref. 2. This paper extends the statistical verification method in Ref. 2 to determine co-occurrence probabilities. The method consists of computing the probability that a severe weather cell (grid location) is detected in the observation data in the neighborhood of the severe weather cell in the forecast data. Probabilities of occurrence at the grid location and in its neighborhood with higher severity, and with lower severity in the observation data compared to that in the forecast data are examined. The method proposed in Refs. 5 through 7 is used for computing the probability that a certain number of cells in the neighborhood of severe weather cells in the forecast data are seen as severe weather cells in the observation data. Finally, the probability of existence of gaps in the observation data in the neighborhood of severe weather cells in forecast data is computed. Gaps are defined as openings between severe weather cells through which an aircraft can safely fly to its intended destination. The rest of the paper is organized as follows. Section II summarizes the statistical verification method described in Ref. 2. The extension of this method for computing the co-occurrence probabilities in discussed in Section HI. Numerical examples using NCWF forecast data and NCWD observation data are presented in Section III to elucidate the characteristics of the co-occurrence probabilities. This section also discusses the procedure for computing throbabilities that the severity of convection in the observation data will be higher or lower in the neighborhood of grid locations compared to that indicated at the grid locations in the forecast data. The probability of coverage of neighborhood grid cells is also described via examples in this section. Section IV discusses the gap detection algorithm and presents a numerical example to illustrate the method. The locations of the detected gaps in the observation data are used along with the locations of convective weather cells in the forecast data to determine the probability of existence of gaps in the neighborhood of these cells. Finally, the paper is concluded in Section V.

Chatterji, Gano B.↗
NASA NTRS2011

Efficient Kriging Algorithms

More efficient versions of an interpolation method, called kriging, have been introduced in order to reduce its traditionally high computational cost. Written in C++, these approaches were tested on both synthetic and real data. Kriging is a best unbiased linear estimator and suitable for interpolation of scattered data points. Kriging has long been used in the geostatistic and mining communities, but is now being researched for use in the image fusion of remotely sensed data. This allows a combination of data from various locations to be used to fill in any missing data from any single location. To arrive at the faster algorithms, sparse SYMMLQ iterative solver, covariance tapering, Fast Multipole Methods (FMM), and nearest neighbor searching techniques were used. These implementations were used when the coefficient matrix in the linear system is symmetric, but not necessarily positive-definite.

Memarsadeghi, Nargess↗
NASA NTRS1990

True covariance simulation of the EUVE (extreme ultra violet explorer) update filter

This paper presents a covariance analysis of the performance and sensitivity of the attitude determination Extended Kalman Filter (EKF) used by the onboard computer (OBC) of the Extreme Ultra Violet Explorer (EUVE) spacecraft. The linearized dynamics and measurement equations of the error states are used in formulating the 'truth model' describing the order of the systems involved. The 'design model' used by the OBC EKF is then obtained by reducing the order of the truth model. The covariance matrix of the EKF which uses the reduced order model is not the correct covariance of the EKF estimation error. A 'true covariance analysis' has to be carried out in order to evaluate the correct accuracy of the OBC generated estimates. The results of such analysis are presented which indicate both the performance and the sensitivity of the OBC EKF.

Bar-Itzhack, I. Y.↗
NASA NTRS1976

Analysis and application of minimum variance discrete time system identification

An on-line minimum variance parameter identifier was developed which embodies both accuracy and computational efficiency. The new formulation resulted in a linear estimation problem with both additive and multiplicative noise. The resulting filter is shown to utilize both the covariance of the parameter vector itself and the covariance of the error in identification. It is proven that the identification filter is mean square covergent and mean square consistent. The MV parameter identification scheme is then used to construct a stable state and parameter estimation algorithm.

Kotob, S.↗
NASA NTRS1976

Ocean color spectra measured off the Oregon coast - Characteristic vectors

The ocean color spectrum is defined as the ratio of the spectrum of light upwelled from the sea to the spectrum of light incident on the sea surface. Ocean color spectra, observed from an airplane flown over waters off Oregon, are analyzed. The original spectra are resolved into fifty-five wavelength bands, each 5 nm wide. The shapes of these spectra are parameterized by, and shown to be accurately recoverable from, their first four principal components. These components are the scalar projections of each spectrum on the first four characteristic vectors of the sample covariance matrix. Regression equations are found with which phytoplankton pigment concentration and water transparency may be estimated as linear functions of the principal components. Pigment concentration estimates thus obtained are imprecise. The poor fit is at least partly due to the inappropriateness of the linear regression model and the neglect of other optically important substances typically present in sea water.

Mueller, J. L.↗
NASA NTRS1988

On the design of the dissipative LQG-type controllers

The design of dissipative linear-quadratic-Gaussian-type compensators for positive real plants is considered. It is shown that if the noise covariance matrices (used as weighting matrices) satisfy certain conditions, the compensator has a strictly positive real transfer function matrix. The stability of the resulting closed-loop system is guaranteed regardless of modeling errors as long as the plant remains positive real. In view of this property, the controller is expected to be useful for vibration suppression in large, flexible space structures.

Lozano-Leal, R.↗
NASA NTRS2009

Turbulent CO2 Flux Measurements by Lidar: Length Scales, Results and Comparison with In-Situ Sensors

The vertical CO2 flux in the atmospheric boundary layer (ABL) is investigated with a Doppler differential absorption lidar (DIAL). The instrument was operated next to the WLEF instrumented tall tower in Park Falls, Wisconsin during three days and nights in June 2007. Profiles of turbulent CO2 mixing ratio and vertical velocity fluctuations are measured by in-situ sensors and Doppler DIAL. Time and space scales of turbulence are precisely defined in the ABL. The eddy-covariance method is applied to calculate turbulent CO2 flux both by lidar and in-situ sensors. We show preliminary mean lidar CO2 flux measurements in the ABL with a time and space resolution of 6 h and 1500 m respectively. The flux instrumental errors decrease linearly with the standard deviation of the CO2 data, as expected. Although turbulent fluctuations of CO2 are negligible with respect to the mean (0.1 %), we show that the eddy-covariance method can provide 2-h, 150-m range resolved CO2 flux estimates as long as the CO2 mixing ratio instrumental error is no greater than 10 ppm and the vertical velocity error is lower than the natural fluctuations over a time resolution of 10 s.

Gilbert, Fabien↗
NASA NTRS1990

True covariance simulation of the EUVE update filter

This paper presents a covariance analysis of the performance and sensitivity of the attitude determination Extended Kalman Filter (EKF) used by the On Board Computer (OBC) of the Extreme Ultra Violet Explorer (EUVE) spacecraft. The linearized dynamics and measurement equations of the error states are used in formulating the 'truth model' describing the real behavior of the systems involved. The 'design model' used by the OBC EKF is then obtained by reducing the order of the truth model. The covariance matrix of the EKF which uses the reduced order model is not the correct covariance of the EKF estimation error. A 'true covariance analysis' has to be carried out in order to evaluate the correct accuracy of the OBC generated estimates. The results of such analysis are presented which indicate both the performance and the sensitivity of the OBC EKF.

Bar-Itzhack, I. Y.↗
NASA NTRS1989

True covariance simulation of the EUVE update filter

A covariance analysis of the performance and sensitivity of the attitude determination Extended Kalman Filter (EKF) used by the On Board Computer (OBC) of the Extreme Ultra Violet Explorer (EUVE) spacecraft is presented. The linearized dynamics and measurement equations of the error states are derived which constitute the truth model describing the real behavior of the systems involved. The design model used by the OBC EKF is then obtained by reducing the order of the truth model. The covariance matrix of the EKF which uses the reduced order model is not the correct covariance of the EKF estimation error. A true covariance analysis has to be carried out in order to evaluate the correct accuracy of the OBC generated estimates. The results of such analysis are presented which indicate both the performance and the sensitivity of the OBC EKF.

Bar-Itzhack, Itzhack Y.↗
DOE OSTI2024

Monitoring covariance in multivariate time series: Comparing machine learning and statistical approaches

Abstract In complex systems with multiple variables monitored at high‐frequency, variables are not only temporally autocorrelated, but they may also be nonlinearly related or exhibit nonstationarity as the inputs or operation changes. One approach to handling such variables is to detrend them prior to monitoring and then apply control charts that assume independence and stationarity to the residuals. Monitoring controlled systems is even more challenging because the control strategy seeks to maintain variables at prespecified mean levels, and to compensate, correlations among variables may change, making monitoring the covariance essential. In this paper, a vector autoregressive model (VAR) is compared with a multivariate random forest (MRF) and a neural network (NN) for detrending multivariate time series prior to monitoring the covariance of the residuals using a multivariate exponentially weighted moving average (MEWMA) control chart. Machine learning models have an advantage when the data's structure is unknown or may change. We design a novel simulation study with nonlinear, nonstationary, and autocorrelated data to compare the different detrending models and subsequent covariance monitoring. The machine learning models have superior performance for nonlinear and strongly autocorrelated data and similar performance for linear data. An illustration with data from a reverse osmosis process is given.

Weix, Derek↗
DOE OSTI2022

Scaled Vecchia Approximation for Fast Computer-Model Emulation

Many scientific phenomena are studied using computer experiments consisting of multiple runs of a computer model while varying the input settings. Gaussian processes (GPs) are a popular tool for the analysis of computer experiments, enabling interpolation between input settings, but direct GP inference is computationally infeasible for large datasets. We adapt and extend a powerful class of GP methods from spatial statistics to enable the scalable analysis and emulation of large computer experiments. Specifically, we apply Vecchia’s ordered conditional approximation in a transformed input space, with each input scaled according to how strongly it relates to the computer-model response. The scaling is learned from the data by estimating parameters in the GP covariance function using Fisher scoring. Our methods are highly scalable, enabling estimation, joint prediction, and simulation in near-linear time in the number of model runs. In several numerical examples, our approach substantially outperformed existing methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1978

An application of the square-root information filter to large scale linear interconnected systems

The paper considers the use of numerically stable square-root information filter (SRIF) algorithms to reduce the computation and storage requirements of a certain class of large-scale linear interconnected systems (multistation satellite tracking is examined as an example). The reductions are in comparison with conventional sequential covariance type formulations. To illustrate the SRIF algorithm: a 40 subsystem, 10 state problem, for example, has its storage requirements reduced by a full order of magnitude (from 84255 to 8100).

Bierman, G. J.↗
NASA NTRS2021

Retrieval Algorithm for the Column CO2 Mixing Ratio from Pulsed Multi-Wavelength Lidar Measurements

The retrieval algorithm for the column mixing ratio of CO2 from the measurements of a pulsed multi-wavelength integrated path differential absorption (IPDA) lidar is described. The lidar samples the shape of the 1572.33 nm CO2 absorption line at 15 or 30 wavelengths. The algorithm uses a least-squares fit between the CO2 line shape computed from a layered 10 atmosphere model to that sampled by the lidar. In addition to the column average CO2 dry air mole fraction (XCO2), several other parameters are also solved simultaneously from the fit. These include the Doppler shift in the received laser signal wavelengths, the product of the surface reflectivity and atmospheric transmission and a linear trend in the lidar receiver’s spectral response. The algorithm can also be used to solve for the average water vapor mixing ratio, which causes a secondary absorption in the wings of the CO2 absorption line under high humidity conditions. The least-squares fit is linearized about the 15 expected XCO2 value which allows the use of a standard linear least-squares fitting method and software tools. The standard deviation of the retrieved XCO2 is obtained from covariance matrix of the fit. An averaging kernel is defined similarly to that used for passive trace-gas sounding. Examples are presented of using the algorithm to retrieve XCO2 from the measurements from NASA Goddard’s airborne CO2 Sounder lidar made at a constant altitude and during spiral-down maneuvers.

Xiaoli Sun↗
DOE OSTI2023

SIF and Vegetation Indices in the US Midwestern Agroecosystems, 2016-2021, Carbon Monitoring System (CMS)

This dataset contains half-hourly ground solar-induced chlorophyll fluorescence (SIF) and vegetation indices including NDVI, EVI, Red edge chlorophyll index, green chlorophyll index, and photochemical reflectance index at seven crop sites in Nebraska and Illinois for the period 2016-2021. Four sites were located at Eddy Covariance (EC) tower sites (sites US-Ne2, US-Ne3, US-UiB, and US-UiC), and three sites were located on private farms (sites Reifsteck, Rund, and Reinhart). The sites were either miscanthus, corn-soybean rotation or corn-corn-soybean rotation. The spectral data for SIF retrieval and hyperspectral reflectance for vegetation index calculation were collected by the FluoSpec2 system, installed near planting, and uninstalled after harvest to collect whole growing-season data. Raw nadir SIF at 760 nm from different algorithms (sFLD, 3FLD, iFLD, SFM) are included. SFM_nonlinear and SFM_linear represent the Spectral fitting method (SFM) with the assumption that fluorescence and reflectance change with wavelength non-linearly and linearly, respectively. Additional data include two SIF correction factors including calibration coefficient adjustment factor (f_cal_corr_QEPRO) and upscaling nadir SIF to eddy covariance footprint factor (ratio_EC footprint, SIF pixel), and measured FPAR from quantum sensors and Rededge NDVI calculated FPAR. The data are provided in comma-separated values (CSV) format.

Ameriflux↗
DOE OSTI2022

ORNL Neutron Cross Section Measurements of 90 Zr

Nuclear criticality modeling and simulations rely on the quality of the existing evaluated nuclear data libraries such as Evaluated Nuclear Data File (ENDF)/B, the Joint Evaluated Fission and Fusion (JEFF) nuclear data library, or the Japanese Evaluated Nuclear Data Library (JENDL). In some cases, the cross-section evaluations of those libraries were found to be deficient in describing criticality benchmarks accurately. More than two decades ago, the US Nuclear Criticality Safety Program (NCSP) established a Nuclear Data (ND) task which encompassed experiments and evaluations. In response to this, the Oak Ridge National Laboratory (ORNL) formed a Nuclear Criticality and Data group which performed ND experiments, data analysis, and evaluations to produce ENDF files for the ND libraries as identified in the NCSP Five-Year Plan. Before being submitted to the ENDF library, files were processed and tested for performance by running benchmark calculations. This procedure was centralized in the ORNL group and is now often referred to as the ND pipeline. NCSP collaborates with the Joint Research Center (JRC) of the European Commission in Geel, Belgium, to perform high-resolution neutron-induced cross section measurements at the Geel Linear Accelerator (GELINA). The objective is to address emerging ND problems in criticality calculations. Difficulties with ND include insufficient neutron energy range, missing covariances, and previously unrecognized inaccuracies with experiments. New neutron total and capture cross sections of 90 Zr in the neutron energy range from 100 eV to several hundred keV were recently performed. These measured data will be used, together with existing high-resolution transmission data from a metallic 90 Zr sample, to improve representation of the cross sections.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Characterization of frequency standard instability by estimation of their covariance matrix

The popular 3-cornered hat method used for evaluating the noise contributions of individual frequency standards is revisited. This method is used in several cases, but sometimes the results are not consistent because one or more estimated clock variances turn out to be negative. Different causes of this unacceptable result have been conjectured: among them one regards the hypothesis of uncorrelated clocks, essential in this method. Since recently realistic cases of correlation between clocks, mainly due to the environmental conditions, have been observed, this paper proposes an entirely revisited version of the 3-cornered hat method which permits to evaluate the individual variances and also the possible covariances between clocks, by relaxing the hypothesis of uncorrelation. The uncertainty and the lack of contemporaneity of the measurement series are assumed to be negligible. The lack of the uncorrelation hypothesis calls for a more general mathematical model leading to an underdetermined linear system. The estimates of the (co)variances of the measurement series us well us those of the individual clocks are introduced by means of the scalar product of the related time series and arranged in the respective covariance matrices S and R. Since covariance matrix is positive definite by definition, the problem consists in estimating the unknown R, subject to the constraint of positive definiteness, from the known S. Unfortunately, this constraint is not sufficient to estimate R. Therefore a suitable optimization criterion is proposed, which assures the positive definiteness of R and, at the same time, minimizes the global correlation among clocks. Examples of frequency instability measurements processed by the "classical" 3-cornered hat method and the here-revisited method are presented showing that the solutions are identical only when the uncorrelation hypothesis doesn't violate the positive definiteness of R.

PatriziaTravella↗
NASA NTRS2008

Identifying Bearing Rotodynamic Coefficients Using an Extended Kalman Filter

An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter's performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.

Miller, Brad A.↗