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All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Applications of singular value analysis and partial-step algorithm for nonlinear orbit determination

An adaptive method in which cruise and nonlinear orbit determination problems can be solved using a single program is presented. It involves singular value decomposition augmented with an extended partial step algorithm. The extended partial step algorithm constrains the size of the correction to the spacecraft state and other solve-for parameters. The correction is controlled by an a priori covariance and a user-supplied bounds parameter. The extended partial step method is an extension of the update portion of the singular value decomposition algorithm. It thus preserves the numerical stability of the singular value decomposition method, while extending the region over which it converges. In linear cases, this method reduces to the singular value decomposition algorithm with the full rank solution. Two examples are presented to illustrate the method's utility.

Ryne, Mark S.↗
NASA NTRS1985

Efficient algorithms for use in probabilistic finite element analysis

This paper investigates the use of Fast Probability Integration (FPI) algorithms in a Finite Element environment. A method allowing the representation of correlated fields in terms of a vector of uncorrelated transformed variables, based on the spectral decomposition of the variance-covariance matrix is developed. The response of the deterministic model corresponding to selected perturbations of these uncorrelated variables is then obtained via a Newton-type iterative scheme. The results of the perturbed problems are used to construct a local representation of the model's behavior in the neighborhood of the deterministic state, which the FPI algorithm will use to estimate the reliability of the system. Although the proposed strategy has thus far only been applied to linear elastostatics, the extension of the method to a broader class of problems appears to be feasible.

Dias, J. B.↗
NASA NTRS2019

Principal Component Analysis of Up-The-Ramp Sampled Infrared Array Data

We describe the results of principal component analysis (PCA) of up-the-ramp sampled infrared (IR) array data from the Hubble Space Telescope wide field camera 3 (WFC3 IR), James Webb Space Telescope NIRSpec, and prototype Wide Field Infrared Survey Telescope’s wide field instrument detectors. These systems use, respectively, Teledyne H1R, H2RG, and H4RG-10 near-IR detector arrays with a variety of IR array controllers. The PCA shows that the Legendre polynomials approximate the principal components of these systems (i.e., they roughly diagonalize the covariance matrix). In contrast to the monomial basis that is widely used for polynomial fitting and linearization today, the Legendre polynomials are an orthonormal basis. They provide a quantifiable, compact, and (nearly) linearly uncorrelated representation of the information content of the data. By fitting a few Legendre polynomials, nearly all of the meaningful information in representative WFC3 astronomical datacubes can be condensed from 15 up-the-ramp samples down to 6 compressible Legendre coefficients per pixel. The higher order coefficients contain time domain information that is lost when one projects up-the-ramp sampled datacubes onto two-dimensional images by fitting a straight line, even if the data are linearized before fitting the line. Going forward, we believe that this time domain information is potentially important for disentangling the various nonlinearities that can affect IR array observations, i.e., inherent pixel nonlinearity, persistence, burn in, brighter-fatter effect, (potentially) nonlinear interpixel capacitance, and perhaps others.

Rauscher, Bernard J.↗
NASA NTRS1995

Causal correlation of foliar biochemical concentrations with AVIRIS spectra using forced entry linear regression

A major goal of airborne imaging spectrometry is to estimate the biochemical composition of vegetation canopies from reflectance spectra. Remotely-sensed estimates of foliar biochemical concentrations of forests would provide valuable indicators of ecosystem function at regional and eventually global scales. Empirical research has shown a relationship exists between the amount of radiation reflected from absorption features and the concentration of given biochemicals in leaves and canopies (Matson et al., 1994, Johnson et al., 1994). A technique commonly used to determine which wavelengths have the strongest correlation with the biochemical of interest is unguided (stepwise) multiple regression. Wavelengths are entered into a multivariate regression equation, in their order of importance, each contributing to the reduction of the variance in the measured biochemical concentration. A significant problem with the use of stepwise regression for determining the correlation between biochemical concentration and spectra is that of 'overfitting' as there are significantly more wavebands than biochemical measurements. This could result in the selection of wavebands which may be more accurately attributable to noise or canopy effects. In addition, there is a real problem of collinearity in that the individual biochemical concentrations may covary. A strong correlation between the reflectance at a given wavelength and the concentration of a biochemical of interest, therefore, may be due to the effect of another biochemical which is closely related. Furthermore, it is not always possible to account for potentially suitable waveband omissions in the stepwise selection procedure. This concern about the suitability of stepwise regression has been identified and acknowledged in a number of recent studies (Wessman et al., 1988, Curran, 1989, Curran et al., 1992, Peterson and Hubbard, 1992, Martine and Aber, 1994, Kupiec, 1994). These studies have pointed to the lack of a physical link between wavelengths chosen by stepwise regression and the biochemical of interest, and this in turn has cast doubts on the use of imaging spectrometry for the estimation of foliar biochemical concentrations at sites distant from the training sites. To investigate this problem, an analysis was conducted on the variation in canopy biochemical concentrations and reflectance spectra using forced entry linear regression.

Dawson, Terence P.↗
NASA NTRS1996

Cardiovascular responses of semi-arboreal snakes to chronic, intermittent hypergravity

Cardiovascular functions were studied in semi-arboreal rat snakes (Elaphe obsoleta) following long-term, intermittent exposure to +1.5 Gz (head-to-tail acceleration) on a centrifuge. Snakes were held in a nearly straight position within horizontal plastic tubes during periods of centrifugation. Centrifugal acceleration, therefore, subjected snakes to a linear force gradient with the maximal force being experienced at the tail. Compared to non-centrifuged controls, Gz-acclimated snakes showed greater increases of heart rate during head-up tilt or acceleration, greater sensitivity of arterial pressure to circulating catecholamines, higher blood levels of corticosterone, and higher blood ratios of prostaglandin F 2 alpha/prostaglandin E2. Cardiovascular tolerance to increased gravity during graded Gz acceleration was measured as the maximum (caudal) acceleration force at which carotid arterial blood flow became null. When such tolerances were adjusted for effects of body size and other continuous variables incorporated into an analysis of covariance, the difference between the adjusted mean values of control and acclimated snakes (2.37 and 2.84 Gz, respectively) corresponded closely to the 0.5 G difference between the acclimation G (1.5) and Earth gravity (1.0). As in other vertebrates, cardiovascular tolerance to Gz stress tended to be increased by acclimation, short body length, high arterial pressure, and comparatively large blood volume. Voluntary body movements were important for promoting carotid blood flow at the higher levels of Gz stress.

NASA Discipline Cardiopulmonary↗
NASA NTRS2004

CDGPS-Based Relative Navigation for Multiple Spacecraft

This thesis investigates the use of Carrier-phase Differential GPS (CDGPS) in relative navigation filters for formation flying spacecraft. This work analyzes the relationship between the Extended Kalman Filter (EKF) design parameters and the resulting estimation accuracies, and in particular, the effect of the process and measurement noises on the semimajor axis error. This analysis clearly demonstrates that CDGPS-based relative navigation Kalman filters yield good estimation performance without satisfying the strong correlation property that previous work had associated with "good" navigation filters. Several examples are presented to show that the Kalman filter can be forced to create solutions with stronger correlations, but these always result in larger semimajor axis errors. These linear and nonlinear simulations also demonstrated the crucial role of the process noise in determining the semimajor axis knowledge. More sophisticated nonlinear models were included to reduce the propagation error in the estimator, but for long time steps and large separations, the EKF, which only uses a linearized covariance propagation, yielded very poor performance. In contrast, the CDGPS-based Unscented Kalman relative navigation Filter (UKF) handled the dynamic and measurement nonlinearities much better and yielded far superior performance than the EKF. The UKF produced good estimates for scenarios with long baselines and time steps for which the EKF would diverge rapidly. A hardware-in-the-loop testbed that is compatible with the Spirent Simulator at NASA GSFC was developed to provide a very flexible and robust capability for demonstrating CDGPS technologies in closed-loop. This extended previous work to implement the decentralized relative navigation algorithms in real time.

Mitchell, Megan Leigh↗
NASA NTRS1993

The Effects of Noise on Polarimetric SAR Data

Polarimetric SAR data can provide a great deal of information about the scattering behavior of the surface under observation. Polarimetric SAR systems often measure the scattering matrices of the areas under observation in linear polarizations (H and V). From the scattering matrix commonly used forms such as the covariance matrix and the Stokes matrix can be easily derived. Other measures derived from polarimetric SAR data include the standard deviation of texture, correlation coefficients between scattering matrix terms, and the mode and variance of phase differences between scattering matrix terms. The effects of additive system noise on these measurements is not often considered in the literature on this subject.

Polarimetric SAR Data analysis↗
NASA NTRS2017

B-plane Evolution Under Highly Non-Keplerian Dynamics

Juno is the second of a series of New Frontiers missions and was launched in 2011. The spacecraft was set en route to Jupiter, and its Jupiter Orbit Insertion occurred on 2016-07-04 after a five-year cruise in deep space. The mission phase just prior to this large maneuver is called approach. As navigation team, we were responsible for precise orbit determination of the Juno spacecraft to ensure a successful orbit insertion. To evaluate the navigation performance we employed the B-plane mapping, where the incoming hyperbolic velocity defines the plane perpendicular to it, and the time to go to hit the plane will directly map into the uncertainties of the target point. The B-plane is a convenient tool when assessing the navigation performance as it is not affected by non-linearities due to the gravitational pull of the targeted body. However, as the Jupiter Orbit Insertion approached we started to realize that the B-plane mapping uncertainties were significantly larger than expected. We found that the B-plane mapping time had tremendous influence on the covariance inflation in the B-plane. Because of the close approach distance during the Jupiter Orbit Insertion and the strong interaction with J2 spherical harmonic coefficient, the Juno dynamics were too far from a Keplerian one assumed for the B-plane mapping. We first discuss the analytical approach of the B-plane mapping uncertainty and perform a numerical analysis to isolate the components of the Juno dynamics that cause the B-plane covariance inflation.

Bordi, John↗
NASA NTRS2018

Understanding Climate-Vegetation Interactions in Global Rainforests Through a GP-Tree Analysis

The tropical rainforests are the largest reserves of terrestrial carbon and, therefore, the future of these rainforests is a question that is of immense importance in the geoscience research community. With the recent severe Amazonian droughts in 2005 and 2010 and on-going drought in the Congo region for more than two decades, there is growing concern that these forests could succumb to precipitation reduction, causing extensive carbon release and feedback to the carbon cycle. However, there is no single ecosystem model that quantifies the relationship between vegetation health in these rainforests and climatic factors. Small scale studies have used statistical correlation measure and simple linear regression to model climate-vegetation interactions, but suffer from the lack of comprehensive data representation as well as simplistic assumptions about dependency of the target on the covariates. In this paper we use genetic programming (GP) based symbolic regression for discovering equations that govern the vegetation climate dynamics in the rainforests. Expecting micro-regions within the rainforests to have unique characteristics compared to the overall general characteristics, we use a modified regression-tree based hierarchical partitioning of the space to build individual models for each partition. The discovery of these equations reveal very interesting characteristics about the Amazon and the Congo rainforests. Our method GP-tree shows that the rainforests exhibit tremendous resiliency in the face of extreme climatic events by adapting to changing conditions.

genetic programming↗
DOE OSTI2024

Application of Partial Least Squares Approaches to Pyroprocessing ER Data

Multivariate approaches show promise for application to process monitoring for safeguards of pyroprocessing. Past MPACT work explored the application of Principal Component Analysis (PCA) to detect off-normal conditions in pyroprocessing electrorefiner (ER) data from in the Hot Fuel Examination Facility (HFEF) at Idaho National Laboratory (INL) known as the Scalable Pyrochemical Recycling testbed (SPyRe) ER. PCA, however, does not consider the output variables. In FY24, multivariate analysis was extended from PCA to Partial Least Squares (PLS) analysis. PLS maximizes the variance between both the input signals and output variables. In the case of this work, PLS was applied in two different manners: Predictive PLS and Discriminant PLS. Predictive PLS maximizes the covariance between the process variables of the ER and the measured U concentration from in-situ voltammetry. Discriminant PLS maximizes the covariance between the process variables and a set of training process “states” such as known off-normal conditions. By projecting into the latent variable space in PLS, the process variables can be regressed onto the outputs and predictions can be made for new data sets. In this work, by applying predictive PLS, a penalized non-linear PLS approach was able to make predictions of concentration based on test and training data and detect when operations were off-normal. However, the predictive PLS does not classify the signals to which off-normal operations are attributable. Discriminant PLS can be used to classify off-normal operations but is inadequate to properly classify specific off-normal classes like power supply faults when the Discriminant PLS model is only specifically trained to detect that off-normal class. When all faults are trained against the observation data, all three operational classes are accurately classified and distinguished. Thus, future application of latent variable techniques should not select any given method, but should use a mixture of PCA, Predictive PLS, and Discriminant PLS.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1989

Gravity field determination and error assessment techniques

Linear estimation theory, along with a new technique to compute relative data weights, was applied to the determination of the Earth's geopotential field and other geophysical model parameters using a combination of satellite ground-based tracking data, satellite altimetry data, and the surface gravimetry data. The relative data weights for the inhomogeneous data sets are estimated simultaneously with the gravity field and other geophysical and orbit parameters in a least squares approach to produce the University of Texas gravity field models. New techniques to perform calibration of the formal covariance matrix for the geopotential solution were developed to obtain a reliable gravity field error estimate. Different techniques, which include orbit residual analysis, surface gravity anomaly residual analysis, subset gravity solution comparisons and consider covariance analysis, were applied to investigate the reliability of the calibration.

Yuan, D. N.↗
NASA NTRS1992

Analysis of the lettuce data from the variable pressure growth chamber at NASA Johnson Space Center: A three-stage nested design model

A model of three-stage nested experimental design was applied to analyze the lettuce data obtained from the variable pressure growth chamber test bed at NASA-Johnson Space Center. From the results of an application of the analysis of variance and covariance on the data set, it was noted that all of the (uncontrollable) factors, Side, Zone, Height and (controllable) PAR (photosynthetically active radiation), had nonhomogeneous effects on the dry weight of the edible biomass of lettuce per pot. Incidentally, the variations accountable to the (uncontrollable) factorial heterogeneities are merely 9 percent and 17 percent of the total variation for both the first and second crop test, respectively. After adjusting for the PAR as a covariate in the no-intercept model, the accountable variations to all the four factors are 94 percent and 92 percent for the first and the second crop test, respectively. With the use of a no-intercept simple linear regression model, the accountable variations to the factor PAR are 92 percent and 90 percent for the first and the second crop test, respectively. Evidently, the (controllable) factor PAR is the dominating one.

Lee, Tze-San↗
NASA NTRS2002

Definition of Contravariant Velocity Components

This is an old issue in computational fluid dynamics (CFD). What is the so-called contravariant velocity or contravariant velocity component? In the article, we review the basics of tensor analysis and give the contravariant velocity component a rigorous explanation. For a given coordinate system, there exist two uniquely determined sets of base vector systems - one is the covariant and another is the contravariant base vector system. The two base vector systems are reciprocal. The so-called contravariant velocity component is really the contravariant component of a velocity vector for a time-independent coordinate system, or the contravariant component of a relative velocity between fluid and coordinates, for a time-dependent coordinate system. The contravariant velocity components are not physical quantities of the velocity vector. Their magnitudes, dimensions, and associated directions are controlled by their corresponding covariant base vectors. Several 2-D (two-dimensional) linear examples and 2-D mass-conservation equation are used to illustrate the details of expressing a vector with respect to the covariant and contravariant base vector systems, respectively.

Hung, Ching-Mao↗
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 NTRS2000

Comparison of On-Orbit Performance of Rate Sensing Gyroscopes

This work presents results from the study of a large volume of spacecraft flight data pertaining to gyroscope performance. We have examined long and short term trends of gyroscope biase of first, an exact solution for the time-dependence of the attitude part of the state error covariance, averaged over the three spacecraft axes, is given. This solution is more complete than the usual cubic polynomial for the variance in that it includes coupling among the three gyroscope axes and includes an important term arising from the initial correlations. Second, several continuous 24-hour spans of gyroscope data are examined to verify the short-term statistical model. This analysis demonstrates that in-flight data can be used to determine the strength of the white noise driving the random walk of the gyroscope bias. This may be useful for postlaunch improvement to the noise model and for diagnosing the health of the gyroscope. Third, the long-term trends in gyroscope biases show a nearly linear systematic variation over time scales of years. This has been found on three different missions. While the random walk model is adequate as a basis for onboard Kalman filters or for state estimation using relatively short time spans, these trends indicate that some applications could benefit by accounting for the secular changes in the biases. One example is a new gyroscope calibration method that is under development that allows for multi-epoch bias solutions.

Sedlak, Joseph↗
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 NTRS1992

Radar sensitivity and antenna scan pattern study for a satellite-based Radar Wind Sounder (RAWS)

Modeling global atmospheric circulations and forecasting the weather would improve greatly if worldwide information on winds aloft were available. Recognition of this led to the inclusion of the LAser Wind Sounder (LAWS) system to measure Doppler shifts from aerosols in the planned for Earth Observation System (EOS). However, gaps will exist in LAWS coverage where heavy clouds are present. The RAdar Wind Sensor (RAWS) is an instrument that could fill these gaps by measuring Doppler shifts from clouds and rain. Previous studies conducted at the University of Kansas show RAWS as a feasible instrument. This thesis pertains to the signal-to-noise ratio (SNR) sensitivity, transmit waveform, and limitations to the antenna scan pattern of the RAWS system. A dop-size distribution model is selected and applied to the radar range equation for the sensitivity analysis. Six frequencies are used in computing the SNR for several cloud types to determine the optimal transmit frequency. the results show the use of two frequencies, one higher (94 GHz) to obtain sensitivity for thinner cloud, and a lower frequency (24 GHz) to obtain sensitivity for thinner cloud, and a lower frequency (24 GHz) for better penetration in rain, provide ample SNR. The waveform design supports covariance estimation processing. This estimator eliminates the Doppler ambiguities compounded by the selection of such high transmit frequencies, while providing an estimate of the mean frequency. the unambiguous range and velocity computation shows them to be within acceptable limits. The design goal for the RAWS system is to limit the wind-speed error to less than 1 ms(exp -1). Due to linear dependence between vectors for a three-vector scan pattern, a reasonable wind-speed error is unattainable. Only the two-vector scan pattern falls within the wind-error limits for azimuth angles between 16 deg to 70 deg. However, this scan only allows two components of the wind to be determined. As a result, a technique is then shown, based on the Z-R-V relationships, that permit the vertical component (i.e., rain) to be computed. Thus the horizontal wind components may be obtained form the covariance estimator and the vertical component from the reflectivity factor. Finally, a new candidate system is introduced which summarizes the parameters taken from previous RAWS studies, or those modified in this thesis.

Stuart, Michael A.↗
NASA NTRS2007

NASA CEV On-Orbit GN&C Analysis

The Orion spacecraft orbit GN&C system will be required to perform both ISS servicing missions and Lunar sortie and outpost crew transportation. While certain aspects of these two missions are complementary, the two missions are also distinct in many ways. Common between the missions is a Low Earth Orbit (LEO) rendezvous, one with the ISS And the other with the LSAM/EDS stack prior to trans-lunar insertion. The lunar missions will additionally require Orion to perform orbit maintenance in LLO, perform contingency lunar orbit operations including RPOD with the LSAM, perform the TEI maneuver sequence, and execute the trans-Earth cruise. The NASA-led team developed a reference configuration orbit GN&C system capable of executing all of these activities with the same navigation sensor suite and control effectors while fully meeting the requirements being developed for System Requirements Review in advance of prime contractor selection. This paper will present an overview of the analyses performed to support system trade studies, demonstrate the feasibility of the NASA reference configuration, and validate the Orion system requirements. These analyses include linear covariance techniques, 3-DOF Monte Carlo simulations, 6-DOF Monte Carlo simulations, and analytical evaluations of GN&C systems performed by the NASA-led Orion team to characterize the sensitivities of Orion s various missions and assess the unique challenges of each. The first part of this paper will describe the trade studies that were performed in order to characterize the RPOD system performance for both the ISS and the lunar missions including development of an RPOD operations concept, RPOD trajectories, contingency scenarios, docking mechanism and associated contact conditions, post-contact thrust issues, relative navigation sensors, relative navigation sensor target infrastructure. The paper will also discuss concepts for both manually-piloted and automatically executed scenarios, as well as the remotely-piloted contingency scenario in LLO. The second part of the paper will discuss the analyses performed for lunar and cislunar GN&C performance including the accuracy of the post-insertion lunar orbit, the ability of Orion to hit a particular Earth return entry corridor, attitude control solutions for long-duration surface operations, and autonomous navigation in support of TEI without ground tracking.

DSouza, Chris↗