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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
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 NTRS1993

Q-Markov covariance equivalent realization and its application to flexible structure identification

The Q-Markov covariance equivalent realization algorithm is applied to NASA's Minimast structure to identify state-space models for the purpose of designing closed-loop controllers, and laboratory test results are shown for the identification and for the closed-loop performance. The paper also presents for the first time a deterministic formulation of covariance parameters from a pulse response, a stochastic formulation of Markov parameters from a white-noise response, and a simple Q-Markov covariance equivalent realization formulation. This requires only pulse laboratory tests or only white-noise laboratory tests to generate Q-Markov covariance equivalent realizations.

Liu, Ketao↗
NASA NTRS2000

Stardust Navigation Covariance Analysis

The Stardust spacecraft was launched on February 7, 1999 aboard a Boeing Delta-II rocket. Mission participants include the National Aeronautics and Space Administration (NASA), the Jet Propulsion Laboratory (JPL), Lockheed Martin Astronautics (LMA) and the University of Washington. The primary objective of the mission is to collect in-situ samples of the coma of comet Wild-2 and return those samples to the Earth for analysis. Mission design and operational navigation for Stardust is performed by the Jet Propulsion Laboratory (JPL). This paper will describe the extensive JPL effort in support of the Stardust pre-launch analysis of the orbit determination component of the mission covariance study. A description of the mission and it's trajectory will be provided first, followed by a discussion of the covariance procedure and models. Predicted accuracy's will be examined as they relate to navigation delivery requirements for specific critical events during the mission. Stardust was launched into a heliocentric trajectory in early 1999. It will perform an Earth Gravity Assist (EGA) on January 15, 2001 to acquire an orbit for the eventual rendezvous with comet Wild-2. The spacecraft will fly through the coma (atmosphere) on the dayside of Wild-2 on January 2, 2004. At that time samples will be obtained using an aerogel collector. After the comet encounter Stardust will return to Earth when the Sample Return Capsule (SRC) will separate and land at the Utah Test Site (UTTR) on January 15, 2006. The spacecraft will however be deflected off into a heliocentric orbit. The mission is divided into three phases for the covariance analysis. They are 1) Launch to EGA, 2) EGA to Wild-2 encounter and 3) Wild-2 encounter to Earth reentry. Orbit determination assumptions for each phase are provided. These include estimated and consider parameters and their associated a-priori uncertainties. Major perturbations to the trajectory include 19 deterministic and statistical maneuvers planned for the mission. The spacecraft is three axis stabilized and has unbalanced thrusters for attitude control. Accelerations due to the attitude control system are treated stochastically. The tracking scenario for the study is patterned after the actual schedule employed during the different phases of the mission. Conventional X-band two-way Doppler and SRA range data was simulated and the standard accuracy for these data types was assumed throughout most of the mission. However, a deweighting scheme was used for the Doppler data during times of low Sun-Earth-Probe angles, especially in the case of the DSM. Optical data is assumed to be available starting at 50 days prior to the comet encounter. The optical data will be used to improve the ephemeris of Wild-2, which is considered crucial to properly target the comet flyby. Results of the covariance analysis are presented for all mission phases. Navigation capability will be discussed in terms of the uncertainty in the encounter B-Plane (B.R and B.T) and linearized time of flight. Delivery errors based on the final maneuver prior to the comet encounter will be presented. The most stringent navigation requirement is for the Earth reentry. The uncertainty in the flight path angle must be less than 0.02 degree (orbit determination and maneuver performance) to assure successful recovery of the SRC. Results presented show that this requirement can be met.

Menon, Premkumar R.↗
NASA NTRS1995

Climatic forcing of carbon-oxygen isotopic covariance in temperate-region marl lakes

Carbon and oxygen stable isotopic compositions of lacustrine carbonate from a southeastern Michigan marl lake display linear covariance over a range of 4.0% Peedee belemnite (PDB) in oxygen and 3.9% (PDB) in carbon. Mechanisms of delta 13 C-delta 18 O coupling conventionally attributed to lake closure in arid-region basins are inapplicable to hydrologically open lake systems. Thus, an alternative explanation of isotopic covariance in temperate region dimictic marl lakes is required. We propose that isotopic covariance is a direct record of change in regional climate. In short-residence-time temperate-region lake basins, summer meteoric precipitation is enriched in 18O relative to winter values, and summer organic productivity enriches epilimnic dissolved inorganic carbon in 13C. Thus, climate change toward longer summers and/or shorter winters could result in greater proportions of warm-month meteoric precipitation, longer durations of warm-month productivity, and net long-term enrichment in carbonate 18O and 13C. Isotopic covariance observed in the Michigan marl lake cores is interpreted to reflect postglacial warming from 10 to 3 ka followed by cooler mean annual temperature, a shift toward greater proportions of seasonal summer precipitation, a shortening of the winter season, or some combination of these three factors.

NASA Discipline Number 52-30↗
NASA NTRS1997

On the Possibility of Ill-Conditioned Covariance Matrices in the First-Order Two-Step Estimator

The first-order two-step nonlinear estimator, when applied to a problem of orbital navigation, is found to occasionally produce first step covariance matrices with very low eigenvalues at certain trajectory points. This anomaly is the result of the linear approximation to the first step covariance propagation. The study of this anomaly begins with expressing the propagation of the first and second step covariance matrices in terms of a single matrix. This matrix is shown to have a rank equal to the difference between the number of first step states and the number of second step states. Furthermore, under some simplifying assumptions, it is found that the basis of the column space of this matrix remains fixed once the filter has removed the large initial state error. A test matrix containing the basis of this column space and the partial derivative matrix relating first and second step states is derived. This square test matrix, which has dimensions equal to the number of first step states, numerically drops rank at the same locations that the first step covariance does. It is formulated in terms of a set of constant vectors (the basis) and a matrix which can be computed from a reference trajectory (the partial derivative matrix). A simple example problem involving dynamics which are described by two states and a range measurement illustrate the cause of this anomaly and the application of the aforementioned numerical test in more detail.

Garrison, James L.↗
NASA NTRS2006

Adapting Covariance Propagation to Account for the Presence of Modeled and Unmodeled Maneuvers

This paper explores techniques that can be used to adapt the standard linearized propagation of an orbital covariance matrix to the case where there is a maneuver and an associated execution uncertainty. A Monte Carlo technique is used to construct a final orbital covariance matrix for a 'propagate-burn-propagate' process that takes into account initial state uncertainty and execution uncertainties in the maneuver magnitude. This final orbital covariance matrix is regarded as 'truth' and comparisons between it and three methods using modified linearized covariance propagation are made. The first method accounts for the maneuver by modeling its nominal effect within the state transition matrix but excludes the execution uncertainty by omitting a process noise matrix from the computation. In the second method, the maneuver is not modeled but the uncertainty in its magnitude is accounted for by the inclusion of a process noise matrix. In the third method, which is essentially a hybrid of the first two, the nominal portion of the maneuver is included via the state transition matrix while a process noise matrix is used to account for the magnitude uncertainty. Since this method also correctly accounts for the presence of the maneuver in the nominal orbit, it is the best method for applications involving the computation of times of closest approach and the corresponding probability of collision, Pc. However, applications for the two other methods exist and are briefly discussed. Despite the fact that the process model ('propagate-burn-propagate') that was studied was very simple - point-mass gravitational effects due to the Earth combined with an impulsive delta-V in the velocity direction for the maneuver - generalizations to more complex scenarios, including high fidelity force models, finite duration maneuvers, and maneuver pointing errors, are straightforward and are discussed in the conclusion.

Schiff, Conrad↗
NASA NTRS2008

Generalized Linear Covariance Analysis

We review and extend in two directions the results of prior work on generalized covariance analysis methods. This prior work allowed for partitioning of the state space into "solve-for" and "consider" parameters, allowed for differences between the formal values and the true values of the measurement noise, process noise, and a priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and a priori solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator s anchor time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the "variance sandpile" and the "sensitivity mosaic," and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.

Carpenter, J. Russell↗
NASA NTRS2014

Generalized Linear Covariance Analysis

This talk presents a comprehensive approach to filter modeling for generalized covariance analysis of both batch least-squares and sequential estimators. We review and extend in two directions the results of prior work that allowed for partitioning of the state space into solve-for'' and consider'' parameters, accounted for differences between the formal values and the true values of the measurement noise, process noise, and textita priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator's epoch time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the variance sandpile'' and the sensitivity mosaic,'' and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.

Navagation↗
NASA NTRS2014

Generalized Linear Covariance Analysis

This talk presents a comprehensive approach to filter modeling for generalized covariance analysis of both batch least-squares and sequential estimators. We review and extend in two directions the results of prior work that allowed for partitioning of the state space into solve-for'' and consider'' parameters, accounted for differences between the formal values and the true values of the measurement noise, process noise, and textita priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator's epoch time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the variance sandpile'' and the sensitivity mosaic,'' and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.

n/a↗
NASA NTRS2015

Empirical State Error Covariance Matrix for Batch Estimation

State estimation techniques effectively provide mean state estimates. However, the theoretical state error covariance matrices provided as part of these techniques often suffer from a lack of confidence in their ability to describe the uncertainty in the estimated states. By a reinterpretation of the equations involved in the weighted batch least squares algorithm, it is possible to directly arrive at an empirical state error covariance matrix. The proposed empirical state error covariance matrix will contain the effect of all error sources, known or not. This empirical error covariance matrix may be calculated as a side computation for each unique batch solution. Results based on the proposed technique will be presented for a simple, two observer and measurement error only problem.

Frisbee, Joe↗
NASA NTRS2016

Covariance Manipulation for Conjunction Assessment

Use of probability of collision (Pc) has brought sophistication to CA. Made possible by JSpOC precision catalogue because provides covariance. Has essentially replaced miss distance as basic CA parameter. Embrace of Pc has elevated methods to 'manipulate' covariance to enable/improve CA calculations. Two such methods to be examined here; compensation for absent or unreliable covariances through 'Maximum Pc' calculation constructs, projection (not propagation) of epoch covariances forward in time to try to enable better risk assessments. Two questions to be answered about each; situations to which such approaches are properly applicable, amount of utility that such methods offer.

Probability↗
NASA NTRSDate not supplied

Validation of Linear Covariance Techniques for Mars Entry, Descent, and Landing Guidance and Navigation Performance Analysis

Current Monte Carlo-based uncertainty analysis methods may require significant computational resources to evaluate the performance of a closed-loop guidance, navigation, and control system. An attractive alternative, particularly during the preliminary and conceptual design phase, is to use linear covariance analysis, which can provide the same statistical information as Monte Carlo methods at a fraction of the computational load. Linear covariance has already been demonstrated in various spaceflight regimes, but only recently has it been applied to atmospheric flight. In this study, a 6-degree-of-freedom formulation of both a linear covariance and Monte Carlo analysis tools are utilized for a Mars entry, descent, and landing scenario which capture both atmospheric and powered flight phases to support precision landing. Comparison of the performance results shows close agreement between the linear covariance and traditional Monte Carlo methods when incorporating an assortment of guidance algorithms and processing a variety of inertial and relative sensor measurements onboard the lander's navigation filter.

James W. Williams↗
NASA NTRSDate not supplied

Structured Covariance Gaussian Networks for Orion Crew Module Aerodynamic Uncertainty Quantification

In this paper we propose a new approach for nonlinear regression and uncertainty quantification. The method is based on a pair of neural networks which parameterize mean and dense covariance functions of a multivariate Gaussian process, trained together to maximize the log-likelihood of observing the given data. The covariance matrix is made positive definite at every input by construction. We also propose a sampling approach that produces viable surrogate function realizations from the Gaussian process. We call the proposed model a Structured Covariance Gaussian Network (SCGN). We illustrate the use of SCGNs for learning an aerodynamic response surface with built-in uncertainty for the Orion crew module. We find that SCGN provides an efficient and systematic way to learn nonlinear functional relationships and dense covariances. We compare results to a baseline Gaussian process regressor and observe that the SCGN provides comparable uncertainty descriptions with improved scalability to dataset size. The sample functions generated by SCGN are fast to evaluate online and are therefore convenient for use in trajectory simulations. These results suggest that SCGN may be a viable computational method for aerodynamic uncertainty quantification.

machine learning↗
NASA NTRSDate not supplied

Structured Covariance Gaussian Networks for Orion Crew Module Aerodynamic Uncertainty Quantification

In this paper we propose a new approach for nonlinear regression and uncertainty quantification. The method is based on a pair of neural networks which parameterize mean and dense covariance functions of a multivariate Gaussian process, trained together to maximize the log-likelihood of observing the given data. The covariance matrix is made positive definite at every input by construction. We also propose a sampling approach that produces viable surrogate function realizations from the Gaussian process. We call the proposed model a Structured Covariance Gaussian Network (SCGN). We illustrate the use of SCGNs for learning an aerodynamic response surface with built-in uncertainty for the Orion crew module. We find that SCGN provides an efficient and systematic way to learn nonlinear functional relationships and dense covariances. We compare results to a baseline Gaussian process regressor and observe that the SCGN provides comparable uncertainty descriptions with improved scalability to dataset size. The sample functions generated by SCGN are fast to evaluate online and are therefore convenient for use in trajectory simulations. These results suggest that SCGN may be a viable computational method for aerodynamic uncertainty quantification.

machine learning↗
DOE OSTI2025

Better practices for inferring ecosystem water use strategy from eddy covariance data

Eddy covariance data are critical for inferring ecosystem water use strategies. Yet, such inferences are sensitive to a range of assumptions applied across studies, hindering our understanding of water use strategies within and across eddy covariance sites. A recent analysis across 151 FLUXNET2015 and AmeriFlux-FLUXNET datasets found that poor model performance was the key driver of non-robust inferences of ecosystem water use strategies. Here, we leverage this previous analysis to (i) identify the specific assumptions that improve inference model performance across most sites, (ii) explain the mechanisms behind the performance improvements, and (iii) check whether better performance improves water use inference. We find that the common practice of fitting a model to canopy conductance (G c ) derived from the evapotranspiration (ET) observations, rather than to observed ET itself, artificially amplifies data errors and degrades the model performance. Next, accounting for vegetation dynamics by applying a growing season filter or incorporating satellite LAI data improves performance, but the former practice may remove soil water stress periods. Lastly, using the leaf-to-air vapor pressure deficit (VPD l ) derived from ET observations as a model input may artificially inflate performance. Based on these results, we recommend selecting observed ET (rather than derived G c ) as the response variable, carefully accounting for vegetation dynamics, and avoiding derived VPD l as a model input; these best practices improve model performance by c. 20% and robustness by c. 80% across all eddy covariance sites. Nevertheless, the performance improvements do not always correspond to more robust inference of water use strategies, as model parameter selection and surface energy budget closure corrections still strongly influence the ecosystem water use parameter estimation in a site-specific manner.

AmeriFlux↗
DOE OSTI2023

Upscaling Wetland Methane Emissions From the FLUXNET–CH4 Eddy Covariance Network (UpCH4 v1.0): Model Development, Network Assessment, and Budget Comparison

Wetlands are responsible for 20%–31% of global methane (CH 4 ) emissions and account for a large source of uncertainty in the global CH 4 budget. Data-driven upscaling of CH 4 fluxes from eddy covariance measurements can provide new and independent bottom-up estimates of wetland CH 4 emissions. Here, we develop a six-predictor random forest upscaling model (UpCH4), trained on 119 site-years of eddy covariance CH 4 flux data from 43 freshwater wetland sites in the FLUXNET-CH4 Community Product. Network patterns in site-level annual means and mean seasonal cycles of CH 4 fluxes were reproduced accurately in tundra, boreal, and temperate regions (Nash-Sutcliffe Efficiency ~0.52–0.63 and 0.53). UpCH4 estimated annual global wetland CH 4 emissions of 146 ± 43 TgCH 4 y –1 for 2001–2018 which agrees closely with current bottom-up land surface models (102–181 TgCH 4 y –1 ) and overlaps with top-down atmospheric inversion models (155–200 TgCH 4 y –1 ). However, UpCH4 diverged from both types of models in the spatial pattern and seasonal dynamics of tropical wetland emissions. We conclude that upscaling of eddy covariance CH 4 fluxes has the potential to produce realistic extra-tropical wetland CH 4 emissions estimates which will improve with more flux data. To reduce uncertainty in upscaled estimates, researchers could prioritize new wetland flux sites along humid-to-arid tropical climate gradients, from major rainforest basins (Congo, Amazon, and SE Asia), into monsoon (Bangladesh and India) and savannah regions (African Sahel) and be paired with improved knowledge of wetland extent seasonal dynamics in these regions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Distinguishing the XUV-induced Coulomb explosion dynamics of iodobenzene using covariance analysis

The primary and secondary fragmentation dynamics of iodobenzene following its ionization at 120 eV were determined using three-dimensional velocity map imaging and covariance analysis. Site-selective iodine 4d ionization was used to populate a range of excited polycationic parent states, which primarily broke apart at the carbon-iodine bond to produce I+ with phenyl or phenyl-like cations (C n H x + or C n H, with n = 1 – 6 and x = 1 – 5). The molecular products were produced with varying degrees of internal excitation and dehydrogenation, leading to stable and unstable outcomes. This further allowed the secondary dynamics of C 6 H x 2+ intermediates to be distinguished using native-frame covariance analysis, which isolated these processes in their own centre-of-mass reference frames. Furthermore, the mass resolution of the imaging mass spectrometer used for these measurements enabled the primary and secondary reaction channels to be specified at the level of individual hydrogen atoms, demonstrating the ability of covariance analysis to comprehensively measure the competing fragmentation channels of aryl cations, including those involving intermediate steps.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Updates from the Covariance Session Committee [Slides]

The CSEWG covariance session template paper was submitted on June 8, 2021 to journal. CSEWG will not publish adjusted VIII.1, but there is interest in adjustment results from the community. Other focus points for the release for VIII.1 include stringent testing of covariances before their release and missing covariances.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗