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All sourcesNASA NTRSDOE OSTI
NASA NTRS2022

Effective Uncertainty Quantification for Multi-Angle Polarimetric Aerosol Remote Sensing Over Ocean

Multi-angle polarimetric (MAP) measurements can enable detailed characterization of aerosol microphysical and optical properties and improve atmospheric correction in ocean color remote sensing. Advanced retrieval algorithms have been developed to obtain multiple geophysical parameters in the atmosphere–ocean system. Theoretical pixel-wise retrieval uncertainties based on error propagation have been used to quantify retrieval performance and determine the quality of data products. However, standard error propagation techniques in high-dimensional retrievals may not always represent true retrieval errors well due to issues such as local minima and the nonlinear dependence of the forward model on the retrieved parameters near the solution. In this work, we analyze these theoretical uncertainty estimates and validate them using a flexible Monte Carlo approach. The Fast Multi-Angular Polarimetric Ocean coLor (FastMAPOL) retrieval algorithm, based on efficient neural network forward models, is used to conduct the retrievals and uncertainty quantification on both synthetic HARP2 (Hyper-Angular Rainbow Polarimeter 2) and AirHARP (airborne version of HARP2) datasets. In addition, for practical application of the uncertainty evaluation technique in operational data processing, we use the automatic differentiation method to calculate derivatives analytically based on the neural network models. Both the speed and accuracy associated with uncertainty quantification for MAP retrievals are addressed in this study. Pixel-wise retrieval uncertainties are further evaluated for the real AirHARP field campaign data. The uncertainty quantification methods and results can be used to evaluate the quality of data products, as well as guide MAP algorithm development for current and future satellite systems such as NASA’s Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission.

PACE↗
NASA NTRS1993

The importance of robust error control in data compression applications

Data compression has become an increasingly popular option as advances in information technology have placed further demands on data storage capabilities. With compression ratios as high as 100:1 the benefits are clear; however, the inherent intolerance of many compression formats to error events should be given careful consideration. If we consider that efficiently compressed data will ideally contain no redundancy, then the introduction of a channel error must result in a change of understanding from that of the original source. While the prefix property of codes such as Huffman enables resynchronisation, this is not sufficient to arrest propagating errors in an adaptive environment. Arithmetic, Lempel-Ziv, discrete cosine transform (DCT) and fractal methods are similarly prone to error propagating behaviors. It is, therefore, essential that compression implementations provide sufficient combatant error control in order to maintain data integrity. Ideally, this control should be derived from a full understanding of the prevailing error mechanisms and their interaction with both the system configuration and the compression schemes in use.

Woolley, S. I.↗
NASA NTRSDate not supplied

Early Information Parameter-Set Analysis for Satellite Close Approaches using Machine Learning

Understanding orbital mechanics is essential in space flight and navigation applications, and leveraging modern force models for flight path projection remains an important aspect in space mission design and operation. However, force models do not capture all the dynamics or perturbations in the space environment and thus are subject to errors in predicting the state vectors. The further out the predicted miss distance between spacecraft is from the time of closest approach (TCA), the larger the propagated errors in the predicted miss distance at TCA is. The dependency on these force models for spacecraft flight state prediction calls for a more reliable method that can quantify, or even reduce, these propagated errors. With recent advances in the field artificial intelligence, specifically in machine and deep learning algorithms, a model that implements these approaches can improve on the modern force model approach. The goal for this work is to provide an early-information decision-making threshold, in order to prioritize risk assessment implementation, given the ongoing increase of space objects. In analyzing the relationship of several parameters from conjunction data messages(CDMs) and solar information, early information becomes viable in miss distance prediction with unsupervised learning techniques, which learn the parameters that are linked together with miss distance and probability of collision (Pc) variables. Another approach implemented for identifying relationships within CDMs is supervised learning, in which a shallow neural network binary classifier learns to distinguish events with Pc values¡108. These parameters detected in the unsupervised process are then applied to a regression neural network, which predicts the miss distance at TCA for a specific event within a given uncertainty bound. For the regression neural network, a Long Short Term Memory (LSTM) neural network is implemented, which yields memory about each time step in an event. Using an LSTM network, the model learns to predict miss distance within 0.2km of the value measured at TCA. Although there is a limited amount of "close miss" data to train a network, the network learns to associate parameters, like large energy dissipation rates with the secondary object, with an elevated Pc

Brianna I. Robertson↗
NASA NTRS1996

An Evaluation of the Measurement Requirements for an In-Situ Wake Vortex Detection System

Results of a numerical simulation are presented to determine the feasibility of estimating the location and strength of a wake vortex from imperfect in-situ measurements. These estimates could be used to provide information to a pilot on how to avoid a hazardous wake vortex encounter. An iterative algorithm based on the method of secants was used to solve the four simultaneous equations describing the two-dimensional flow field around a pair of parallel counter-rotating vortices of equal and constant strength. The flow field information used by the algorithm could be derived from measurements from flow angle sensors mounted on the wing-tip of the detecting aircraft and an inertial navigation system. The study determined the propagated errors in the estimated location and strength of the vortex which resulted from random errors added to theoretically perfect measurements. The results are summarized in a series of charts and a table which make it possible to estimate these propagated errors for many practical situations. The situations include several generator-detector airplane combinations, different distances between the vortex and the detector airplane, as well as different levels of total measurement error.

Fuhrmann, Henri D.↗
NASA NTRS2005

Bias Reduction and Filter Convergence for Long Range Stereo

We are concerned here with improving long range stereo by filtering image sequences. Traditionally, measurement errors from stereo camera systems have been approximated as 3-D Gaussians, where the mean is derived by triangulation and the covariance by linearized error propagation. However, there are two problems that arise when filtering such 3-D measurements. First, stereo triangulation suffers from a range dependent statistical bias; when filtering this leads to over-estimating the true range. Second, filtering 3-D measurements derived via linearized error propagation leads to apparent filter divergence; the estimator is biased to under-estimate range. To address the first issue, we examine the statistical behavior of stereo triangulation and show how to remove the bias by series expansion. The solution to the second problem is to filter with image coordinates as measurements instead of triangulated 3-D coordinates.

robotics↗
NASA NTRS1990

A numerical algorithm to propagate navigation error covariance matrices associated with generalized strapdown inertial measurement units

The design and operation of a Strapdown Navigation Analysis Program (SNAP) developed to perform covariance analysis on spacecraft inertial-measurement-unit (IMU) navigation errors are described and demonstrated. Consideration is given to the IMU modeling subroutine (with user-specified sensor characteristics), the data input procedures, state updates and the simulation of instrument failures, the determination of the nominal trajectory, the mapping-matrix and Monte Carlo covariance-matrix propagation methods, and aided-navigation simulation. Numerical results are presented in tables for sample applications involving (1) the Galileo/IUS spacecraft from its deployment from the Space Shuttle to a point 10 to the 8th ft from the center of the earth and (2) the TDRS-C/IUS spacecraft from Space Shuttle liftoff to a point about 2 h before IUS deployment. SNAP is shown to give reliable results for both cases, with good general agreement between the mapping-matrix and Monte Carlo predictions.

Weir, Kent A.↗
NASA NTRS2008

Tolerance and UQ4SIM: Nimble Uncertainty Documentation and Analysis Software

Ultimately, scientific numerical models need quantified output uncertainties so that modeling can evolve to better match reality. Documenting model input uncertainties and variabilities is a necessary first step toward that goal. Without known input parameter uncertainties, model sensitivities are all one can determine, and without code verification, output uncertainties are simply not reliable. The basic premise of uncertainty markup is to craft a tolerance and tagging mini-language that offers a natural, unobtrusive presentation and does not depend on parsing each type of input file format. Each file is marked up with tolerances and optionally, associated tags that serve to label the parameters and their uncertainties. The evolution of such a language, often called a Domain Specific Language or DSL, is given in [1], but in final form it parallels tolerances specified on an engineering drawing, e.g., 1 +/- 0.5, 5 +/- 10%, 2 +/- 10 where % signifies percent and o signifies order of magnitude. Tags, necessary for error propagation, can be added by placing a quotation-mark-delimited tag after the tolerance, e.g., 0.7 +/- 20% 'T_effective'. In addition, tolerances might have different underlying distributions, e.g., Uniform, Normal, or Triangular, or the tolerances may merely be intervals due to lack of knowledge (uncertainty). Finally, to address pragmatic considerations such as older models that require specific number-field formats, C-style format specifiers can be appended to the tolerance like so, 1.35 +/- 10U_3.2f. As an example of use, consider figure 1, where a chemical reaction input file is has been marked up to include tolerances and tags per table 1. Not only does the technique provide a natural method of specifying tolerances, but it also servers as in situ documentation of model uncertainties. This tolerance language comes with a utility to strip the tolerances (and tags), to provide a path to the nominal model parameter file. And, as shown in [1], having the ability to quickly mark and identify model parameter uncertainties facilitates error propagation, which in turn yield output uncertainties.

Kleb, Bil↗
NASA NTRS2013

Orion Exploration Flight Test-1 Contingency Drogue Deploy Velocity Trigger

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

Gay, Robert S.↗
NASA NTRS2014

Detecting Change in Urban Areas at Continental Scales with MODIS Data

Urbanization is one of the most important components of global environmental change, yet most of what we know about urban areas is at the local scale. Remote sensing of urban expansion across large areas provides information on the spatial and temporal patterns of growth that are essential for understanding differences in socioeconomic and political factors that spur different forms of development, as well the social, environmental, and climatic impacts that result. However, mapping urban expansion globally is challenging: urban areas have a small footprint compared to other land cover types, their features are small, they are heterogeneous in both material composition and configuration, and the form and rates of new development are often highly variable across locations. Here we demonstrate a methodology for monitoring urban land expansion at continental to global scales using Moderate Resolution Imaging Spectroradiometer (MODIS) data. The new method focuses on resolving the spectral and temporal ambiguities between urban/non-urban land and stable/changed areas by: (1) spatially constraining the study extent to known locations of urban land; (2) integrating multitemporal data from multiple satellite data sources to classify c. 2010 urban extent; and (3) mapping newly built areas (2000-2010) within the 2010 urban land extent using a multi-temporal composite change detection approach based on MODIS 250 m annual maximum enhanced vegetation index (EVI). We test the method in 15 countries in East-Southeast Asia experiencing different rates and manifestations of urban expansion. A two-tiered accuracy assessment shows that the approach characterizes urban change across a variety of socioeconomic/political and ecological/climatic conditions with good accuracy (70-91% overall accuracy by country, 69-89% by biome). The 250 m EVI data not only improve the classification results, but are capable of distinguishing between change and no-change areas in urban areas. Over 80% of the error in the change detection can be related to definitional issues or error propagation, rather than algorithm error. As such, these methods hold great potential for routine monitoring of urban change, as well as for providing a consistent and up-to-date dataset on urban extent and expansion for a rapidly evolving region.

Urban areas↗
NASA NTRS1996

Two Reduced Resolution Filter Approaches to Data Assimilation

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

Todling, Ricardo↗
NASA NTRS1973

Effect of channel errors on delta modulation transmission

We have considered the response of a variable step size delta modulator communication system, to errors caused by a noisy channel. For the particular adaptive delta modulation scheme proposed by Song, Garodnick, and Schilling (1971), we have a simple analytic formulation of the output error propagation due to a single channel error. It is shown that single channel errors cause a change in the amplitude and dc level of the output, but do not otherwise affect the shape of the output waveform. At low channel error rates, these effects do not cause any degradation in audio transmission. Higher channel error rates cause overflow or saturation of the step size register. We present relationships between channel error rate, register size, and the probability of register overflow.

Rosenberg, W. J.↗
NASA NTRS2013

Estimating Root Mean Square Errors in Remotely Sensed Soil Moisture over Continental Scale Domains

Root Mean Square Errors (RMSE) in the soil moisture anomaly time series obtained from the Advanced Scatterometer (ASCAT) and the Advanced Microwave Scanning Radiometer (AMSR-E; using the Land Parameter Retrieval Model) are estimated over a continental scale domain centered on North America, using two methods: triple colocation (RMSETC ) and error propagation through the soil moisture retrieval models (RMSEEP ). In the absence of an established consensus for the climatology of soil moisture over large domains, presenting a RMSE in soil moisture units requires that it be specified relative to a selected reference data set. To avoid the complications that arise from the use of a reference, the RMSE is presented as a fraction of the time series standard deviation (fRMSE). For both sensors, the fRMSETC and fRMSEEP show similar spatial patterns of relatively highlow errors, and the mean fRMSE for each land cover class is consistent with expectations. Triple colocation is also shown to be surprisingly robust to representativity differences between the soil moisture data sets used, and it is believed to accurately estimate the fRMSE in the remotely sensed soil moisture anomaly time series. Comparing the ASCAT and AMSR-E fRMSETC shows that both data sets have very similar accuracy across a range of land cover classes, although the AMSR-E accuracy is more directly related to vegetation cover. In general, both data sets have good skill up to moderate vegetation conditions.

Remotely sensed soil moisture validation↗
NASA NTRS1986

A theoretical analysis of the round-off propagation in different Kalman filter implementations

A theoretical analysis is made of the error propagation due to numerical round-off for four different Kalman filter implementations: the conventional Kalman filter, the square root covariance filter, the square root information filter and the Chandrasekhar square root filter. From these error models, new insights about the applicability of the different filters and their sensitivity to round-off, is obtained. It is shown that the CKF may become completely unreliable when the original plant is unstable, and that this is easily circumvented by a number of techniques. The square root filters, often quoted to possess a conditioning or sensitivity that is the square root of that of the CKF, are shown to possess this property only for the computation of the covariance of the filtered signal and not for the computation of the Kalman gain or the filtered estimate. Finally, the Chandrasekhar filter is shown to be numerically unstable.

Verhaegen, M.↗
NASA NTRS1983

Uncertainty methodology for in-flight thrust determination

A methodology is proposed for the evaluation of uncertainty in the in-flight determination of aircraft thrust, which provides error traceability to a national standards laboratory, and is independent of the procedure used to calculate or measure thrust in flight, thereby yielding a consistent means for the evaluation of measurement capabilities. Attention is given to the factors of measurement error, precision, bias, uncertainty, error estimation and classification, error propagation, ground testing, and the related problems of model bias error, model precision error, and the uncertainty limit.

Adams, G. R.↗
NASA NTRS1993

Relaxing consistency in recoverable distributed shared memory

Relaxed memory consistency models have recently been proposed to tolerate memory access latency in both hardware and software distributed shared memory systems. In recoverable shared memory multiprocessors, relaxing consistency has the added benefit of reducing the number of checkpoints needed to avoid rollback propagation. In this paper, we introduce new checkpointing algorithms that take advantage of relaxed consistency to reduce the performance overhead of checkpointing. We also introduce a scheme based on lazy relaxed consistency, that reduces both checkpointing overhead and the overhead of avoiding error propagation in systems with error latency. Multiprocessor address traces are used to evaluate the relaxed consistency approach to checkpointing with distributed shared memory.

Janssens, Bob↗
NASA NTRS1993

Relaxing consistency in recoverable distributed shared memory

Relaxed memory consistency models tolerate increased memory access latency in both hardware and software distributed shared memory systems. In recoverable systems, relaxing consistency has the added benefit of reducing the number of checkpoints needed to avoid rollback propagation. In this paper, we introduce new checkpointing algorithms that take advantage of relaxed consistency to reduce the performance overhead of checkpointing. We also introduce a scheme based on lazy relaxed consistency, that reduces both checkpointing overhead and the overhead of avoiding error propagation in systems with error latency. We use multiprocessor address traces to evaluate the relaxed consistency approach to checkpointing with distributed shared memory.

Janssens, Bob↗
NASA NTRS2012

Apparatus, Method and Program Storage Device for Determining High-Energy Neutron/Ion Transport to a Target of Interest

An apparatus, method and program storage device for determining high-energy neutron/ion transport to a target of interest. Boundaries are defined for calculation of a high-energy neutron/ion transport to a target of interest; the high-energy neutron/ion transport to the target of interest is calculated using numerical procedures selected to reduce local truncation error by including higher order terms and to allow absolute control of propagated error by ensuring truncation error is third order in step size, and using scaling procedures for flux coupling terms modified to improve computed results by adding a scaling factor to terms describing production of j-particles from collisions of k-particles; and the calculated high-energy neutron/ion transport is provided to modeling modules to control an effective radiation dose at the target of interest.

Wilson, John W.↗
NASA NTRS1982

Propagation of local errors in the solutions of the differential equations for orbital elements

The propagation of errors in the solutions of the differential equations for the orbital elements of perturbed two-body motion is investigated. It is shown that the error in the time-element grows linearly for differential equations for orbital elements when only perturbations are present on the right-hand side, cubically for formulations which have a two-body term on the right-hand side, and linearly for formulations based upon extended phase space Hamiltonians.

Bond, V. R.↗