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NASA NTRS1986

A robust adaptive flightpath reconstruction technique

Computational schemes are presented that allow accurate reconstruction of an aircraft's flightpath in real-time. The reconstruction of the flightpath is formulated as a linear state reconstruction problem, which can be solved via Kalman filtering (KF) techniques. This imposes some conditions upon the flight-test equipment. A reliable square root covariance KF (SRCF) implementation is chosen and further developed into a fully adaptive flightpath reconstruction scheme. Therefore, the basic SRCF is modified in order to cope with several practical problems such as: the automatic control of the convergence of the recursive KF calculations, time varying zero-bias errors on the input signal of the system model used in the KF, and the changing aircraft dynamics owing to a change in reference flight condition. The developed solutions for these problems are all implemented in a numerically stable way, which guarantees the overall flightpath reconstruction scheme to be robust. Furthermore, some special features of the used system model are exploited to make the algorithmic implementation very efficient. An experimental simulation study using simulated flight test data demonstrated these different capabilities.

Verhaegen, M. H.↗

NASA NTRSDate not supplied

A Generalized, Compactly-Supported Correlation Function for Data Assimilation Applications

Correlation functions play an essential role in modern data assimilation, where they are used to model covariances given a set of tunable parameters or applied as tapering functions to localize covariances in ensemble-based schemes. One of the most widely-used correlation functions in data assimilation is the Gaspari and Cohn (1999) piecewise-rational, compactly-supported parametric correlation function (hereafter referred to as GC99). The GC99 correlation function is useful due to its tunable cut-off parameter c and Gaussian-like shape achieved when the parameter a is set to one-half. These properties are attractive for tapering functions in data assimilation applications. However, the GC99 correlation function is homogeneous over Euclidean 3-space and isotropic when restricted to the sphere, properties that may be less than ideal for some geophysical applications. GC99 is also compactly-supported on a sphere of fixed radius, which requires tuning of the cut-off parameter c that can depend on the specific application. This work presents a generalization of the GC99 correlation function that allows the cut-off parameter c and shape parameter a to vary over space to gain more flexibility in shape while maintaining its compact support property. The function, which we call the Generalized Gaspari Cohn (GenGC) correlation function, introduces inhomogeneity in Euclidean 3-space and anisotropy when restricted to the sphere by allowing both parameters c and a to vary, as functions, over the spatial domain. The GC99 correlation function is a special case of GenGC where the functions c and a are held constant, as fixed parameters rather than functions. The GenGC correlation function also generalizes the follow-on to the work of Gaspari and Cohn (1999) presented in Gaspari et al. (2006), which allowed a to vary while keeping c fixed. We illustrate through simple one- and two-dimensional examples the variety of inhomogeneous and anisotropic correlation functions GenGC can produce by varying c and a over space, and suggest applications where they may be useful in data assimilation, such as covariance modeling or localization. In particular, we describe how the GenGC correlation function can be used to construct covariances using correlation length and variance fields derived from dynamics. For example, the correlation length field for advective dynamics is governed by a partial differential equation (PDE) in N spatial dimensions, where N is the number of space dimensions of the state. Correlation length fields can be determined from this PDE and used with GenGC to construct the corresponding correlations. We can then approximate the full covariance by rescaling by the variance, which also satisfies a PDE in N spatial dimensions for advective dynamics. Thus we can approximate the full covariance without solving the covariance PDE, which is in 2N spatial dimensions, by solving just two PDEs each in only N spatial dimensions. This approach to evolving the correlation length and variance fields, then reconstructing the correlations using GenGC, is suggested as an alternative to current methods of covariance modeling in data assimilation algorithms.

GC99↗

NASA NTRS1999

Autonomous Image Analysis for Future Mars Missions

To explore high priority landing sites and to prepare for eventual human exploration, future Mars missions will involve rovers capable of traversing tens of kilometers. However, the current process by which scientists interact with a rover does not scale to such distances. Specifically, numerous command cycles are required to complete even simple tasks, such as, pointing the spectrometer at a variety of nearby rocks. In addition, the time required by scientists to interpret image data before new commands can be given and the limited amount of data that can be downlinked during a given command cycle constrain rover mobility and achievement of science goals. Experience with rover tests on Earth supports these concerns. As a result, traverses to science sites as identified in orbital images would require numerous science command cycles over a period of many weeks, months or even years, perhaps exceeding rover design life and other constraints. Autonomous onboard science analysis can address these problems in two ways. First, it will allow the rover to preferentially transmit "interesting" images, defined as those likely to have higher science content. Second, the rover will be able to anticipate future commands. For example, a rover might autonomously acquire and return spectra of "interesting" rocks along with a high-resolution image of those rocks in addition to returning the context images in which they were detected. Such approaches, coupled with appropriate navigational software, help to address both the data volume and command cycle bottlenecks that limit both rover mobility and science yield. We are developing fast, autonomous algorithms to enable such intelligent on-board decision making by spacecraft. Autonomous algorithms developed to date have the ability to identify rocks and layers in a scene, locate the horizon, and compress multi-spectral image data. We are currently investigating the possibility of reconstructing a 3D surface from a sequence of images acquired by a robotic arm camera. This would then allow the return of a single completely in focus image constructed only from those portions of individual images that lie within the camera's depth of field. Output from these algorithms could be used to autonomously obtain rock spectra, determine which images should be transmitted to the ground, or to aid in image compression. We will discuss these algorithms and their performance during a recent rover field test.

Gulick, V. C.↗

NASA NTRS2009

Efficient Model-Based Diagnosis Engine

An efficient diagnosis engine - a combination of mathematical models and algorithms - has been developed for identifying faulty components in a possibly complex engineering system. This model-based diagnosis engine embodies a twofold approach to reducing, relative to prior model-based diagnosis engines, the amount of computation needed to perform a thorough, accurate diagnosis. The first part of the approach involves a reconstruction of the general diagnostic engine to reduce the complexity of the mathematical-model calculations and of the software needed to perform them. The second part of the approach involves algorithms for computing a minimal diagnosis (the term "minimal diagnosis" is defined below). A somewhat lengthy background discussion is prerequisite to a meaningful summary of the innovative aspects of the present efficient model-based diagnosis engine. In model-based diagnosis, the function of each component and the relationships among all the components of the engineering system to be diagnosed are represented as a logical system denoted the system description (SD). Hence, the expected normal behavior of the engineering system is the set of logical consequences of the SD. Faulty components lead to inconsistencies between the observed behaviors of the system and the SD (see figure). Diagnosis - the task of finding faulty components - is reduced to finding those components, the abnormalities of which could explain all the inconsistencies. The solution of the diagnosis problem should be a minimal diagnosis, which is a minimal set of faulty components. A minimal diagnosis stands in contradistinction to the trivial solution, in which all components are deemed to be faulty, and which, therefore, always explains all inconsistencies.

Fijany, Amir↗

NASA NTRS1979

Feasibility of automated dropsize distributions from holographic data using digital image processing techniques

An automated technique for measuring particle diameters and their spatial coordinates from holographic reconstructions is being developed. Preliminary tests on actual cold-flow holograms of impinging jets indicate that a suitable discriminant algorithm consists of a Fourier-Gaussian noise filter and a contour thresholding technique. This process identifies circular as well as noncircular objects. The desired objects (in this case, circular or possibly ellipsoidal) are then selected automatically from the above set and stored with their parametric representations. From this data, dropsize distributions as a function of spatial coordinates can be generated and combustion effects due to hardware and/or physical variables studied.

Feinstein, S. P.↗

NASA NTRS1992

Upper Atmosphere Research Satellite (UARS) Microwave Limb Sounder (MLS) mapping - Validation, early results and applications

The results of limitation studies performed with the UARS MLS are presented. A consistent set of algorithms allows the extraction of the spectral coefficients in time and longitude from asynoptically sampled satellite data and the subsequent reconstruction of synoptic maps from that spectral information. In addition to providing synoptic maps, the asynoptic technique allows the use of standard spectral analysis tools such as autocorrelation and cross correlation.

Elson, Lee S.↗

NASA NTRS1998

Developing Information Power Grid Based Algorithms and Software

This exploratory study initiated our effort to understand performance modeling on parallel systems. The basic goal of performance modeling is to understand and predict the performance of a computer program or set of programs on a computer system. Performance modeling has numerous applications, including evaluation of algorithms, optimization of code implementations, parallel library development, comparison of system architectures, parallel system design, and procurement of new systems. Our work lays the basis for the construction of parallel libraries that allow for the reconstruction of application codes on several distinct architectures so as to assure performance portability. Following our strategy, once the requirements of applications are well understood, one can then construct a library in a layered fashion. The top level of this library will consist of architecture-independent geometric, numerical, and symbolic algorithms that are needed by the sample of applications. These routines should be written in a language that is portable across the targeted architectures.

Dongarra, Jack↗

NASA NTRS2019

Land ice height-retrieval algorithm for NASA's ICESat-2 photon-counting laser altimeter

The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2) and its sole scientific instrument, the Advanced Topographic Laser Altimeter System (ATLAS), was launched on 15 September 2018 with a primary goal of measuring changes in the surface of the Earth's land ice (glaciers and ice sheets). ATLAS is a photon-counting laser altimeter, which records the transit time of individual photons in order to reconstruct surface height along track. The ground-track pattern repeats every 91 days such that changes in ice sheet surface height can be estimated through time. In this paper, we describe the set of algorithms that have been developed for ICESat-2 to retrieve ice sheet surface height from the geolocated photons for the Land Ice Along-Track Height Product (ATL06), and demonstrate their output and performance using a synthetic dataset over various land-ice surfaces and under different cloud conditions. We show that the ATL06 algorithm is expected to perform at the level required to meet the ICESat-2 science objectives for land ice.

ICESat-2↗

NASA NTRS2009

Trajectory Reconstruction of the ST-9 Sounding Rocket Experiment Using IMU and Landmark Data

This paper presents trajectory reconstruction of the ST-9 sounding rocket experiment using the onboard IMU data and descent imagery. The raw IMU accelerometer measurements are first converted into inertial acceleration and then used in trajectory integration. The descent images are pre-processed using a map-matching algorithm and unique landmarks for each image are created. Using the converted IMU data and descent images, the result from dead-reckoning and the kinematic-fix approaches are first compared with the GPS measurements. Then, both the IMU data and landmarks are processed together using a batch least-squares filter and the position, velocity, stochastic acceleration, and camera orientation of each image are estimated. The reconstructed trajectory is compared with the GPS data and the corresponding formal uncertainties are presented. The result shows that IMU data and descent images processed with a batch filter algorithm provide the trajectory accuracy required for pin-point landing.

Park, Ryan S.↗

NASA NTRS2003

An advanced model-based diagnosis engine

We have developed a new and powerful diagnosis engine that overcomes the limitations of the existing systematic methods of general diagnosis through a two-fold approach. First, we propose a novel and compact reconstruction of the General Diagnosis Engine, one of the most fundamental approaches to model-based diagnoses. We then present a novel algorithmic approach for calculation of minimal diagnosis set.

model-based diagnosis hitting set problem integer ↗

NASA NTRS2012

Resolution Enhancement of MODIS-Derived Water Indices for Studying Persistent Flooding

Monitoring coastal marshes for persistent flooding and salinity stress is a high priority issue in Louisiana. Remote sensing can identify environmental variables that can be indicators of marsh habitat conditions, and offer timely and relatively accurate information for aiding wetland vegetation management. Monitoring activity accuracy is often limited by mixed pixels which occur when areas represented by the pixel encompasses more than one cover type. Mixtures of marsh grasses and open water in 250m Moderate Resolution Imaging Spectroradiometer (MODIS) data can impede flood area estimation. Flood mapping of such mixtures requires finer spatial resolution data to better represent the cover type composition within 250m MODIS pixel. Fusion of MODIS and Landsat can improve both spectral and temporal resolution of time series products to resolve rapid changes from forcing mechanisms like hurricane winds and storm surge. For this study, using a method for estimating sub-pixel values from a MODIS time series of a Normalized Difference Water Index (NDWI), using temporal weighting, was implemented to map persistent flooding in Louisiana coastal marshes. Ordinarily NDWI computed from daily 250m MODIS pixels represents a mixture of fragmented marshes and water. Here, sub-pixel NDWI values were derived for MODIS data using Landsat 30-m data. Each MODIS pixel was disaggregated into a mixture of the eight cover types according to the classified image pixels falling inside the MODIS pixel. The Landsat pixel means for each cover type inside a MODIS pixel were computed for the Landsat data preceding the MODIS image in time and for the Landsat data succeeding the MODIS image. The Landsat data were then weighted exponentially according to closeness in date to the MODIS data. The reconstructed MODIS data were produced by summing the product of fractional cover type with estimated NDWI values within each cover type. A new daily time series was produced using both the reconstructed 250-m MODIS, with enhanced features, and the approximated daily 30-m high-resolution image based on Landsat data. The algorithm was developed and tested over the Calcasieu-Sabine Basin, which was heavily inundated by storm surge from Hurricane Ike to study the extent and duration of flooding following the storm. Time series for 2000-2009, covering flooding events by Hurricane Rita in 2005 and Hurricane Ike in 2008, were derived. High resolution images were formed for all days in 2008 between the first cloud free Landsat scene and the last cloud-free Landsat scene. To refine and validate flooding maps, each time series was compared to Louisiana Coastwide Reference Monitoring System (CRMS) station water levels adjusted to marsh to optimize thresholds for MODIS-derived time series of NDWI. Seasonal fluctuations were adjusted by subtracting ten year average NDWI for marshes, excluding the hurricane events. Results from different NDWI indices and a combination of indices were compared. Flooding persistence that was mapped with higher-resolution data showed some improvement over the original MODIS time series estimates. The advantage of this novel technique is that improved mapping of extent and duration of inundation can be provided.

Underwood, L. W.↗

NASA NTRS1994

Advanced technology development multi-color holography

Several key aspects of multi-color holography and some non-conventional ways to study the holographic reconstructions are considered. The error analysis of three-color holography is considered in detail with particular example of a typical triglycine sulfate crystal growth situation. For the numerical analysis of the fringe patterns, a new algorithm is introduced with experimental verification using sugar-water solution. The role of the phase difference among component holograms is also critically considered with examples of several two- and three-color situations. The status of experimentation on two-color holography and fabrication of a small breadboard system is also reported. Finally, some successful demonstrations of unconventional ways to study holographic reconstructions are described. These methods are deflectometry and confocal optical processing using some Spacelab III holograms.

Vikram, Chandra S.↗

NASA NTRS1989

Image gathering and restoration - Information and visual quality

A method is investigated for optimizing the end-to-end performance of image gathering and restoration for visual quality. To achieve this objective, one must inevitably confront the problems that the visual quality of restored images depends on perceptual rather than mathematical considerations and that these considerations vary with the target, the application, and the observer. The method adopted in this paper is to optimize image gathering informationally and to restore images interactively to obtain the visually preferred trade-off among fidelity resolution, sharpness, and clarity. The results demonstrate that this method leads to significant improvements in the visual quality obtained by the traditional digital processing methods. These traditional methods allow a significant loss of visual quality to occur because they treat the design of the image-gathering system and the formulation of the image-restoration algorithm as two separate tasks and fail to account for the transformations between the continuous and the discrete representations in image gathering and reconstruction.

Mccormick, Judith A.↗

NASA NTRS1990

Solution algorithms for the two-dimensional Euler equations on unstructured meshes

The objective of the study was to analyze implicit techniques employed in structured grid algorithms for solving two-dimensional Euler equations and extend them to unstructured solvers in order to accelerate convergence rates. A comparison is made between nine different algorithms for both first-order and second-order accurate solutions. Higher-order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The discussion is illustrated by results for flow over a transonic circular arc.

Whitaker, D. L.↗

NASA NTRS2007

POD Model Reconstruction for Gray-Box Fault Detection

Proper orthogonal decomposition (POD) is the mathematical basis of a method of constructing low-order mathematical models for the "gray-box" fault-detection algorithm that is a component of a diagnostic system known as beacon-based exception analysis for multi-missions (BEAM). POD has been successfully applied in reducing computational complexity by generating simple models that can be used for control and simulation for complex systems such as fluid flows. In the present application to BEAM, POD brings the same benefits to automated diagnosis. BEAM is a method of real-time or offline, automated diagnosis of a complex dynamic system.The gray-box approach makes it possible to utilize incomplete or approximate knowledge of the dynamics of the system that one seeks to diagnose. In the gray-box approach, a deterministic model of the system is used to filter a time series of system sensor data to remove the deterministic components of the time series from further examination. What is left after the filtering operation is a time series of residual quantities that represent the unknown (or at least unmodeled) aspects of the behavior of the system. Stochastic modeling techniques are then applied to the residual time series. The procedure for detecting abnormal behavior of the system then becomes one of looking for statistical differences between the residual time series and the predictions of the stochastic model.

Park, Han↗

NASA NTRS2001

A New Ensemble Canonical Correlation Prediction Scheme for Seasonal Precipitation

Department of Mathematical Sciences, University of Alberta, Edmonton, Canada This paper describes the fundamental theory of the ensemble canonical correlation (ECC) algorithm for the seasonal climate forecasting. The algorithm is a statistical regression sch eme based on maximal correlation between the predictor and predictand. The prediction error is estimated by a spectral method using the basis of empirical orthogonal functions. The ECC algorithm treats the predictors and predictands as continuous fields and is an improvement from the traditional canonical correlation prediction. The improvements include the use of area-factor, estimation of prediction error, and the optimal ensemble of multiple forecasts. The ECC is applied to the seasonal forecasting over various parts of the world. The example presented here is for the North America precipitation. The predictor is the sea surface temperature (SST) from different ocean basins. The Climate Prediction Center's reconstructed SST (1951-1999) is used as the predictor's historical data. The optimally interpolated global monthly precipitation is used as the predictand?s historical data. Our forecast experiments show that the ECC algorithm renders very high skill and the optimal ensemble is very important to the high value.

Kim, Kyu-Myong↗

NASA NTRS1975

On the effect of timing errors in run length codes

Many redundancy removal algorithms employ some sort of run length code. Blocks of timing words are coded with synchronization words inserted between blocks. The probability of incorrectly reconstructing a sample because of a channel error in the timing data is a monotonically nondecreasing function of time since the last synchronization word. In this paper we compute the 'probability that the accumulated magnitude of timing errors equal zero' as a function of time since the last synchronization word for a zero-order predictor (ZOP). The result is valid for any data source that can be modeled by a first-order Markov chain and any digital channel that can be modeled by a channel transition matrix. An example is presented.

Wilkins, L. C.↗

NASA NTRS1991

The analysis of a rocket tomography measurement of the N2+3914A emission and N2 ionization rates in an auroral arc

Techniques were developed for recovering two-dimensional distributions of auroral volume emission rates from rocket photometer measurements made in a tomographic spin scan mode. These tomographic inversion procedures are based upon an algebraic reconstruction technique (ART) and utilize two different iterative relaxation techniques for solving the problems associated with noise in the observational data. One of the inversion algorithms is based upon a least squares method and the other on a maximum probability approach. The performance of the inversion algorithms, and the limitations of the rocket tomography technique, were critically assessed using various factors such as (1) statistical and non-statistical noise in the observational data, (2) rocket penetration of the auroral form, (3) background sources of emission, (4) smearing due to the photometer field of view, and (5) temporal variations in the auroral form. These tests show that the inversion procedures may be successfully applied to rocket observations made in medium intensity aurora with standard rocket photometer instruments. The inversion procedures have been used to recover two-dimensional distributions of auroral emission rates and ionization rates from an existing set of N2+3914A rocket photometer measurements which were made in a tomographic spin scan mode during the ARIES auroral campaign. The two-dimensional distributions of the 3914A volume emission rates recoverd from the inversion of the rocket data compare very well with the distributions that were inferred from ground-based measurements using triangulation-tomography techniques and the N2 ionization rates derived from the rocket tomography results are in very good agreement with the in situ particle measurements that were made during the flight. Three pre-prints describing the tomographic inversion techniques and the tomographic analysis of the ARIES rocket data are included as appendices.

Mcdade, Ian C.↗