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NASA NTRS2001

B-spline Method in Fluid Dynamics

B-spline functions are bases for piecewise polynomials that possess attractive properties for complex flow simulations : they have compact support, provide a straightforward handling of boundary conditions and grid nonuniformities, and yield numerical schemes with high resolving power, where the order of accuracy is a mere input parameter. This paper reviews the progress made on the development and application of B-spline numerical methods to computational fluid dynamics problems. Basic B-spline approximation properties is investigated, and their relationship with conventional numerical methods is reviewed. Some fundamental developments towards efficient complex geometry spline methods are covered, such as local interpolation methods, fast solution algorithms on cartesian grid, non-conformal block-structured discretization, formulation of spline bases of higher continuity over triangulation, and treatment of pressure oscillations in Navier-Stokes equations. Application of some of these techniques to the computation of viscous incompressible flows is presented.

Botella, Olivier↗

NASA NTRS2003

HEASARC Software Archive

(1) Chandra Archive: SAO has maintained the interfaces through which HEASARC gains access to the Chandra Data Archive. At HEASARC's request, we have implemented an anonymous ftp copy of a major part of the public archive and we keep that archive up-to- date. SAO has participated in the ADEC interoperability working group, establishing guidelines or interoperability standards and prototyping such interfaces. We have provided an NVO-based prototype interface, intending to serve the HEASARC-led NVO demo project. HEASARC's Astrobrowse interface was maintained and updated. In addition, we have participated in design discussions surrounding HEASARC's Caldb project. We have attended the HEASARC Users Group meeting and presented CDA status and developments. (2) Chandra CALDB: SA0 has maintained and expanded the Chandra CALDB by including four new data file types, defining the corresponding CALDB keyword/identification structures. We have provided CALDB upgrades for the public (CIAO) and for Standard Data Processing. Approximately 40 new files have been added to the CALDB in these version releases. There have been in the past year ten of these CALDB upgrades, each with unique index configurations. In addition, with the inputs from software, archive, and calibration scientists, as well as CIAO/SDP software developers, we have defined a generalized expansion of the existing CALDB interface and indexing structure. The purpose of this is to make the CALDB more generally applicable and useful in new and future missions that will be supported archivally by HEASARC. The generalized interface will identify additional configurational keywords and permit more extensive calibration parameter and boundary condition specifications for unique file selection. HEASARC scientists and developers from SAO and GSFC have become involved in this work, which is expected to produce a new interface for general use within the current year. (3) DS9: One of the decisions that came from last year's HEADCC meeting was to make the ds9 image display program the primary vehicle for displaying line graphics (as well as images). The first step required to make this possible was to enhance the line graphics capabilities of ds9. SAO therefore spent considerable effort upgrading ds9 to use Tcl 8.4 so that the BLT line graphics package could be built and imported into ds9 from source code, rather than from a pre-built (and generally outdated) shared library. This task, which is nearly complete, allows us to extend BLT as needed for the HEAD community. Following HEADCC discussion concerning archiving and the display of archived data, we extended ds9 to support full access to many astronomical Web-based archives sites, including HEASARC, MAST, CHANDRA, SKYVIEW, ADS, NED, SIMBAD, IRAS, NVRO, SAO TDC, and FIRST. Using ds9's new internal Web access capabilities, these archives can be accessed via their Web page. FITS images, plots, spectra, and journal abstracts can be referenced, down-loaded, and displayed directly and easily in ds9. For more information, see: http://hea-www.harvard.edu/saord/ds9. Also after the HEADCC discussion concerning region filtering, we extended the Funtools sample implementation of region filtering as described in: http://hea-www.harvard.edu/saord/funtools/regions.html. In particular, we added several new composite regions for event and image filtering, including elliptical and box annuli. We also extended the panda (Pie AND Annulus) region support to include box pandas and elliptical pandas. These new composite regions are especially useful in programs that need to count photons in each separate region using only a single pass through the data. Support for these new regions was added to ds9. In the same vein, we developed new region support for filtering images using simple FITS image masks, i.e. 8-bit or 16-bit FITS images where the value of a pixel is the region id number for that pixel. Other important enhancements to DS9 this year, include supporor multiple world coordinate systems, three dimensional event file binning, image smoothing, region groups and tags, the ability to save images in a number of image formats (such as JPEG, TIFF, PNG, FITS), improvements in support for integrating external analysis tools, and support for the virtual observatory. In particular, a full-featured web browser has been implemented within D S 9 . This provides support for full access to HEASARC archive sites such as SKYVIEW and W3BROWSE, in addition to other astronomical archives sites such as MAST, CHANDRA, ADS, NED, SIMBAD, IRAS, NVRO, SA0 TDC, and FIRST. From within DS9, the archives can be searched, and FITS images, plots, spectra, and journal abstracts can be referenced, downloaded and displayed The web browser provides the basis for the built-in help facility. All DS9 documentation, including the reference manual, FAQ, Know Features, and contact information is now available to the user without the need for external display applications. New versions of DS9 maybe downloaded and installed using this facility. Two important features used in the analysis of high energy astronomical data have been implemented in the past year. The first is support for binning photon event data in three dimensions. By binning the third dimension in time or energy, users are easily able to detect variable x-ray sources and identify other physical properties of their data. Second, a number of fast smoothing algorithms have been implemented in DS9, which allow users to smooth their data in real time. Algorithms for boxcar, tophat, and gaussian smoothing are supported.

White, Nicholas↗

NASA NTRS2011

Multiangle Implementation of Atmospheric Correction (MAIAC):: Radiative Transfer Basis and Look-up Tables - 1

This paper describes a radiative transfer basis of the algorithm MAIAC which performs simultaneous retrievals of atmospheric aerosol and bidirectional surface reflectance from the Moderate Resolution Imaging Spectroradiometer (MODIS). The retrievals are based on an accurate semianalytical solution for the top-of-atmosphere reflectance expressed as an explicit function of three parameters of the Ross-Thick Li-Sparse model of surface bidirectional reflectance. This solution depends on certain functions of atmospheric properties and geometry which are precomputed in the look-up table (LUT). This paper further considers correction of the LUT functions for variations of surface pressure/height and of atmospheric water vapor, which is a common task in the operational remote sensing. It introduces a new analytical method for the water vapor correction of the multiple ]scattering path radiance. It also summarizes the few basic principles that provide a high efficiency and accuracy of the LUT ]based radiative transfer for the aerosol/surface retrievals and optimize the size of LUT. For example, the single-scattering path radiance is calculated analytically for a given surface pressure and atmospheric water vapor. The same is true for the direct surface-reflected radiance, which along with the single-scattering path radiance largely defines the angular dependence of measurements. For these calculations, the aerosol phase functions and kernels of the surface bidirectional reflectance model are precalculated at a high angular resolution. The other radiative transfer functions depend rather smoothly on angles because of multiple scattering and can be calculated at coarser angular resolution to reduce the LUT size. At the same time, this resolution should be high enough to use the nearest neighbor geometry angles to avoid costly three ]dimensional interpolation. The pressure correction is implemented via linear interpolation between two LUTs computed for the standard and reduced pressure levels. A linear mixture and a modified linear mixture methods are used to represent different aerosol types in the aerosol/surface retrievals from several base models of the fine and coarse aerosol fractions. In summary, the developed LUT algorithm allows fast high-accuracy simulations of the outgoing radiance with full variability of the atmospheric and surface bidirectional reflectance properties for the aerosol/surface remote sensing.

Lyapustin, Alexei↗

NASA NTRS2015

A Sampling Based Approach to Spacecraft Autonomous Maneuvering with Safety Specifications

This paper presents a methods for safe spacecraft autonomous maneuvering that leverages robotic motion-planning techniques to spacecraft control. Specifically the scenario we consider is an in-plan rendezvous of a chaser spacecraft in proximity to a target spacecraft at the origin of the Clohessy Wiltshire Hill frame. The trajectory for the chaser spacecraft is generated in a receding horizon fashion by executing a sampling based robotic motion planning algorithm name Fast Marching Trees (FMT) which efficiently grows a tree of trajectories over a set of probabillistically drawn samples in the state space. To enforce safety the tree is only grown over actively safe samples for which there exists a one-burn collision avoidance maneuver that circularizes the spacecraft orbit along a collision-free coasting arc and that can be executed under potential thrusters failures. The overall approach establishes a provably correct framework for the systematic encoding of safety specifications into the spacecraft trajectory generations process and appears amenable to real time implementation on orbit. Simulation results are presented for a two-fault tolerant spacecraft during autonomous approach to a single client in Low Earth Orbit.

Spacecraft↗

NASA NTRS2014

Airborne Demonstration of FPGA Implementation of Fast Lossless Hyperspectral Data Compression System

Efficient on-board lossless hyperspectral data compression reduces data volume in order to meet NASA and DoD limited downlink capabilities. The technique also improves signature extraction, object recognition and feature classification capabilities by providing exact reconstructed data on constrained downlink resources. At JPL a novel, adaptive and predictive technique for lossless compression of hyperspectral data was recently developed. This technique uses an adaptive filtering method and achieves a combination of low complexity and compression effectiveness that far exceeds state-of-the-art techniques currently in use. The JPL-developed 'Fast Lossless' algorithm requires no training data or other specific information about the nature of the spectral bands for a fixed instrument dynamic range. It is of low computational complexity and thus well-suited for implementation in hardware.

data compression↗

NASA NTRS2017

Bayesian Treatment of Prospective LISA Parameter Estimation for Massive Black Hole Mergers

A full understanding of LISA (Laser Interferometer Space Antenna)'s science capability will require accurate models of incident waveform signals and the instrumental response. While Fisher matrix analysis is useful for some estimates, a full Bayesian treatment is needed for important cases at the limit of LISA's capability. We will apply fast analysis algorithms enabling accurate treatment with EOB (effective-one-body) waveforms and the full-featured LISA response to study the significance of higher spherical harmonics and mergers in LISA analysis.

Baker, John G.↗

NASA NTRS2015

M-MRAC for SPHERES

This paper presents application of the modified reference model MRAC (M-MRAC) method to control the relative position and orientation of a cluster of satellites known collectively as the Synchronized Position Hold, Engage, Reorient Experimental Satellites (SPHERES). The approach uses fast estimation algorithms to achieve guaranteed tracking of reference commands for both input and output signals in the presence of uncertainties in mass and inertia data and external disturbances. The tracking errors can be systematically decreased by the proper selection of the design parameters in the identification model. The generated control signals have acceptable magnitudes and exhibit no oscillations. The benefits of the method are demonstrated in numerical simulations.

Relative motion↗

NASA NTRS2021

Autonomous Off-road Navigation over Extreme Terrains with Perceptually-challenging Conditions

We propose a framework for resilient autonomous navigation in perceptuallychallenging unknown environments with mobility-stressing elements such asuneven surfaces with rocks and boulders, steep slopes, negative obstacles like cliffsand holes, and narrow passages. Environments are GPS-denied and perceptuallydegradedwith variable lighting from dark to lit and obscurants (dust, fog, smoke).Lack of prior maps and degraded communication eliminates the possibility of prioror off-board computation or operator intervention. This necessitates real-time onboardcomputation using noisy sensor data. To address these challenges, we proposea resilient architecture that exploits redundancy and heterogeneity in sensing modalities.Further resilience is achieved by triggering recovery behaviors upon failure.We propose a fast settling algorithm to generate robust multi-fidelity traversabilityestimates in real-time. The proposed approach was deployed on multiple physicalsystems including skid-steer and tracked robots, high-speed RC car and legged robotsand as a part of Team CoSTAR’s effort to theDARPASubterranean Challenge, wherethe team won 2nd and 1st place in the Tunnel and Urban Circuit, respectively.

Agha-mohammadi, Ali-akbar↗

NASA NTRSDate not supplied

Quantum-Accelerated Distributed Algorithms for Approximate Steiner Trees and Directed Minimum Spanning Trees

We present two algorithms in the Quantum CONGEST-CLIQUE model of distributed computation that succeed with high probability; One for producing an approximately optimal Steiner Tree, and one for producing an exact Minimum Directed Spanning tree. These use O(n1/4) rounds of communication and O(n9/4) messages, leading to a quantum speedup in round and message complexity compared to any known algorithms in the classical CONGEST-CLIQUE model (vs O(n1/3) and O(n7/3)). At a high level, we achieve these results by combining classical algorithms with fast quantum subroutines. Further, these problems can not be sped up in the CONGEST (non-clique) setting, and we characterize the constants involved.

Phillip Kerger↗

NASA NTRS1981

Digital SAR processing using a fast polynomial transform

A new digital processing algorithm based on the fast polynomial transform is developed for producing images from Synthetic Aperture Radar data. This algorithm enables the computation of the two dimensional cyclic correlation of the raw echo data with the impulse response of a point target, thereby reducing distortions inherent in one dimensional transforms. This SAR processing technique was evaluated on a general-purpose computer and an actual Seasat SAR image was produced. However, regular production runs will require a dedicated facility. It is expected that such a new SAR processing algorithm could provide the basis for a real-time SAR correlator implementation in the Deep Space Network.

Butman, S.↗

NASA NTRS1984

Digital SAR processing using a fast polynomial transform

Truong, T. K.↗

NASA NTRS1989

Algorithm for Atmospheric Corrections of Aircraft and Satellite Imagery

A simple and fast atmospheric correction algorithm is described which is used to correct radiances of scattered sunlight measured by aircraft and/or satellite above a uniform surface. The atmospheric effect, the basic equations, a description of the computational procedure, and a sensitivity study are discussed. The program is designed to take the measured radiances, view and illumination directions, and the aerosol and gaseous absorption optical thickness to compute the radiance just above the surface, the irradiance on the surface, and surface reflectance. Alternatively, the program will compute the upward radiance at a specific altitude for a given surface reflectance, view and illumination directions, and aerosol and gaseous absorption optical thickness. The algorithm can be applied for any view and illumination directions and any wavelength in the range 0.48 micron to 2.2 micron. The relation between the measured radiance and surface reflectance, which is expressed as a function of atmospheric properties and measurement geometry, is computed using a radiative transfer routine. The results of the computations are presented in a table which forms the basis of the correction algorithm. The algorithm can be used for atmospheric corrections in the presence of a rural aerosol. The sensitivity of the derived surface reflectance to uncertainties in the model and input data is discussed.

Fraser, Robert S.↗

NASA NTRS1992

Algorithm for atmospheric corrections of aircraft and satellite imagery

A simple and fast atmospheric correction algorithm is described which is used to correct radiances of scattered sunlight measured by aircraft and/or satellite above a uniform surface. The atmospheric effect, the basic equations, a description of the computational procedure, and a sensitivity study are discussed. The program is designed to take the measured radiances, view and illumination directions, and the aerosol and gaseous absorption optical thickness to compute the radiance just above the surface, the irradiance on the surface, and surface reflectance. Alternatively, the program will compute the upward radiance at a specific altitude for a given surface reflectance, view and illumination directions, and aerosol and gaseous absorption optical thickness. The algorithm can be applied for any view and illumination directions and any wavelength in the range 0.48 micron to 2.2 microns. The relation between the measured radiance and surface reflectance, which is expressed as a function of atmospheric properties and measurement geometry, is computed using a radiative transfer routine. The results of the computations are presented in a table which forms the basis of the correction algorithm. The algorithm can be used for atmospheric corrections in the presence of a rural aerosol. The sensitivity of the derived surface reflectance to uncertainties in the model and input data is discussed.

Fraser, R. S.↗

NASA NTRS1988

Least-Squares Frequency-Acquisition Algorithm

Algorithm finds frequency and phase of sinudoidal signal in presence of noise. Algorithm is special case of more-general, adaptive-paramenter-estimation techniques. Computational requirements of algorithm comparable to corresponding fast-Fourier-transform (FFT) algorithm. Algorithm works directly in time domain, whereas FFT algorithm transforms data into frequency domain for estimation and detection and requires secondary algorithm to interpolate between frequencies.

Kumar, Rajendra↗

NASA NTRS2009

Progressive Classification Using Support Vector Machines

An algorithm for progressive classification of data, analogous to progressive rendering of images, makes it possible to compromise between speed and accuracy. This algorithm uses support vector machines (SVMs) to classify data. An SVM is a machine learning algorithm that builds a mathematical model of the desired classification concept by identifying the critical data points, called support vectors. Coarse approximations to the concept require only a few support vectors, while precise, highly accurate models require far more support vectors. Once the model has been constructed, the SVM can be applied to new observations. The cost of classifying a new observation is proportional to the number of support vectors in the model. When computational resources are limited, an SVM of the appropriate complexity can be produced. However, if the constraints are not known when the model is constructed, or if they can change over time, a method for adaptively responding to the current resource constraints is required. This capability is particularly relevant for spacecraft (or any other real-time systems) that perform onboard data analysis. The new algorithm enables the fast, interactive application of an SVM classifier to a new set of data. The classification process achieved by this algorithm is characterized as progressive because a coarse approximation to the true classification is generated rapidly and thereafter iteratively refined. The algorithm uses two SVMs: (1) a fast, approximate one and (2) slow, highly accurate one. New data are initially classified by the fast SVM, producing a baseline approximate classification. For each classified data point, the algorithm calculates a confidence index that indicates the likelihood that it was classified correctly in the first pass. Next, the data points are sorted by their confidence indices and progressively reclassified by the slower, more accurate SVM, starting with the items most likely to be incorrectly classified. The user can halt this reclassification process at any point, thereby obtaining the best possible result for a given amount of computation time. Alternatively, the results can be displayed as they are generated, providing the user with real-time feedback about the current accuracy of classification.

Wagstaff, Kiri↗

NASA NTRS2012

A Fast and Efficient Version of the TwO-Moment Aerosol Sectional (TOMAS) Global Aerosol Microphysics Model

This study develops more computationally efficient versions of the TwO-Moment Aerosol Sectional (TOMAS) microphysics algorithms, collectively called Fast TOMAS. Several methods for speeding up the algorithm were attempted, but only reducing the number of size sections was adopted. Fast TOMAS models, coupled to the GISS GCM II-prime, require a new coagulation algorithm with less restrictive size resolution assumptions but only minor changes in other processes. Fast TOMAS models have been evaluated in a box model against analytical solutions of coagulation and condensation and in a 3-D model against the original TOMAS (TOMAS-30) model. Condensation and coagulation in the Fast TOMAS models agree well with the analytical solution but show slightly more bias than the TOMAS-30 box model. In the 3-D model, errors resulting from decreased size resolution in each process (i.e., emissions, cloud processing wet deposition, microphysics) are quantified in a series of model sensitivity simulations. Errors resulting from lower size resolution in condensation and coagulation, defined as the microphysics error, affect number and mass concentrations by only a few percent. The microphysics error in CN70CN100 (number concentrations of particles larger than 70100 nm diameter), proxies for cloud condensation nuclei, range from 5 to 5 in most regions. The largest errors are associated with decreasing the size resolution in the cloud processing wet deposition calculations, defined as cloud-processing error, and range from 20 to 15 in most regions for CN70CN100 concentrations. Overall, the Fast TOMAS models increase the computational speed by 2 to 3 times with only small numerical errors stemming from condensation and coagulation calculations when compared to TOMAS-30. The faster versions of the TOMAS model allow for the longer, multi-year simulations required to assess aerosol effects on cloud lifetime and precipitation.

Lee, Yunha↗

NASA NTRSDate not supplied

Fast Radiative Transfer Model and Retrieval Algorithm Development for Satellite Remote Sensing Applications

The radiative transfer model (RTM) has a wide range of applications in satellite remote sensing and atmospheric radiation studies. For example, it can be used as a forward model for an inversion algorithm and a satellite data assimilation system, or as a L1 data simulator for pre-launch end-to-end satellite sensor performance studies. However, millions of line-by-line (LBL) radiative transfer calculations at fine monochromatic frequencies are needed in order to properly calculate spectral contributions of water vapor and trace gases in the atmosphere in infrared and solar spectral regions. Therefore, fast, and accurate radiative transfer models are needed. A Principal Component-based radiative transfer model (PCRTM) was developed at NASA Langley to fulfil this need. The PCRTM can simulate the top-of-atmosphere (TOA) radiance or reflectance spectra from 250 nm to 2000 micrometers with several orders of magnitude faster speed as compared to a LBL RTM. It is also extremely accurate compared to LBL RTM benchmarks. The PCRTM model has been developed for hyperspectral sensors such as AIRS, CrIS, IASI, NAST-I, SHIS, CPF, TEMPO, EMIT, OMI, and SCIAMACHY. By using the PCRTM as forward model for an inversion algorithm, one can reduce the data dimension significantly while maintaining original information content by compressing the TOA radiance spectrum into PC-scores. The PCRTM can directly compute the PC-scores and their derivatives with respect to retrieved parameters. Examples of using various PCRTM inversion algorithms to retrieve atmospheric temperature, water vapor, and trace gas profiles, as well as cloud and surface properties from satellite hyperspectral remote sensors will be given. Some of the algorithms have been transitioned to NASA's Goddard Earth Sciences Data and Information Services Center (GES DISC) for public access of high-quality L2 and L3 data.

Xu Liu↗

NASA NTRS1987

FPT Algorithm for Two-Dimensional Cyclic Convolutions

Fast-polynomial-transform (FPT) algorithm computes two-dimensional cyclic convolution of two-dimensional arrays of complex numbers. New algorithm uses cyclic polynomial convolutions of same length. Algorithm regular, modular, and expandable.

Truong, Trieu-Kie↗