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NASA NTRS2005

Comparison of Response Surface Construction Methods for Derivative Estimation Using Moving Least Squares, Kriging and Radial Basis Functions

Response construction methods using Moving Least Squares (MLS), Kriging and Radial Basis Functions (RBF) are compared with the Global Least Squares (GLS) method in three numerical examples for derivative generation capability. Also, a new Interpolating Moving Least Squares (IMLS) method adopted from the meshless method is presented. It is found that the response surface construction methods using the Kriging and RBF interpolation yields more accurate results compared with MLS and GLS methods. Several computational aspects of the response surface construction methods also discussed.

Krishnamurthy, Thiagarajan↗

NASA NTRS2002

Aeroacoustic Flow Phenomena Accurately Captured by New Computational Fluid Dynamics Method

One of the challenges in the computational fluid dynamics area is the accurate calculation of aeroacoustic phenomena, especially in the presence of shock waves. One such phenomenon is "transonic resonance," where an unsteady shock wave at the throat of a convergent-divergent nozzle results in the emission of acoustic tones. The space-time Conservation-Element and Solution-Element (CE/SE) method developed at the NASA Glenn Research Center can faithfully capture the shock waves, their unsteady motion, and the generated acoustic tones. The CE/SE method is a revolutionary new approach to the numerical modeling of physical phenomena where features with steep gradients (e.g., shock waves, phase transition, etc.) must coexist with those having weaker variations. The CE/SE method does not require the complex interpolation procedures (that allow for the possibility of a shock between grid cells) used by many other methods to transfer information between grid cells. These interpolation procedures can add too much numerical dissipation to the solution process. Thus, while shocks are resolved, weaker waves, such as acoustic waves, are washed out.

Blech, Richard A.↗

NASA NTRS2005

Generic Sensor Modeling Using Pulse Method

Recent development of high spatial resolution satellites such as IKONOS, Quickbird and Orbview enable observation of the Earth's surface with sub-meter resolution. Compared to the 30 meter resolution of Landsat 5 TM, the amount of information in the output image was dramatically increased. In this era of high spatial resolution, the estimation of spatial quality of images is gaining attention. Historically, the Modulation Transfer Function (MTF) concept has been used to estimate an imaging system's spatial quality. Sometimes classified by target shapes, various methods were developed in laboratory environment utilizing sinusoidal inputs, periodic bar patterns and narrow slits. On-orbit sensor MTF estimation was performed on 30-meter GSD Landsat4 Thematic Mapper (TM) data from the bridge pulse target as a pulse input . Because of a high resolution sensor s small Ground Sampling Distance (GSD), reasonably sized man-made edge, pulse, and impulse targets can be deployed on a uniform grassy area with accurate control of ground targets using tarps and convex mirrors. All the previous work cited calculated MTF without testing the MTF estimator's performance. In previous report, a numerical generic sensor model had been developed to simulate and improve the performance of on-orbit MTF estimating techniques. Results from the previous sensor modeling report that have been incorporated into standard MTF estimation work include Fermi edge detection and the newly developed 4th order modified Savitzky-Golay (MSG) interpolation technique. Noise sensitivity had been studied by performing simulations on known noise sources and a sensor model. Extensive investigation was done to characterize multi-resolution ground noise. Finally, angle simulation was tested by using synthetic pulse targets with angles from 2 to 15 degrees, several brightness levels, and different noise levels from both ground targets and imaging system. As a continuing research activity using the developed sensor model, this report was dedicated to MTF estimation via pulse input method characterization using the Fermi edge detection and 4th order MSG interpolation method. The relationship between pulse width and MTF value at Nyquist was studied including error detection and correction schemes. Pulse target angle sensitivity was studied by using synthetic targets angled from 2 to 12 degrees. In this report, from the ground and system noise simulation, a minimum SNR value was suggested for a stable MTF value at Nyquist for the pulse method. Target width error detection and adjustment technique based on a smooth transition of MTF profile is presented, which is specifically applicable only to the pulse method with 3 pixel wide targets.

Helder, Dennis L.↗

NASA NTRS2005

Polynomial Expressions for Estimating Elastic Constants From the Resonance of Circular Plates

Two approaches were taken to make convenient spread sheet calculations of elastic constants from resonance data and the tables in ASTM C1259 and E1876: polynomials were fit to the tables; and an automated spread sheet interpolation routine was generated. To compare the approaches, the resonant frequencies of circular plates made of glass, hardened maraging steel, alpha silicon carbide, silicon nitride, tungsten carbide, tape cast NiO-YSZ, and zinc selenide were measured. The elastic constants, as calculated via the polynomials and linear interpolation of the tabular data in ASTM C1259 and E1876, were found comparable for engineering purposes, with the differences typically being less than 0.5 percent. Calculation of additional v values at t/R between 0 and 0.2 would allow better curve fits. This is not necessary for common engineering purposes, however, it might benefit the testing of emerging thin structures such as fuel cell electrolytes, gas conversion membranes, and coatings when Poisson s ratio is less than 0.15 and high precision is needed.

Salem, Jonathan A.↗

NASA NTRS2006

Comparisons of Temporal and Spatial Trends in the Spatially Complete Global Spectral Surface Albedos Products

Five years of spatially complete snow-free land surface albedo data have been prepared using high quality white-sky and black-sky land surface albedo observations (MOD43B3) from the MODIS instrument aboard NASA's Terra satellite platform. The data were generated using an updated ecosystem-dependent temporal interpolation technique. In this paper, we describe the refinements in the technique and the creation of a spatially complete snow-free five-year aggregate climatology product. This paper also describes an error analysis of the interpolation technique. The filled albedo products are examined through comparisons of temporal and spatial trends for pixels that have been filled versus pixels that have been retained in the original MOD43B3 values. The variability in the trends showcase how the filling technique maintains the pixel-level spatial, spectral, and temporal integrity of the MOD43B3 data. These comparisons are made for both a single-year of filled data, year 2002, and for the five-year aggregate climatology product.

Moody, Eric G.↗

NASA NTRS2005

Multi-reference evaluation of uncertainty in earth orientation parameter measurements

Uncertainties in polar motion and length-of-day measurements are evaluated empirically using several data series from the space-geodetic techniques of the global positioning system (GPS), satellite laser ranging (SLR), and very long baseline interferometry (VLBI) during 1997-2002. In the evaluation procedure employed here, known as the three-corner hat (TCH) technique, the signal common to each series is eliminated by forming pair-wise differences between the series, thus requiring no assumed values for the 'truth' signal. From the variances of the differenced series, the uncertainty of each series can be recovered when reasonable assumptions are made about the correlations between the series. In order to form the pair-wise differences, the series data must be given at the same epoch. All measurement data sets studied here were sampled at noon (UTC); except for the VLBI series, whose data are interpolated to noon and whose UT1 values are also numerically differentiated to obtain LOD. The numerical error introduced to the VLBI values by the interpolation and differentiation is shown to be comparable in magnitude to the values determined by the TCH method for the uncertainties of the VLBI series. The TCH estimates for the VLBI series are corrupted by such numerical errors mostly as a result of the relatively large data intervals. Of the remaining data sets studied here, it is found that the IGS Final combined series has the smallest polar motion and length-of-day uncertainties.

Combination↗

NASA NTRS2006

Characterization and Modeling of Indium Gallium Antimonide Avalanche Photodiode and of Indium Gallium Arsenide Two-band Detector

A model of the optical properties of Al(x)Ga(1-x)As(y)Sb(1-y) and In(x)Ga(1-x)As(y)Sb(1-y) is presented, including the refractive, extinction, absorption and reflection coefficients in terms of the optical dielectric function of the materials. Energy levels and model parameters for each binary compound are interpolated to obtain the needed ternaries and quaternaries for various compositions. Bowing parameters are considered in the interpolation scheme to take into account the deviation of the calculated ternary and quaternary values from experimental data due to lattice disorders. The inclusion of temperature effects is currently being considered.

Source record↗

NASA NTRS2007

Numerical Uncertainty Quantification for Radiation Analysis Tools

Recently a new emphasis has been placed on engineering applications of space radiation analyses and thus a systematic effort of Verification, Validation and Uncertainty Quantification (VV&UQ) of the tools commonly used for radiation analysis for vehicle design and mission planning has begun. There are two sources of uncertainty in geometric discretization addressed in this paper that need to be quantified in order to understand the total uncertainty in estimating space radiation exposures. One source of uncertainty is in ray tracing, as the number of rays increase the associated uncertainty decreases, but the computational expense increases. Thus, a cost benefit analysis optimizing computational time versus uncertainty is needed and is addressed in this paper. The second source of uncertainty results from the interpolation over the dose vs. depth curves that is needed to determine the radiation exposure. The question, then, is what is the number of thicknesses that is needed to get an accurate result. So convergence testing is performed to quantify the uncertainty associated with interpolating over different shield thickness spatial grids.

Anderson, Brooke↗

NASA NTRS1994

Networked differential GPS system

An embodiment of the present invention relates to a worldwide network of differential GPS reference stations (NDGPS) that continually track the entire GPS satellite constellation and provide interpolations of reference station corrections tailored for particular user locations between the reference stations Each reference station takes real-time ionospheric measurements with codeless cross-correlating dual-frequency carrier GPS receivers and computes real-time orbit ephemerides independently. An absolute pseudorange correction (PRC) is defined for each satellite as a function of a particular user's location. A map of the function is constructed, with iso-PRC contours. The network measures the PRCs at a few points, so-called reference stations and constructs an iso-PRC map for each satellite. Corrections are interpolated for each user's site on a subscription basis. The data bandwidths are kept to a minimum by transmitting information that cannot be obtained directly by the user and by updating information by classes and according to how quickly each class of data goes stale given the realities of the GPS system. Sub-decimeter-level kinematic accuracy over a given area is accomplished by establishing a mini-fiducial network.

Mueller, K. Tysen↗

NASA NTRS2009

Characteristics of Whipple Shield Performance in the Shatter Regime

Between the onset of projectile fragmentation and the assumption of rear wall failure due to an impulsive load, multi-wall ballistic limit equations are linearly interpolated to provide reasonable yet conservative predictions of perforation thresholds with conveniently simple mathematics. Although low velocity and hypervelocity regime predictions are based on analytical expressions, there is no such scientific foundation for predictions in the intermediate (or shatter) regime. As the debris flux in low earth orbit (LEO) becomes increasingly dominated by manmade pollution, the profile of micrometeoroid and orbital debris (MMOD) risk shifts continually towards lower velocities. For the International Space Station (ISS), encounter velocities below 7 km/s now constitute approximately 50% of the penetration risk. Considering that the transition velocity from shatter to hypervelocity impact regimes described by common ballistic limit equations (e.g. new non-optimum Whipple shield equation [1]) occurs at 7 km/s, 50% of station risk is now calculated based on failure limit equations with little analytical foundation. To investigate projectile and shield behavior for impact conditions leading to projectile fragmentation and melt, a series of hypervelocity impact tests have been performed on aluminum Whipple shields. In the experiments projectile diameter, bumper thickness, and shield spacing were kept constant, while rear wall thickness was adjusted to determine spallation and perforation limits at various impact velocities and angles. The results, shown in Figure 1 for normal and 45 impacts, demonstrated behavior that was not sufficiently described by the simplified linear interpolation of the NNO equation (also shown in Figure 1). Hopkins et al. [2] investigated the performance of a nominally-identical aluminum Whipple shield, identifying the effects of phase change in the shatter regime. The results (conceptually represented in Figure 2) were found to agree well with those obtained in this study at normal incidence, suggesting that shielding performance in the shatter regime could be well described by considering more complex phase conditions than currently implemented in most BLEs. Furthermore, evidence of these phase effects were found in the oblique test results, providing the basis for an empirical description of these effects that can be applied in MMOD risk assessment software. In this paper, results of the impact experiments are presented, and characteristics of target damage are evaluated. A comparison of intermediate velocity impact failure mechanisms in current BLEs are discussed and compared to the findings of the experimental study. Risk assessment calculations have been made on a simplified structure using currently implemented penetration equations and predicted limits from the experimental program, and the variation in perceived mission risk is discussed. It was found that ballistic limit curves that explicitly incorporated phase change effects within the intermediate regime lead to a decrease in predicted MMOD risk for ISS-representative orbits. When considered for all Whipple-based shielding configurations onboard the ISS, intermediate phase change effects could lead to significant variations in predicted mission risk.

Ryan, Shannon↗

NASA NTRS2009

Modeling and Simulation of Variable Mass, Flexible Structures

The advent of the new Ares I launch vehicle has highlighted the need for advanced dynamic analysis tools for variable mass, flexible structures. This system is composed of interconnected flexible stages or components undergoing rapid mass depletion through the consumption of solid or liquid propellant. In addition to large rigid body configuration changes, the system simultaneously experiences elastic deformations. In most applications, the elastic deformations are compatible with linear strain-displacement relationships and are typically modeled using the assumed modes technique. The deformation of the system is approximated through the linear combination of the products of spatial shape functions and generalized time coordinates. Spatial shape functions are traditionally composed of normal mode shapes of the system or even constraint modes and static deformations derived from finite element models of the system. Equations of motion for systems undergoing coupled large rigid body motion and elastic deformation have previously been derived through a number of techniques [1]. However, in these derivations, the mode shapes or spatial shape functions of the system components were considered constant. But with the Ares I vehicle, the structural characteristics of the system are changing with the mass of the system. Previous approaches to solving this problem involve periodic updates to the spatial shape functions or interpolation between shape functions based on system mass or elapsed mission time. These solutions often introduce misleading or even unstable numerical transients into the system. Plus, interpolation on a shape function is not intuitive. This paper presents an approach in which the shape functions are held constant and operate on the changing mass and stiffness matrices of the vehicle components. Each vehicle stage or component finite element model is broken into dry structure and propellant models. A library of propellant models is used to describe the distribution of mass in the fuel tank or Solid Rocket Booster (SRB) case for various propellant levels. Based on the mass consumed by the liquid engine or SRB, the appropriate propellant model is coupled with the dry structure model for the stage. Then using vehicle configuration data, the integrated vehicle model is assembled and operated on by the constant system shape functions. The system mode shapes and frequencies can then be computed from the resulting generalized mass and stiffness matrices for that mass configuration. The rigid body mass properties of the vehicle are derived from the integrated vehicle model. The coupling terms between the vehicle rigid body motion and elastic deformation are also updated from the constant system shape functions and the integrated vehicle model. This approach was first used to analyze variable mass spinning beams and then prototyped into a generic dynamics simulation engine. The resulting code was tested against Crew Launch Vehicle (CLV-)class problems worked in the TREETOPS simulation package and by Wilson [2]. The Ares I System Integration Laboratory (SIL) is currently being developed at the Marshall Space Flight Center (MSFC) to test vehicle avionics hardware and software in a hardware-in-the-loop (HWIL) environment and certify that the integrated system is prepared for flight. The Ares I SIL utilizes the Ares Real-Time Environment for Modeling, Integration, and Simulation (ARTEMIS) tool to simulate the launch vehicle and stimulate avionics hardware. Due to the presence of vehicle control system filters and the thrust oscillation suppression system, which are tuned to the structural characteristics of the vehicle, ARTEMIS must incorporate accurate structural models of the Ares I launch vehicle. The ARTEMIS core dynamics simulation models the highly coupled nature of the vehicle flexible body dynamics, propellant slosh, and vehicle nozzle inertia effects combined with mass and flexible body properties that vary significant with time during the flight. All forces that act on the vehicle during flight must be simulated, including deflected engine thrust force, spatially distributed aerodynamic forces, gravity, and reaction control jet thrust forces. These forces are used to excite an integrated flexible vehicle, slosh, and nozzle dynamics model for the vehicle stack that simulates large rigid body translations and rotations along with small elastic deformations. Highly effective matrix math operations on a distributed, threaded high-performance simulation node allow ARTEMIS to retain up to 30 modes of flex for real-time simulation. Stage elements that separate from the stack during flight are propagated as independent rigid six degrees of freedom (6DOF) bodies. This paper will present the formulation of the resulting equations of motion, solutions to example problems, and describe the resulting dynamics simulation engine within ARTEMIS.

Tobbe, Patrick A.↗

NASA NTRS2007

PREDICTS

PREDICTS is a computer program that predicts the frequencies, as functions of time, of signals to be received by a radio science receiver in this case, a special-purpose digital receiver dedicated to analysis of signals received by an antenna in NASA s Deep Space Network (DSN). Unlike other software used in the DSN, PREDICTS does not use interpolation early in the calculations; as a consequence, PREDICTS is more precise and more stable. The precision afforded by the other DSN software is sufficient for telemetry; the greater precision afforded by PREDICTS is needed for radio-science experiments. In addition to frequencies as a function of time, PREDICTS yields the rates of change and interpolation coefficients for the frequencies and the beginning and ending times of reception, transmission, and occultation. PREDICTS is applicable to S-, X-, and Ka-band signals and can accommodate the following link configurations: (1) one-way (spacecraft to ground), (2) two-way (from a ground station to a spacecraft to the same ground station), and (3) three-way (from a ground transmitting station to a spacecraft to a different ground receiving station).

Zhou, Hanying↗

NASA NTRS2008

Uplink Array Concept Demonstration with the EPOXI Spacecraft

Uplink array technology is currently being developed for NASA's Deep Space Network (DSN) to provide greater range and data throughput for future NASA missions, including manned missions to Mars and exploratory missions to the outer planets, the Kuiper belt, and beyond. Here we describe a novel technique for generating the frequency predicts that are used to compensate for relative Doppler, derived from interpolated earth position and spacecraft ephemerides. The method described here guarantees velocity and range estimates that are consistent with each other, hence one can always be recovered from the other. Experimental results have recently proven that these frequency predicts are accurate enough to maintain the phase of a three element array at the EPOXI spacecraft for three hours. Previous methods derive frequency predicts directly from interpolated relative velocities. However, these velocities were found to be inconsistent with the corresponding spacecraft range, meaning that range could not always be recovered accurately from the velocity predicts, and vice versa. Nevertheless, velocity-based predicts are also capable of maintaining uplink array phase calibration for extended periods, as demonstrated with the EPOXI spacecraft, however with these predicts important range and phase information may be lost. A comparison of the steering-vector method with velocity-based techniques for generating precise frequency predicts specifically for uplink array applications is provided in the following sections.

spacecraft uplink commands↗

NASA NTRS2008

Pointing-Vector and Velocity Based Frequency Predicts for Deep-Space Uplink Array Applications

uplink arraying↗

NASA NTRS2011

Efficient Kriging Algorithms

More efficient versions of an interpolation method, called kriging, have been introduced in order to reduce its traditionally high computational cost. Written in C++, these approaches were tested on both synthetic and real data. Kriging is a best unbiased linear estimator and suitable for interpolation of scattered data points. Kriging has long been used in the geostatistic and mining communities, but is now being researched for use in the image fusion of remotely sensed data. This allows a combination of data from various locations to be used to fill in any missing data from any single location. To arrive at the faster algorithms, sparse SYMMLQ iterative solver, covariance tapering, Fast Multipole Methods (FMM), and nearest neighbor searching techniques were used. These implementations were used when the coefficient matrix in the linear system is symmetric, but not necessarily positive-definite.

Memarsadeghi, Nargess↗

NASA NTRS2010

A Final Approach Trajectory Model for Current Operations

Predicting accurate trajectories with limited intent information is a challenge faced by air traffic management decision support tools in operation today. One such tool is the FAA's Terminal Proximity Alert system which is intended to assist controllers in maintaining safe separation of arrival aircraft during final approach. In an effort to improve the performance of such tools, two final approach trajectory models are proposed; one based on polynomial interpolation, the other on the Fourier transform. These models were tested against actual traffic data and used to study effects of the key final approach trajectory modeling parameters of wind, aircraft type, and weight class, on trajectory prediction accuracy. Using only the limited intent data available to today's ATM system, both the polynomial interpolation and Fourier transform models showed improved trajectory prediction accuracy over a baseline dead reckoning model. Analysis of actual arrival traffic showed that this improved trajectory prediction accuracy leads to improved inter-arrival separation prediction accuracy for longer look ahead times. The difference in mean inter-arrival separation prediction error between the Fourier transform and dead reckoning models was 0.2 nmi for a look ahead time of 120 sec, a 33 percent improvement, with a corresponding 32 percent improvement in standard deviation.

Gong, Chester↗

NASA NTRS2010

Transfer of Satellite Rainfall Uncertainty from Gauged to Ungauged Regions at Regional and Seasonal Timescales

Hydrologists and other users need to know the uncertainty of the satellite rainfall data sets across the range of time/space scales over the whole domain of the data set. Here, uncertainty' refers to the general concept of the deviation' of an estimate from the reference (or ground truth) where the deviation may be defined in multiple ways. This uncertainty information can provide insight to the user on the realistic limits of utility, such as hydrologic predictability, that can be achieved with these satellite rainfall data sets. However, satellite rainfall uncertainty estimation requires ground validation (GV) precipitation data. On the other hand, satellite data will be most useful over regions that lack GV data, for example developing countries. This paper addresses the open issues for developing an appropriate uncertainty transfer scheme that can routinely estimate various uncertainty metrics across the globe by leveraging a combination of spatially-dense GV data and temporally sparse surrogate (or proxy) GV data, such as the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar and the Global Precipitation Measurement (GPM) mission Dual-Frequency Precipitation Radar. The TRMM Multi-satellite Precipitation Analysis (TMPA) products over the US spanning a record of 6 years are used as a representative example of satellite rainfall. It is shown that there exists a quantifiable spatial structure in the uncertainty of satellite data for spatial interpolation. Probabilistic analysis of sampling offered by the existing constellation of passive microwave sensors indicate that transfer of uncertainty for hydrologic applications may be effective at daily time scales or higher during the GPM era. Finally, a commonly used spatial interpolation technique (kriging), that leverages the spatial correlation of estimation uncertainty, is assessed at climatologic, seasonal, monthly and weekly timescales. It is found that the effectiveness of kriging is sensitive to the type of uncertainty metric, time scale of transfer and the density of GV data within the transfer domain. Transfer accuracy is lowest at weekly timescales with the error doubling from monthly to weekly.However, at very low GV data density (<20% of the domain), the transfer accuracy is too low to show any distinction as a function of the timescale of transfer.

Tang, Ling↗

NASA NTRS2011

Sensitivity of Spaceborne and Ground Radar Comparison Results to Data Analysis Methods and Constraints

With the availability of active weather radar observations from space from the Precipitation Radar (PR) on board the Tropical Rainfall Measuring Mission (TR.MM) satellite, numerous studies have been performed comparing PR reflectivity and derived rain rates to similar observations from ground-based weather radars (GR). These studies have used a variety of algorithms to compute matching PR and GR volumes for comparison. Most studies have used a fixed 3-dimensional Cartesian grid centered on the ground radar, onto which the PR and GR data are interpolated using a proprietary approach and/or commonly available GR analysis software (e.g., SPRINT, REORDER). Other studies have focused on the intersection of the PR and GR viewing geometries either explicitly or using a hybrid of the fixed grid and PR/GR common fields of view. For the Dual-Frequency Precipitation Radar (DPR) of the upcoming Global Precipitation Measurement (GPM) mission, a prototype DPR/GR comparison algorithm based on similar TRMM PR data has been developed that defines the common volumes in terms of the geometric intersection of PR and GR rays, where smoothing of the PR and GR data are minimized and no interpolation is performed. The PR and GR volume-averaged reflectivity values of each sample volume are accompanied by descriptive metadata, for attributes including the variability and maximum of the reflectivity within the sample volume, and the fraction of range gates in the sample average having reflectivity values above an adjustable detection threshold (typically taken to be 18 dBZ for the PR). Sample volumes are further characterized by rain type (Stratiform or Convective), proximity to the melting layer, underlying surface (land/water/mixed), and the time difference between the PR and GR observations. The mean reflectivity differences between the PR and GR can differ between data sets produced by the different analysis methods; and for the GPM prototype, by the type of constraints and categorization applied to the data. In this paper, we will show results comparing the 3-D gridded analysis "black box" approach to the GPM prototype volume-matching approach, using matching TRMM PR and WSR-88D ground radar data. The affects of applying data constraints and data categorizations on the volume-matched data to the results will be shown, and explanations of the differences in terms of data and analysis algorithm characteristics will be presented. Implications of the differences to the determination of PR/DPR calibration differences and use of ground radar data to evaluate the PR and DPR attenuation correction algorithms will be discussed.

Morris, Kenneth R.↗