The effects of interspacecraft communication time tag error on formation estimation
Formation estimation requires inter-spacecraft communication links to exchange sensor measurements and internal data.
formation flying estimation time tag error↗
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Observers for a class of systems with nonlinearities satisfying an incremental quadratic inequality
We consider the problem of state estimation from nonlinear time-varying system whose nonlinearities satisfy an incremental quadratic inequality. Observers are presented which guarantee that the state estimation error exponentially converges to zero.
linear matrix inequalities↗
Aerosol Indirect Effect Studies at Southern Great Plains During the May 2003 Intensive Operations Period
During May 2003 the Department of Energy's Atmospheric Radiation Measurement Program conducted an Intensive Operations Period (IOP) to measure the radiative effects of aerosol and clouds. A suite of both in situ and remote sensing measurements were available to measure aerosol and cloud parameters. This paper has three main goals: First, it focuses on comparison between in situ retrievals of the radiatively important drop effective radius r(sub e) and various satellite, airborne, and surface remote sensing retrievals of the same parameter. On 17 May 2003, there was a fortuitous, near-simultaneous sampling of a stratus cloud by five different methods. The retrievals of r(sub e) agree with one another to within approx.20%, which is approximately the error estimate for most methods. Second, a methodology for deriving a best estimate of r(sub e) from these different instruments, with their different physical properties and sampling volumes, is proposed and applied to the 17 May event. Third, the paper examines the response of r(sub e) to changes in aerosol on 3 days during the experiment and examines the consistency of remote sensing and in situ measurements of the effect of aerosol on r(sub e). It is shown that in spite of the generally good agreement in derived r(sub e), the magnitude of the response of r(sub e), to changes in aerosol is quite sensitive to the method of retrieving r(sub e) and to the aerosol proxy for cloud condensation nuclei. Nonphysical responses are sometimes noted, and it is suggested that further work needs to be done to refine these techniques.
Feingold, Graham↗
Lightning Charge Retrievals: Dimensional Reduction, LDAR Constraints, and a First Comparison with LIS Satellite Data
A "dimensional reduction" (DR) method is introduced for analyzing lightning field changes (DELTAEs) whereby the number of unknowns in a discrete two-charge model is reduced from the standard eight (x, y, z, Q, x', y', z', Q') to just four (x, y, z, Q). The four unknowns (x, y, z, Q) are found by performing a numerical minimization of a chi-square function. At each step of the minimization, an Overdetermined Fixed Matrix (OFM) method is used to immediately retrieve the best "residual source" (x', y', z', Q'), given the values of (x, y, z, Q). In this way, all 8 parameters (x, y, z, Q, x', y', z', Q') are found, yet a numerical search of only 4 parameters (x, y, z, Q) is required. The DR method has been used to analyze lightning-caused DeltaEs derived from multiple ground-based electric field measurements at the NASA Kennedy Space Center (KSC) and USAF Eastern Range (ER). The accuracy of the DR method has been assessed by comparing retrievals with data provided by the Lightning Detection And Ranging (LDAR) system at the KSC-ER, and from least squares error estimation theory, and the method is shown to be a useful "stand-alone" charge retrieval tool. Since more than one charge distribution describes a finite set of DELTAEs (i.e., solutions are non-unique), and since there can exist appreciable differences in the physical characteristics of these solutions, not all DR solutions are physically acceptable. Hence, an alternative and more accurate method of analysis is introduced that uses LDAR data to constrain the geometry of the charge solutions, thereby removing physically unacceptable retrievals. The charge solutions derived from this method are shown to compare well with independent satellite- and ground-based observations of lightning in several Florida storms.
Koshak, W. J.↗
Consistency of Post-Newtonian Waveforms with Numerical Relativity
General relativity predicts the gravitational radiation signatures of mergers of compact binaries,such as coalescing binary black hole systems. Derivations of waveform predictions for such systems are required for optimal scientific analysis of observational gravitational wave data, and have so far been achieved primarily with the aid of the post-Newtonian (PN) approximation. The quaIity of this treatment is unclear, however, for the important late inspiral portion. We derive late-inspiral wave forms via a complementary approach, direct numerical simulation of Einstein's equations, which has recently matured sufficiently for such applications. We compare waveform phasing from simulations covering the last approximately 14 cycles of gravitational radiation from an equal-mass binary system of nonspinning black holes with corresponding 3PN and 3.5PN waveforms. We find phasing agreement consistent with internal error estimates based in either approach, at the level of one radian over approximately 10 cycles. The result suggests that PN waveforms for this system are effective roughly until the system reaches its last stable orbit just prior to the final merger.
Baker, John G.↗
Efficient Implementation of an Optimal Interpolator for Large Spatial Data Sets
Scattered data interpolation is a problem of interest in numerous areas such as electronic imaging, smooth surface modeling, and computational geometry. Our motivation arises from applications in geology and mining, which often involve large scattered data sets and a demand for high accuracy. The method of choice is ordinary kriging. This is because it is a best unbiased estimator. Unfortunately, this interpolant is computationally very expensive to compute exactly. For n scattered data points, computing the value of a single interpolant involves solving a dense linear system of size roughly n x n. This is infeasible for large n. In practice, kriging is solved approximately by local approaches that are based on considering only a relatively small'number of points that lie close to the query point. There are many problems with this local approach, however. The first is that determining the proper neighborhood size is tricky, and is usually solved by ad hoc methods such as selecting a fixed number of nearest neighbors or all the points lying within a fixed radius. Such fixed neighborhood sizes may not work well for all query points, depending on local density of the point distribution. Local methods also suffer from the problem that the resulting interpolant is not continuous. Meyer showed that while kriging produces smooth continues surfaces, it has zero order continuity along its borders. Thus, at interface boundaries where the neighborhood changes, the interpolant behaves discontinuously. Therefore, it is important to consider and solve the global system for each interpolant. However, solving such large dense systems for each query point is impractical. Recently a more principled approach to approximating kriging has been proposed based on a technique called covariance tapering. The problems arise from the fact that the covariance functions that are used in kriging have global support. Our implementations combine, utilize, and enhance a number of different approaches that have been introduced in literature for solving large linear systems for interpolation of scattered data points. For very large systems, exact methods such as Gaussian elimination are impractical since they require 0(n(exp 3)) time and 0(n(exp 2)) storage. As Billings et al. suggested, we use an iterative approach. In particular, we use the SYMMLQ method, for solving the large but sparse ordinary kriging systems that result from tapering. The main technical issue that need to be overcome in our algorithmic solution is that the points' covariance matrix for kriging should be symmetric positive definite. The goal of tapering is to obtain a sparse approximate representation of the covariance matrix while maintaining its positive definiteness. Furrer et al. used tapering to obtain a sparse linear system of the form Ax = b, where A is the tapered symmetric positive definite covariance matrix. Thus, Cholesky factorization could be used to solve their linear systems. They implemented an efficient sparse Cholesky decomposition method. They also showed if these tapers are used for a limited class of covariance models, the solution of the system converges to the solution of the original system. Matrix A in the ordinary kriging system, while symmetric, is not positive definite. Thus, their approach is not applicable to the ordinary kriging system. Therefore, we use tapering only to obtain a sparse linear system. Then, we use SYMMLQ to solve the ordinary kriging system. We show that solving large kriging systems becomes practical via tapering and iterative methods, and results in lower estimation errors compared to traditional local approaches, and significant memory savings compared to the original global system. We also developed a more efficient variant of the sparse SYMMLQ method for large ordinary kriging systems. This approach adaptively finds the correct local neighborhood for each query point in the interpolation process.
Memarsadeghi, Nargess↗
Consistency of Post-Newtonian Waveforms with Numerical Relativity
General relativity predicts the gravitational radiation signatures of mergers of compact binaries, such as coalescing binary black hole systems. Derivations of waveform predictions for such systems are required for optimal scientific analysis of observational gravitational wave data, and have so far been achieved primarily with the aid of the post-Newtonian (PN) approximation. The quality of this treatment is unclear, however, for the important late inspiral portion. We derive late-inspiral waveforms via a complementary approach, direct numerical simulation of Einstein's equations, which has recently matured sufficiently for such applications. We compare waveform phasing from simulations covering the last approximately 14 cycles of gravitational radiation from an equal-mass binary system of nonspinning black holes with the corresponding 3PN and 3.5PN orbital phasing. We find agreement consistent with internal error estimates based on either approach at the level of one radian over approximately 10 cycles. The result suggests that PN waveforms for this system are effective roughly until the system reaches its last stable orbit just prior to the final merger/
Baker, John G.↗
Lightning Charge Retrievals: Dimensional Reduction, LDAR Constraints, and a First Comparison with LIS Satellite Data
A "dimensional reduction" ("DR") method is introduced for analyzing lightning field changes ((Delta)Es) whereby the number of unknowns in a discrete two-charge model is reduced from the standard eight (x, y, z, Q, x', y', z', Q') to just four (x, y, z, Q). The four unknowns (x, y, z, Q) are found by performing a numerical minimization of a chi-square function. At each step of the minimization, an overdetermined fixed matrix (OFM) method is used to immediately retrieve the best "residual source" (x', y', z', Q'), given the values of (x, y, z, Q). In this way, all eight parameters Ix. y, z, Q, x', y', z', Q') are found, yet a numerical search of only four parameters (x, y, z, Q) is required. The DR method has been used to analyze lightning-caused (Delta)Es derived from multiple ground-based electric field measurements at the NASA Kennedy Space Center (KSC) and U.S. Air Force Eastern Range (ER). The accuracy of the DR method has been assessed by comparing retrievals with data provided by the lightning detection and ranging (LDAR) system at the KSC-ER. and from least squares error estimation theory, and the method is shown to be a useful "stand alone" charge retrieval tool. Since more than one charge distribution describes a finite set of (Delta)Es (i.e., solutions are nonunique), and since there can be appreciable differences in the physical characteristics of these solutions, not all DR solutions are physically acceptable. Hence. an alternative and more accurate method of analysis is introduced that uses LDAR data to constrain the geometry of the charge solutions. thereby removing physically unacceptable retrievals. The charge solutions derived from this method are shown to compare well with independent satellite- and ground-based observations of lightning m several Florida storms.
Koshak, W. J.↗
Using Observations of Deep Convective Systems to Constrain Atmospheric Column Absorption of Solar Radiation in the Optically Thick Limit
Atmospheric column absorption of solar radiation A(sub col) is a fundamental part of the Earth's energy cycle but is an extremely difficult quantity to measure directly. To investigate A(sub col), we have collocated satellite-surface observations for the optically thick Deep Convective Systems (DCS) at the Department of Energy Atmosphere Radiation Measurement (ARM) Tropical Western Pacific (TWP) and Southern Great Plains (SGP) sites during the period of March 2000 December 2004. The surface data were averaged over a 2-h interval centered at the time of the satellite overpass, and the satellite data were averaged within a 1 deg X 1 deg area centered on the ARM sites. In the DCS, cloud particle size is important for top-of-atmosphere (TOA) albedo and A(sub col) although the surface absorption is independent of cloud particle size. In this study, we find that the A(sub col) in the tropics is approximately 0.011 more than that in the middle latitudes. This difference, however, disappears, i.e., the A(sub col) values at both regions converge to the same value (approximately 0.27 of the total incoming solar radiation) in the optically thick limit (tau greater than 80). Comparing the observations with the NASA Langley modified Fu_Liou 2-stream radiative transfer model for optically thick cases, the difference between observed and model-calculated surface absorption, on average, is less than 0.01, but the model-calculated TOA albedo and A(sub col) differ by 0.01 to 0.04, depending primarily on the cloud particle size observation used. The model versus observation discrepancies found are smaller than many previous studies and are just within the estimated error bounds. We did not find evidence for a large cloud absorption anomaly for the optically thick limit of extensive ice cloud layers. A more modest cloud absorption difference of 0.01 to 0.04 cannot yet be ruled out. The remaining uncertainty could be reduced with additional cases, and by reducing the current uncertainty in cloud particle size.
Dong, Xiquan↗
Evaluation and Assimilation of Cloud Cleared Radiances for AIRS in GEOS-5
The use of clear (cloud-free) channels for AIRS in GEOS-5 had shown positive impact on forecast skills in both hemispheres. However, improvements in forecast skills due to the assimilation of AIRS data are less impressive since the number of assimilated channels from AIRS is much larger than that from other Infrared sounders such as HIRS-3 onboard NOAA 15-17 satellites. This limitation of AIRS radiance data to improve the forecast skill is mainly due to the fact that channels capable of peaking below clouds are not used in the assimilation and yet those have highest vertical resolving capability of AIRS instrument are concentrated in the lower troposphere. On average, the percentage of AIRS footprints completely clear for all channels is less than 10%. The percentage of assimilated AIRS channel radiances however ranges from 100% for channels peaking in the upper stratosphere, above the cloud, to no more that 5% in the lower atmosphere due to cloud contamination. Our current ability to model and predict clouds accurately in global model, and to fully characterize and parameterize optical properties of cloud particles in radiative transfer model are the two major obstacles prohibiting us to use cloudy radiance directly in the assimilation. To further improve forecast skill using AIRS data, we ought to use the channels peaking below the clouds in the troposphere, which can be accomplished by assimilating cloud-cleared radiance. The cloud-cleared radiance data for AIRS used in this study were obtained from optimal cloud clearing procedures developed by researchers at CIMSS of University of Wisconsin at Madison to retrieve clear column radiances for all AIRS channels by collocating multi-band MODIS IR clear radiance observations with the AIRS cloudy radiances on a single footprint basis. Two adjacent AIRS cloudy footprints are used to retrieve one AIRS cloud-cleared radiance spectrum and no background information (first guess) is needed. To assimilate the cloud-cleared radiance data, the errors of the cloud-cleared radiances need to be addressed. The details of convolving AIRS radiances with MODIS spectral response function and comparison with MODIS-measured cloud-free radiance will be presented. The range of errors of cloud-cleared radiances for AIRS using collocated MODIS clear and near-by AIRS clear data will be shown. The NASA. global data assimilation model, GEOS-5, is used to evaluate and assimilate the cloud-cleared radiance for AIRS. The residues between the cloud-cleared brightness temperature and the simulated brightness temperature from background (i.e., OMFs) will be investigated. The quality control procedures will be documented based on error estimation and the OMFs. Finally, the impacts between assimilation of clear channel radiances and cloud-cleared radiances will be addressed.
Liu, Hui-chun↗
Improved Surface Parameter Retrievals using AIRS/AMSU Data
The AIRS Science Team Version 5.0 retrieval algorithm became operational at the Goddard DAAC in July 2007 generating near real-time products from analysis of AIRS/AMSU sounding data. This algorithm contains many significant theoretical advances over the AIRS Science Team Version 4.0 retrieval algorithm used previously. Two very significant developments of Version 5 are: 1) the development and implementation of an improved Radiative Transfer Algorithm (RTA) which allows for accurate treatment of non-Local Thermodynamic Equilibrium (non-LTE) effects on shortwave sounding channels; and 2) the development of methodology to obtain very accurate case by case product error estimates which are in turn used for quality control. These theoretical improvements taken together enabled a new methodology to be developed which further improves soundings in partially cloudy conditions. In this methodology, longwave C02 channel observations in the spectral region 700 cm(exp -1) to 750 cm(exp -1) are used exclusively for cloud clearing purposes, while shortwave C02 channels in the spectral region 2195 cm(exp -1) 2395 cm(exp -1) are used for temperature sounding purposes. This allows for accurate temperature soundings under more difficult cloud conditions. This paper further improves on the methodology used in Version 5 to derive surface skin temperature and surface spectral emissivity from AIRS/AMSU observations. Now, following the approach used to improve tropospheric temperature profiles, surface skin temperature is also derived using only shortwave window channels. This produces improved surface parameters, both day and night, compared to what was obtained in Version 5. These in turn result in improved boundary layer temperatures and retrieved total O3 burden.
Susskind, Joel↗
Data Assimilation Experiments using Quality Controlled AIRS Version 5 Temperature Soundings
The AIRS Science Team Version 5 retrieval algorithm has been finalized and is now operational at the Goddard DAAC in the processing (and reprocessing) of all AlRS data. Version 5 contains accurate case-by-case error estimates for most derived products, which are also used for quality control. We have conducted forecast impact experiments assimilating AlRS quality controlled temperature profiles using the NASA GEOS-5 data assimilation system, consisting of the NCEP GSI analysis coupled with the NASA FVGCM. Assimilation of quality controlled temperature profiles resulted in significantly improved forecast skill in both the Northern Hemisphere and Southern Hemisphere Extra-Tropics, compared to that obtained from analyses obtained when all data used operationally by NCEP except for AlRS data is assimilated. Experiments using different Quality Control thresholds for assimilation of AlRS temperature retrievals showed that a medium quality control threshold performed better than a tighter threshold, which provided better overall sounding accuracy; or a looser threshold, which provided better spatial coverage of accepted soundings. We are conducting more experiments to further optimize this balance of spatial coverage and sounding accuracy from the data assimilation perspective. In all cases, temperature soundings were assimilated well below cloud level in partially cloudy cases. The positive impact of assimilating AlRS derived atmospheric temperatures all but vanished when only AIRS stratospheric temperatures were assimilated. Forecast skill resulting from assimilation of AlRS radiances uncontaminated by clouds, instead of AlRS temperature soundings, was only slightly better than that resulting from assimilation of only stratospheric AlRS temperatures. This reduction in forecast skill is most likely the result of significant loss of tropospheric information when only AIRS radiances unaffected by clouds are used in the data assimilation process.
Susskind, Joel↗
Controller for Driving a Piezoelectric Actuator at Resonance
A digital control system based partly on an extremum-seeking control algorithm tracks the changing resonance frequency of a piezoelectric actuator or an electrically similar electromechanical device that is driven by a sinusoidal excitation signal and is required to be maintained at or near resonance in the presence of uncertain, changing external loads and disturbances. Somewhat more specifically, on the basis of measurements of the performance of the actuator, this system repeatedly estimates the resonance frequency and alters the excitation frequency as needed to keep it at or near the resonance frequency. In the original application for which this controller was developed, the piezoelectric actuator is part of an ultrasonic/sonic drill/corer. Going beyond this application, the underlying principles of design and operation are generally applicable to tracking changing resonance frequencies of heavily perturbed harmonic oscillators. Resonance-frequency-tracking analog electronic circuits are commercially available, but are not adequate for the present purpose for several reasons: The input/output characteristics of analog circuits tend to drift, often necessitating recalibration, especially whenever the same controller is used in driving a different resonator. In the case of an actuator in a system that has multiple modes characterized by different resonance frequencies, an analog controller can tune erroneously to one of the higher-frequency modes. The lack of programmability of analog controllers is problematic when faults occur, and is especially problematic for preventing tuning to a higher-frequency mode. In contrast, a digital controller can be programmed to restrict itself to a specified frequency range and to maintain stability even when the affected resonator is driven at high power and subjected to uncertain disturbances and variable loads. The present digital control system (see figure) is implemented by means of an algorithm that comprises three main subalgorithms: a hill-climbing control algorithm, an estimation-based extremum-seeking control (ESC) algorithm, and a supervisory algorithm. The hill-climbing algorithm is useful for coarse tracking to find and remain within the vicinity of the resonance. The ESC algorithm is not capable of coarse resonance tracking, but is capable of fine resonance tracking once the estimates of parameters generated by the hill-climbing algorithm have converged sufficiently. On the basis of the parameter-estimation errors, the supervisory algorithm switches operation to whichever of the other two algorithms performs best at a given time.
Aldrich, Jack↗
Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality
We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.
observers↗
Measuring Massive Black Hole Binaries with LISA
The coalescence of two massive black holes produces gravitational waves (GWs) which can be detected by the space-based detector LISA. By measuring these waves, LISA can determine the various parameters which characterize the source. Measurements of the black hole masses and spins will provide information about the growth of black holes and their host galaxies over time. Measurements of a source's sky position and distance may help astronomers identify an electromagnetic counterpart to the GW event. The counterpart's redshift, combined with the GW-measured luminosity distance, can then be used to measure the Hubble constant and the dark energy parameter $w$. Because the potential science output is so high, it is useful to know in advance how well LISA can measure source parameters for a wide range of binaries. We calculate expected parameter estimation errors using the well-known Fisher matrix method. Our waveform model includes the physics of spin precession, as well as subleading harmonics. When these higher-order effects are not included, strong degeneracies between some parameters cause them to be poorly determined by a GW measurement. When precession and subleading harmonics are properly included, the degeneracies are broken, reducing parameter errors by one to several orders of magnitude.
Lang, Ryan N.↗
Fast Switching and Precision Relative Astrometry at the DSN
A) We are developing new techniques to improve astrometric accuracy: 1) Reducing switching time (approx. 60s) and angular separation (approx.1deg) between quasars; 2) Use of phase delay & bandpass calibration; 3) Techniques also applicable with future DSN Array. B) Initial set of observations carried out at the DSN show great promise. C) Continue DSN observations using fainter calibrators to study robustness and to verify and validate error estimates. (Eventually demo technique with spacecraft measurements). D) Viability of technique depends on existence of sufficient number of calibrators. (Determining what fraction of radio sources are compact at the VLBA) E) May be able to use calibrators with flux density approx. 50 mJy with calibrator 1deg. G) Relative precision of approx.0.5 nrad may be achievable. E) Absolute measurement always depends on knowledge of calibrator position. (Catalog maintained and improved).
Deep Space Network (DSN)↗
Error Representation in Time For Compressible Flow Calculations
Time plays an essential role in most real world fluid mechanics problems, e.g. turbulence, combustion, acoustic noise, moving geometries, blast waves, etc. Time dependent calculations now dominate the computational landscape at the various NASA Research Centers but the accuracy of these computations is often not well understood. In this presentation, we investigate error representation (and error control) for time-periodic problems as a prelude to the investigation of feasibility of error control for stationary statistics and space-time averages. o These statistics and averages (e.g. time-averaged lift and drag forces) are often the output quantities sought by engineers. o For systems such as the Navier-Stokes equations, pointwise error estimates deteriorate rapidly which increasing Reynolds number while statistics and averages may remain well behaved.
Barth, Timothy J.↗
Elemental Composition of 433 Eros: New Calibration of the NEAR-Shoemaker XRS Data
We present a new calibration of the elemental-abundance data for Asteroid 433 Fros taken by the X-ray spectrometer (XRS) aboard the NEAR-Shoemaker spacecraft. (NEAR is an acronym for "Near-Earth Asteroid Rendezvous,") Quintification of the asteroid surface elemental abundance ratios depends critically on accurate knowledge of the incident solar X-ray spectrum, which was monitored simultaneously with asteroid observations. Previously published results suffered from incompletely characterized systematic uncertainties due to an imperfect ground calibrations of the NEAR gas solar monitor. The solar monitor response function and associated uncertainties have now been characterized by cross-calibration of a large sample of NEAR solar monitor flight data against. contemporary broadband solar X-ray data from the Earth-orbiting GOES-8 (Geostationary Operational Environmental Satellite). The results have been used to analyze XRS spectra acquired from Eros during eight major solar flares (including three that have not previously been reported). The end product of this analysis is a revised set of Eros surface elemental abundance ratios with new error estimates that more accurately reflect the remaining uncertainties in the solar flare spectra: Mg/Si=.753 +0.078/-0.055, Al/Si=0.069 +/-0.055, S/Si=0.005+/-0.008, Ca/Si=0.060+0.023/-0.024, and Fe/Si= 1.578+0.338/-0.320. These revised abundance ratios are consitent within cited uncertainties with the results of Nittler et al. [Nittler, L.R., and 14 colleagues, 2001. Meteorit Planet. Sci 36, 1673-1695] and thus support the prior conclusions that 433 Eros has major-element composition simular to ordinary chondrites with the exception of a stong depletoin in sulfur, most likely caused by space weathering.
Lim, Lucy F.↗