Methods for injection-error analysis and their comparison.
Statistical techniques for missile injection error analysis, discussing direct and adjoint methods
STATISTICAL ANALYSIS↗
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Main Geomagnetic Field Models from Oersted and Magsat Data Via a Rigorous General Inverse Theory with Error Bounds
The purpose of the grant was to study how prior information about the geomagnetic field can be used to interpret surface and satellite magnetic measurements, to generate quantitative descriptions of prior information that might be so used, and to use this prior information to obtain from satellite data a model of the core field with statistically justifiable error estimates. The need for prior information in geophysical inversion has long been recognized. Data sets are finite, and faithful descriptions of aspects of the earth almost always require infinite-dimensional model spaces. By themselves, the data can confine the correct earth model only to an infinite-dimensional subset of the model space. Earth properties other than direct functions of the observed data cannot be estimated from those data without prior information about the earth. Prior information is based on what the observer already knows before the data become available. Such information can be "hard" or "soft". Hard information is a belief that the real earth must lie in some known region of model space. For example, the total ohmic dissipation in the core is probably less that the total observed geothermal heat flow out of the earth's surface. (In principle, ohmic heat in the core can be recaptured to help drive the dynamo, but this effect is probably small.) "Soft" information is a probability distribution on the model space, a distribution that the observer accepts as a quantitative description of her/his beliefs about the earth. The probability distribution can be a subjective prior in the sense of Bayes or the objective result of a statistical study of previous data or relevant theories.
Backus, George E.↗
Error Estimation of An Ensemble Statistical Seasonal Precipitation Prediction Model
This NASA Technical Memorandum describes an optimal ensemble canonical correlation forecasting model for seasonal precipitation. Each individual forecast is based on the canonical correlation analysis (CCA) in the spectral spaces whose bases are empirical orthogonal functions (EOF). The optimal weights in the ensemble forecasting crucially depend on the mean square error of each individual forecast. An estimate of the mean square error of a CCA prediction is made also using the spectral method. The error is decomposed onto EOFs of the predictand and decreases linearly according to the correlation between the predictor and predictand. Since new CCA scheme is derived for continuous fields of predictor and predictand, an area-factor is automatically included. Thus our model is an improvement of the spectral CCA scheme of Barnett and Preisendorfer. The improvements include (1) the use of area-factor, (2) the estimation of prediction error, and (3) the optimal ensemble of multiple forecasts. The new CCA model is applied to the seasonal forecasting of the United States (US) precipitation field. The predictor is the sea surface temperature (SST). The US Climate Prediction Center's reconstructed SST is used as the predictor's historical data. The US National Center for Environmental Prediction's optimally interpolated precipitation (1951-2000) is used as the predictand's historical data. Our forecast experiments show that the new ensemble canonical correlation scheme renders a reasonable forecasting skill. For example, when using September-October-November SST to predict the next season December-January-February precipitation, the spatial pattern correlation between the observed and predicted are positive in 46 years among the 50 years of experiments. The positive correlations are close to or greater than 0.4 in 29 years, which indicates excellent performance of the forecasting model. The forecasting skill can be further enhanced when several predictors are used.
Shen, Samuel S. P.↗
Sampling errors in the measurement of rain and hail parameters
Attention is given to a general derivation of the fractional standard deviation (FSD) of any integrated property X such that X(D) = cD to the n. This work extends that of Joss and Waldvogel (1969). The equation is applicable to measuring integrated properties of cloud, rain or hail populations (such as water content, precipitation rate, kinetic energy, or radar reflectivity) which are subject to statistical sampling errors due to the Poisson distributed fluctuations of particles sampled in each particle size interval and the weighted sum of the associated variances in proportion to their contribution to the integral parameter to be measured. Universal curves are presented which are applicable to the exponential size distribution permitting FSD estimation of any parameters from n = 0 to n = 6. The equations and curves also permit corrections for finite upper limits in the size spectrum and a realistic fall speed law.
Gertzman, H. S.↗
Validity of the two-level model for Viterbi decoder gap-cycle performance
A two-level model has previously been proposed for approximating the performance of a Viterbi decoder which encounters data received with periodically varying signal-to-noise ratio. Such cyclically gapped data is obtained from the Very Large Array (VLA), either operating as a stand-alone system or arrayed with Goldstone. This approximate model predicts that the decoder error rate will vary periodically between two discrete levels with the same period as the gap cycle. It further predicts that the length of the gapped portion of the decoder error cycle for a constraint length K decoder will be about K-1 bits shorter than the actual duration of the gap. The two-level model for Viterbi decoder performance with gapped data is subjected to detailed validation tests. Curves showing the cyclical behavior of the decoder error burst statistics are compared with the simple square-wave cycles predicted by the model. The validity of the model depends on a parameter often considered irrelevant in the analysis of Viterbi decoder performance, the overall scaling of the received signal or the decoder's branch-metrics. Three scaling alternatives are examined: optimum branch-metric scaling and constant branch-metric scaling combined with either constant noise-level scaling or constant signal-level scaling. The simulated decoder error cycle curves roughly verify the accuracy of the two-level model for both the case of optimum branch-metric scaling and the case of constant branch-metric scaling combined with constant noise-level scaling. However, the model is not accurate for the case of constant branch-metric scaling combined with constant signal-level scaling.
Dolinar, S.↗
Network problem threshold
Network transmission errors such as collisions, CRC errors, misalignment, etc. are statistical in nature. Although errors can vary randomly, a high level of errors does indicate specific network problems, e.g. equipment failure. In this project, we have studied the random nature of collisions theoretically as well as by gathering statistics, and established a numerical threshold above which a network problem is indicated with high probability.
Gejji, Raghvendra, R.↗
Digital decorrelator saves time and expense in acoustic testing of structures
Instantaneous signals from coherent random sound field are summed and time delayed to avoid introducing vectorial addition errors. Resultant statistically independent signals are applied to spectrometer. Displayed sound pressure level is proportional to square root of sum of squares of sound pressure levels taken over frequency range of interest.
Nakich, R. B.↗
Mercury's perihelion advance - Determination by radar.
Measurement of echo delays of radar signals transmitted from earth to Mercury, yielding an accurate value for the advance of the latter's perihelion position. Given that the sun's gravitational quadrupole moment is negligible, the result in terms of the Eddington-Robertson parameters is (2 + 2 gamma-beta)/3 approximately equal to 1.005 plus or minus 0.007, where gamma = beta = 1 in general relativity, and where 0.007 represents the statistical standard error. Inclusion of the probable contribution of systematic errors raises the uncertainty to about 0.02.
Shapiro, I. I.↗
Statistics of the residual refraction errors in laser ranging data
A theoretical model for the range error covariance was derived by assuming that the residual refraction errors are due entirely to errors in the meteorological data which are used to calculate the atmospheric correction. The properties of the covariance function are illustrated by evaluating the theoretical model for the special case of a dense network of weather stations uniformly distributed within a circle.
Gardner, C. S.↗
GPS-aided Space Shuttle navigation
In the present paper, specific GPS (Global Positioning System) aided Shuttle navigation are presented as examples of the navigation performance prediction process. The process described is a statistical covariance error analysis. To facilitate detailing, the process is broken down into four portions with sharply limited interfaces. Considerations of mission scenarios form one distinct package of computer routines. Simulation of the onboard navigation filter is another facet of the process, as are the larger system covariance program and the GPS segment covariance simulation. The combination of these computer tools permits proper evaluation of the multitude of correlated error sources affecting GPS-aided Shuttle navigation.
Matchett, G.↗
Statistical theory for estimating sampling errors of regional radiation averages based on satellite measurements
The processes which determine the weather and climate are driven by the radiation received by the earth and the radiation subsequently emitted. A knowledge of the absorbed and emitted components of radiation is thus fundamental for the study of these processes. In connection with the desire to improve the quality of long-range forecasting, NASA is developing the Earth Radiation Budget Experiment (ERBE), consisting of a three-channel scanning radiometer and a package of nonscanning radiometers. A set of these instruments is to be flown on both the NOAA-F and NOAA-G spacecraft, in sun-synchronous orbits, and on an Earth Radiation Budget Satellite. The purpose of the scanning radiometer is to obtain measurements from which the average reflected solar radiant exitance and the average earth-emitted radiant exitance at a reference level can be established. The estimate of regional average exitance obtained will not exactly equal the true value of the regional average exitance, but will differ due to spatial sampling. A method is presented for evaluating this spatial sampling error.
Smith, G. L.↗
Compton telescope observations of gamma rays from SN 1987A
Results are reported of observations of a significant excess of gamma rays at energies of 1.0-2.5 MeV from the direction of SN 1987A, 418 days after detonation. Two features at 1.21 and 1.88 MeV are attributed to the 1.238 MeV and the combined 1.771, 2.015, and 2.035 MeV line emissions from the decay of Co-56 in the expanding ejecta with respective fluxes of (4.6 +/-1.4 +/-1.2) x 10 exp -4 and (3.5 +/-0.9 +/-0.9) x 10 exp -4 gamma/sq cm s, where the first error is statistical and the second systematic. The obtained energy resolution of 11 percent did not permit a definite separation of the 1.771-MeV line from the two other lines at 2.015 and 2.035 MeV that form the group at 1.88 MeV. The line fluxes were obtained after correcting for the north-south effect and the continuum.
Ait-Ouamer, Farid↗
Finite grid radius and thickness effects on retarding potential analyzer measured suprathermal electron density and temperature
The effect of finite grid radius and thickness on the electron current measured by planar retarding potential analyzers (RPAs) is analyzed numerically. Depending on the plasma environment, the current is significantly reduced below that which is calculated using a theoretical equation derived for an idealized RPA having grids with infinite radius and vanishingly small thickness. A correction factor to the idealized theoretical equation is derived for the Pioneer Venus (PV) orbiter RPA (ORPA) for electron gasses consisting of one or more components obeying Maxwell statistics. The error in density and temperature of Maxwellian electron distributions previously derived from ORPA data using the theoretical expression for the idealized ORPA is evaluated by comparing the densities and temperatures derived from a sample of PV ORPA data using the theoretical expression with and without the correction factor.
Knudsen, William C.↗
TOPEX/POSEIDON tides estimated using a global inverse model
Altimetric data from the TOPEX/POSEIDON mission will be used for studies of global ocean circulation and marine geophysics. However, it is first necessary to remove the ocean tides, which are aliased in the raw data. The tides are constrained by the two distinct types of information: the hydrodynamic equations which the tidal fields of elevations and velocities must satisfy, and direct observational data from tide gauges and satellite altimetry. Here we develop and apply a generalized inverse method, which allows us to combine rationally all of this information into global tidal fields best fitting both the data and the dynamics, in a least squares sense. The resulting inverse solution is a sum of the direct solution to the astronomically forced Laplace tidal equations and a linear combination of the representers for the data functionals. The representer functions (one for each datum) are determined by the dynamical equations, and by our prior estimates of the statistics or errors in these equations. Our major task is a direct numerical calculation of these representers. This task is computationally intensive, but well suited to massively parallel processing. By calculating the representers we reduce the full (infinite dimensional) problem to a relatively low-dimensional problem at the outset, allowing full control over the conditioning and hence the stability of the inverse solution. With the representers calculated we can easily update our model as additional TOPEX/POSEIDON data become available. As an initial illustration we invert harmonic constants from a set of 80 open-ocean tide gauges. We then present a practical scheme for direct inversion of TOPEX/POSEIDON crossover data. We apply this method to 38 cycles of geophysical data records (GDR) data, computing preliminary global estimates of the four principal tidal constituents, M(sub 2), S(sub 2), K(sub 1) and O(sub 1). The inverse solution yields tidal fields which are simultaneously smoother, and in better agreement with altimetric and ground truth data, than previously proposed tidal models. Relative to the 'default' tidal corrections provided with the TOPEX/POSEIDON GDR, the inverse solution reduces crossover difference variances significantly (approximately 20-30%), even though only a small number of free parameters (approximately equal to 1000) are actually fit to the crossover data.
Egbert, Gary D.↗
Ozone Profiles in the Baltimore-Washington Region (2006-2011): Satellite Comparisons and DISCOVER-AQ Observations
Much progress has been made in creating satellite products for tracking the pollutants ozone and NO2 in the troposphere. Yet, in mid-latitude regions where meteorological interactions with pollutants are complex, accuracy can be difficult to achieve, largely due to persistent layering of some constituents. We characterize the layering of ozone soundings and related species measured from aircraft over two ground sites in suburban Washington, DC (Beltsville, MD, 39.05N; 76.9W) and Baltimore (Edgewood, MD, 39.4N; 76.3W) during the July 2011 DISCOVER-AQ (Deriving Information on Surface Conditions from Column and Vertically Resolved Observations Relevant to Air Quality) experiment. First, we compare column-ozone amounts from the Beltsville and Edgewood sondes with data from overpassing satellites. Second, processes influencing ozone profile structure are analyzed using Laminar Identification and tracers: sonde water vapor, aircraft CO and NOy. Third, Beltsville ozone profiles and meteorological influences in July 2011 are compared to those from the summers of 2006-2010. Sonde-satellite offsets in total ozone during July 2011 at Edgewood and Beltsville, compared to the Ozone Monitoring Instrument (OMI), were 3 percent mean absolute error, not statistically significant. The disagreement between an OMIMicrowave Limb Sounder-based tropospheric ozone column and the sonde averaged 10 percent at both sites, with the sonde usually greater than the satellite. Laminar Identification (LID), that distinguishes ozone segments influenced by convective and advective transport, reveals that on days when both stations launched ozonesondes, vertical mixing was stronger at Edgewood. Approximately half the lower free troposphere sonde profiles have very dry laminae, with coincident aircraft spirals displaying low CO (80-110 ppbv), suggesting stratospheric influence. Ozone budgets at Beltsville in July 2011, determined with LID, as well as standard meteorological indicators, resemble those of 4 of the previous 5 summers. The penetration of stratospheric air throughout the troposphere appears to be typical for summer conditions in the Baltimore-Washington region.
satellite validation↗
Data Analysis & Statistical Methods for Command File Errors
No abstract available
Spacecraft Message File↗
Modeling the Proton Radiation Belt With Van Allen Probes Relativistic Electron-Proton Telescope Data
An empirical model of the proton radiation belt is constructed from data taken during 2013-2017 by the Relativistic Electron-Proton Telescopes on the Van Allen Probes satellites. The model intensity is a function of time, kinetic energy in the range 18-600 megaelectronvolts, equatorial pitch angle, and L shell of proton guiding centers. Data are selected, on the basis of energy deposits in each of the nine silicon detectors, to reduce background caused by hard proton energy spectra at low L. Instrument response functions are computed by Monte Carlo integration, using simulated proton paths through a simplified structural model, to account for energy loss in shielding material for protons outside the nominal field of view. Overlap of energy channels, their wide angular response, and changing satellite orientation require the model dependencies on all three independent variables be determined simultaneously. This is done by least squares minimization with a customized steepest descent algorithm. Model uncertainty accounts for statistical data error and systematic error in the simulated instrument response. A proton energy spectrum is also computed from data taken during the 8 January 2014 solar event, to illustrate methods for the simpler case of an isotropic and homogeneous model distribution. Radiation belt and solar proton results are compared to intensities computed with a simplified, on-axis response that can provide a good approximation under limited circumstances.
Selesnick, R. S.↗
Mind the Gap: Addressing Data Gaps and Assessing Noise Mismodeling in LISA
Due to the sheer complexity of the Laser Interferometer Space Antenna (LISA) space mission, data gaps arising from instrumental irregularities and/or scheduled maintenance are unavoidable. Focusing on merger-dominated massive black hole binary signals, we test the appropriateness of the Whittle-likelihood on gapped data in a variety of cases. From first principles, we derive the likelihood valid for gapped data in both the time and frequency domains. Cheap-to-evaluate proxies to p-p plots are derived based on a Fisher-based formalism, and verified through Bayesian techniques. Our tools allow to predict the altered variance in the parameter estimates that arises from noise mismodeling, as well as the information loss represented by the broadening of the posteriors. The result of noise mismodeling with gaps is sensitive to the characteristics of the noise model, with strong low-frequency (red) noise and strong high-frequency (blue) noise giving statistically significant fluctuations in recovered parameters. We demonstrate that the introduction of a tapering window reduces statistical inconsistency errors, at the cost of less precise parameter estimates. We also show that the assumption of independence between inter-gap segments appears to be a fair approximation even if the data set is inherently coherent. However, if one instead assumes fictitious correlations in the data stream, when the data segments are actually independent, then the resultant parameter recoveries could be inconsistent with the true parameters. The theoretical and numerical practices that are presented in this work could readily be incorporated into global-fit pipelines operating on gapped data.
LISA↗