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Higher order statistics, especially 2nd order statistics, have been used to study ocean processes for many years in the past, and occupy an appreciable part of the research literature on physical oceanography. They in turn form part of a much larger field of study in statistical fluid mechanics.
Microwave radiometers use radio spectrum dedicated to sensing the environment. As wireless communications and other active services proliferate, this allocated spectrum is nearly being crowded out. The potential result is corrupted satellite measurements of the weather, the climate, and the environment. We present an analog RFI detector for microwave radiometers intended to mitigate the above risks. The double detector (DD) for RFI detection includes a square-law diode detector with short integration time for measuring the total power out of the radiometer, followed by a second diode detector which acts as a higher-order statistical fourth-moment detector. See Figure 1 for block diagram of the system. This novel design which uses purely analog components at radio andlor intermediate frequencies allows the system to easily augment conventional radiometer architectures used in both airborne and space borne instruments. An equivalent high-speed digital design would add an impractical level of cost and complexity to radiometer designs using today's technology.
National Aeronautics and Space Administration (NASA)'s future communication architecture is evaluating cognitive technologies and increased system intelligence. These technologies are expected to reduce the operational complexity of the network, increase science data return, and reduce interference to self and others. In order to increase situational awareness, signal classification algorithms could be applied to identify users and distinguish sources of interference. A significant amount of previous work has been done in the area of automatic signal classification for military and commercial applications. As a preliminary step, we seek to develop a system with the ability to discern signals typically encountered in satellite communication. Proposed is an automatic modulation classifier which utilizes higher order statistics (cumulants) and an estimate of the signal-to-noise ratio. These features are extracted from baseband symbols and then processed by a neural network for classification. The modulation types considered are phase-shift keying (PSK), amplitude and phase-shift keying (APSK),and quadrature amplitude modulation (QAM). Physical layer properties specific to the Digital Video Broadcasting - Satellite- Second Generation (DVB-S2) standard, such as pilots and variable ring ratios, are also considered. This paper will provide simulation results of a candidate modulation classifier, and performance will be evaluated over a range of signal-to-noise ratios, frequency offsets, and nonlinear amplifier distortions.
National Aeronautics and Space Administration (NASA)'s future communication architecture is evaluating cognitive technologies and increased system intelligence. These technologies are expected to reduce the operational complexity of the network, increase science data return, and reduce interference to self and others. In order to increase situational awareness, signal classification algorithms could be applied to identify users and distinguish sources of interference. A significant amount of previous work has been done in the area of automatic signal classification for military and commercial applications. As a preliminary step, we seek to develop a system with the ability to discern signals typically encountered in satellite communication. Proposed is an automatic modulation classifier which utilizes higher order statistics (cumulants) and an estimate of the signal-to-noise ratio. These features are extracted from baseband symbols and then processed by a neural network for classification. The modulation types considered are phase-shift keying (PSK), amplitude and phase-shift keying (APSK),and quadrature amplitude modulation (QAM). Physical layer properties specific to the Digital Video Broadcasting - Satellite- Second Generation (DVB-S2) standard, such as pilots and variable ring ratios, are also considered. This paper will provide simulation results of a candidate modulation classifier, and performance will be evaluated over a range of signal-to-noise ratios, frequency offsets, and nonlinear amplifier distortions.
We present several different methods for generating realistic predictive covariance, including Monte-Carlo simulations and more direct linear methods which require the addition of process noise. The Monte-Carlo simulation starts with an epoch uncertainty sample basis and propagates each trial to a time of interest in the future. The variance-covariance of the state elements as well as other higher order sample statistics can be readily computed from the propagated sample. While this method preserves the nonlinear effects on the propagated uncertainty, it is computationally intensive as a statistically significant sample size must be considered in the propagation process. Moreover, if the epoch covariance is optimistic, this can result in an underestimation of the prediction error. Another method is to propagate a state sensitivity matrix simultaneously with the satellite state, which allows the epoch covariances to be propagated forward in a linear fashion. This method does not preserve the non-linearity of the satellite state uncertainty but is much less computationally intensive. The propagated state covariance is the scaled to represent the realistic level of GPM state uncertainty via a "e-tuning process." The tuning process generates an inflation factor based on the observed error statistics of the predictive satellite trajectories when compared to the definitive ones. Difference tuning strategies are considered and compared via Goodness-of-Fit method testing for the Gaussian properties of the scaled covariance.
Simulated aeroelastic responses of a nonlinear pitch and plunge apparatus are analyzed using various statistical signal processing techniques including higher-order spectral methods. A MATLAB version of the Nonlinear Aeroelastic Testbed Apparatus (NATA) at the Texas A&M University is used to generate various aeroelastic response data including limit cycle oscillations (LCO). Traditional and higher-order spectral (HOS) methods are applied to the simulated aeroelastic responses. Higher-order spectral methods are used to identify critical signatures that indicate the transition from linear to nonlinear (LCO) aeroelastic behavior.
We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the onset of hierarchical clustering. This success is found at a considerable higher non-linearity than is usual for perturbation theory. Whether a truncation of the initial power-spectrum in hierarchical models retains this improvement will be analyzed in a forthcoming work.
We simulate the scientific performance of the Nancy Grace Roman Space Telescope High Latitude Survey (HLS) on dark energy and modified gravity. The 1.6-yr HLS Reference survey is currently envisioned to image 2000 deg2 in multiple bands to a depthof∼26.5 in Y, J, H and to cover the same area with slit-less spectroscopy beyond z=3. The combination of deep, multiband photometry and deep spectroscopy will allow scientists to measure the growth and geometry of the Universe through a variety of cosmological probes (e.g. weak lensing, galaxy clusters, galaxy clustering, BAO, Type Ia supernova) and, equally, it will allow an exquisite control of observational and astrophysical systematic effects. In this paper, we explore multiprobe strategies that can be implemented, given the telescope’s instrument capabilities. We model cosmological probes individually and jointly and account for correlated systematics and statistical uncertainties due to the higher order moments of the density field. We explore different levels of observational systematics for the HLS survey (photo-z and shear calibration) and ultimately run a joint likelihood analysis in N-dim parameter space. We find that the HLS reference survey alone can achieve a standard dark energy FoM of>300 when including all probes. This assumes no information from external data sets, we assume a flat universe however, and includes realistic assumptions for systematics. Our study of the HLS reference survey should be seen as part of a future community-driven effort to simulate and optimize the science return of the Roman Space Telescope.
The NASA Moderate Resolution Imaging Spectroradiometer (MODIS), launched onboard the Terra and Aqua spacecrafts, began Earth observations on February 24, 2000 and June 24,2002, respectively. Among the algorithms developed and applied to this sensor, a suite of cloud products includes cloud masking/detection, cloud-top properties (temperature, pressure), and optical properties (optical thickness, effective particle radius, water path, and thermodynamic phase). All cloud algorithms underwent numerous changes and enhancements between for the latest Collection 5 production version; this process continues with the current Collection 6 development. We will show example MODIS Collection 5 cloud climatologies derived from global spatial . and temporal aggregations provided in the archived gridded Level-3 MODIS atmosphere team product (product names MOD08 and MYD08 for MODIS Terra and Aqua, respectively). Data sets in this Level-3 product include scalar statistics as well as 1- and 2-D histograms of many cloud properties, allowing for higher order information and correlation studies. In addition to these statistics, we will show trends and statistical significance in annual and seasonal means for a variety of the MODIS cloud properties, as well as the time required for detection given assumed trends. To assist in climate model evaluation, we have developed a MODIS cloud simulator with an accompanying netCDF file containing subsetted monthly Level-3 statistical data sets that correspond to the simulator output. Correlations of cloud properties with ENSO offer the potential to evaluate model cloud sensitivity; initial results will be discussed.
We use a nonstationary generalization of the higher-order structure function technique to investigate statistical properties of the magnetic field fluctuations recorded by MESSENGER spacecraft during its first flyby (01/14/2008) through the near-Mercury space environment, with the emphasis on key boundary regions participating in the solar wind - magnetosphere interaction. Our analysis shows, for the first time, that kinetic-scale fluctuations play a significant role in the Mercury's magnetosphere up to the largest resolvable timescale (approx.20 s) imposed by the signal nonstationariry, suggesting that turbulence at this plane I is largely controlled by finite Larmor radius effects. In particular, we report the presence of a highly turbulent and extended foreshock system filled with packets of ULF oscillations, broad-band intermittent fluctuations in the magnetosheath, ion-kinetic turbulence in the central plasma sheet of Mercury's magnetotail, and kinetic-scale fluctuations in the inner current sheet encountered at the outbound (dawn-side) magnetopause. Overall, our measurements indicate that the Hermean magnetosphere, as well as the surrounding region, are strongly affected by non-MHD effects introduced by finite sizes of cyclotron orbits of the constituting ion species. Physical mechanisms of these effects and their potentially critical impact on the structure and dynamics of Mercury's magnetic field remain to be understood.
The parameterization of the stably stratified atmospheric boundary layer is a difficult issue, which has a large impact on the medium-range weather forecasts and on climate integrations. A non-strongly stratified arctic case is simulated by nineteen single-column turbulence schemes. The statistics from the Large-eddy simulation (LES) intercomparison made for the same case by eight different models are used as a guiding reference. The single-column parameterizations include research schemes and operational schemes from major forecast and climate research centres. First order schemes, a large number of turbulence kinetic energy closures, and other proposals have submitted results. There is a large spread in the results; in general, the operational schemes mix more efficiently than the research ones, and the TKE and other higher order closures give results closer to the LES statistics. The sensitivities of the schemes to the parameters of their turbulence closures are partially explored.
We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of scales. The Lagrangian theory of gravitational instability of Friedmann-Lemaitre cosmogonies is compared with numerical simulations. We study the dynamics of hierarchical models as a second step. In the first step we analyzed the performance of the Lagrangian schemes for pancake models, the difference being that in the latter models the initial power spectrum is truncated. This work probed the quasi-linear and weakly non-linear regimes. We here explore whether the results found for pancake models carry over to hierarchical models which are evolved deeply into the non-linear regime. We smooth the initial data by using a variety of filter types and filter scales in order to determine the optimal performance of the analytical models, as has been done for the 'Zel'dovich-approximation' - hereafter TZA - in previous work. We find that for spectra with negative power-index the second-order scheme performs considerably better than TZA in terms of statistics which probe the dynamics, and slightly better in terms of low-order statistics like the power-spectrum. However, in contrast to the results found for pancake models, where the higher-order schemes get worse than TZA at late non-linear stages and on small scales, we here find that the second-order model is as robust as TZA, retaining the improvement at later stages and on smaller scales. In view of these results we expect that the second-order truncated Lagrangian model is especially useful for the modelling of standard dark matter models such as Hot-, Cold-, and Mixed-Dark-Matter.
The current DSN frame synchronization procedure is based on monitoring the decoded bit stream for the appearance of a sync marker sequence that is transmitted once every data frame. The possibility of obtaining frame synchronization by processing the raw received channel symbols rather than the decoded bits is explored. Performance results are derived for three channel symbol sync methods, and these are compared with results for decoded bit sync methods reported elsewhere. It is shown that each class of methods has advantages or disadvantages under different assumptions on the frame length, the global acquisition strategy, and the desired measure of acquisition timeliness. It is shown that the sync statistics based on decoded bits are superior to the statistics based on channel symbols, if the desired operating region utilizes a probability of miss many orders of magnitude higher than the probability of false alarm. This operating point is applicable for very large frame lengths and minimal frame-to-frame verification strategy. On the other hand, the statistics based on channel symbols are superior if the desired operating point has a miss probability only a few orders of magnitude greater than the false alarm probability. This happens for small frames or when frame-to-frame verifications are required.
It has been shown by Brown and Emslie (1988) that any optically thin thermal bremsstrahlung source must emit an energy spectrum L(epsilon)(keV/s per keV) which has the property that higher derivatives alternate in sign. In this short note, this test is applied to the 'superhot' component discussed by Lin et al. (1981) in order to determine whether a strictly thermal interpretation of this component is valid. All statistically significant higher derivatives do indeed have the correct sign; this strengthens the identification of this component as due to a thermal source.
Through a combination of small scale statistics and flow visualization it is shown that the small scales of a numerically generated turbulent flow are strongly aligned around vortex tubes. Movies of the time developing flow will be used to illustrate the nature of these structures. An inertial subrange is found with a Kolmogorov constant, alpha, equal to 2.45. This is consistent with simulated and measured values for the skewness, but disagrees with experimental values for the Kolmogorov constant, which usually range between 1.4 to 1.7.
The orbital debris environment of objects larger than 1 sq met. in low Earth orbit (LEO) is fairly well defined. Objects of this size and altitude are tracked by NORAD with sufficient accuracy that collisions can be avoided by maneuvering a spacecraft away from regions of close approach. However for sizes smaller and at the higher geosynchrnous altitudes, the environment is not so well defined, and must be approached statistically. In order to determine if a significant number of these particles exist, or can be realistically produced, to cause a problem, a combination of modeling and data gathering is required.
A direct numerical simulation of high speed reacting and non-reacting flows for H2-air systems is presented. The calculations are made for a convective Mach number of 0.38 with hyperbolic tangent initial profile and finite rate chemical reactions. A higher-order numerical method is used in time accurate mode to time advance the solution to a statistical steady state. About 600 time slices of all the variables are then stored for statistical analysis. It is shown that most of the problems of high-speed combustion with air are characterized by relatively weak heat release. The present study shows that: (1) the convective speed is reduced by heat release by about 10 percent at this convective Mach number M(sub c) = 0.38; (2) the variation of the mean and rms fluctuation of temperature can be explained on the basis of temperature fluctuation between the flame temperature and the ambient; (3) the growth rate with heat release is reduced by 7 percent; and (4) the entrainment is reduced by 25 percent with heat release. These differences are small in comparison with incompressible flow dynamics, and are argued to be due to the reduced importance of heat release in comparison with the large enthalpy gradients resulting from the large-scale vortex dynamics. It is finally suggested that the problems of reduced mixing in high-speed flows are not severely complicated by heat release.
We report on the first 10 identifications of sources serendipitously detected by the Nuclear Spectroscopic Telescope Array (NuSTAR) to provide the first sensitive census of the cosmic X-ray background source population at approximately greater than 10 keV. We find that these NuSTAR-detected sources are approximately 100 times fainter than those previously detected at approximately greater than 10 keV and have a broad range in redshift and luminosity (z = 0.020-2.923 and L(sub 10-40 keV) approximately equals 4 × 10(exp 41) - 5 × 10(exp 45) erg per second; the median redshift and luminosity are z approximately equal to 0.7 and L(sub 10-40 keV) approximately equal to 3 × 10(exp 44) erg per second, respectively. We characterize these sources on the basis of broad-band approximately equal to 0.5 - 32 keV spectroscopy, optical spectroscopy, and broad-band ultraviolet-to-mid-infrared spectral energy distribution analyses. We find that the dominant source population is quasars with L(sub 10-40 keV) greater than 10(exp 44) erg per second, of which approximately 50% are obscured with N(sub H) approximately greater than 10(exp 22) per square centimeters. However, none of the 10 NuSTAR sources are Compton thick (N(sub H) approximately greater than 10(exp 24) per square centimeters) and we place a 90% confidence upper limit on the fraction of Compton-thick quasars (L(sub 10-40 keV) greater than 10(exp 44) erg per second) selected at approximately greater than 10 keV of approximately less than 33% over the redshift range z = 0.5 - 1.1. We jointly fitted the rest-frame approximately equal to 10-40 keV data for all of the non-beamed sources with L(sub 10-40 keV) greater than 10(exp 43) erg per second to constrain the average strength of reflection; we find R less than 1.4 for gamma = 1.8, broadly consistent with that found for local active galactic nuclei (AGNs) observed at approximately greater than 10 keV. We also constrain the host-galaxy masses and find a median stellar mass of approximately 10(exp 11) solar mass, a factor approximately 5 times higher than the median stellar mass of nearby high-energy selected AGNs, which may be at least partially driven by the order of magnitude higher X-ray luminosities of the NuSTAR sources. Within the low source-statistic limitations of our study, our results suggest that the overall properties of the NuSTAR sources are broadly similar to those of nearby high-energy selected AGNs but scaled up in luminosity and mass.