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Results for “variance estimation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Precision in the evaluation of Landsat autocorrelation - The terrain effect

The autocorrelation present in Landsat data can be described by a two-parameter model. Presence of this autocorrelation seriously inflates estimates of the variance of a set of pixels. The degree of inflation is always serious but varies markedly according to the values of the parameters phi and Theta. Thus corrections of the effects of the model require precise estimates of these parameters. Two hypotheses are proposed to explain the variation of phi with location. Several lines of evidence are presented which support the idea that phi is induced directly by the autocorrelation structure of the terrain being sensed. It is suggested that use of this relation will allow economical estimates of phi for any scene of interest.

Craig, R. G.↗
NASA NTRS1972

Noncommuting observables in quantum detection and estimation theory

Basing decisions and estimates on simultaneous approximate measurements of noncommuting observables in a quantum receiver is shown to be equivalent to measuring commuting projection operators on a larger Hilbert space than that of the receiver itself. The quantum-mechanical Cramer-Rao inequalities derived from right logarithmic derivatives and symmetrized logarithmic derivatives of the density operator are compared, and it is shown that the latter give superior lower bounds on the error variances of individual unbiased estimates of arrival time and carrier frequency of a coherent signal. For a suitably weighted sum of the error variances of simultaneous estimates of these, the former yield the superior lower bound under some conditions.

Helstrom, C. W.↗
NASA NTRS1974

Noncommuting observables in quantum detection and estimation theory

Basing decisions and estimates on simultaneous approximate measurements of noncommuting observables in a quantum receiver is shown to be equivalent to measuring commuting projection operators on a large Hilbert space than that of the receiver itself. The quantum-mechanical Cramer-Rao inequalities derived from right logarithmic derivatives and symmetrized logarithmic derivatives of the density operator are compared, and it is shown that the latter give superior lower bounds on the error variances of individual unbiased estimates of arrival time and carrier frequency of a coherent signal. For a suitably weighted sum of the error variances of simultaneous estimates of these, the former yield the superior lower bound under some conditions.

Helstrom, C. W.↗
DOE OSTI2018

Optimally configuring a measurement system to detect diversions from a nuclear fuel cycle

The civilian nuclear fuel cycle is an industrial process that produces electrical power from the nuclear fission of uranium. Using a measurement system to accurately account for nuclear material, such as uranium, in a fuel cycle is important because of the possible loss or diversion of this potentially dangerous material. A measurement system is defined by a set of measurement methods, or “devices,” used to account for material flows and inventory values at specific locations in the fuel cycle. Here, we develop a simulation-optimization algorithm and an integer-programming model to find the best, or near-best, resource-limited measurement system with a high degree of confidence. The simulation-optimization algorithm minimizes a weighted sum of false positive and false negative diversion-detection probabilities while accounting for material quantities and measurement errors across a finite, discrete time horizon in hypothetical non-diversion and diversion contexts. In each time period, the estimated cumulative material unaccounted for is compared to a fixed or an optimized threshold value to assess if a “significant amount of material” is lost from a measurement system. The integer-programming model minimizes the population variance of the estimated material loss, i.e., material unaccounted for, in a measurement system. We analyze three potential problems in nuclear fuel cycle measurement systems: (i) given location-dependent device precisions, find the configuration of n devices at n locations ( n = 3) that gives the lowest corresponding objective values using the simulation-optimization algorithm and integer-programming model, (ii) find the location at which improving device precision reduces objective values the most using the simulation-optimization algorithm, and determine the effect of measurement frequency on measurement system configurations and objective values using the simulation-optimization algorithm. We obtain comparable results for each problem at least an order of magnitude faster than existing methods do. Using an optimized, rather than fixed, detection threshold in the simulation-optimization algorithm reduces the weighted sum of false positive and false negative probabilities.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2015

Variance reduction through robust design of boundary conditions for stochastic hyperbolic systems of equations

We consider a hyperbolic system with uncertainty in the boundary and initial data. Our aim is to show that different boundary conditions give different convergence rates of the variance of the solution. This means that we can with the same knowledge of data get a more or less accurate description of the uncertainty in the solution. A variety of boundary conditions are compared and both analytical and numerical estimates of the variance of the solution are presented. As an application, we study the effect of this technique on Maxwell's equations as well as on a subsonic outflow boundary for the Euler equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1992

Phase noise in pulsed Doppler lidar and limitations on achievable single-shot velocity accuracy

The smaller sampling volumes afforded by Doppler lidars compared to radars allows for spatial resolutions at and below some sheer and turbulence wind structure scale sizes. This has brought new emphasis on achieving the optimum product of wind velocity and range resolutions. Several recent studies have considered the effects of amplitude noise, reduction algorithms, and possible hardware related signal artifacts on obtainable velocity accuracy. We discuss here the limitation on this accuracy resulting from the incoherent nature and finite temporal extent of backscatter from aerosols. For a lidar return from a hard (or slab) target, the phase of the intermediate frequency (IF) signal is random and the total return energy fluctuates from shot to shot due to speckle; however, the offset from the transmitted frequency is determinable with an accuracy subject only to instrumental effects and the signal to noise ratio (SNR), the noise being determined by the LO power in the shot noise limited regime. This is not the case for a return from a media extending over a range on the order of or greater than the spatial extent of the transmitted pulse, such as from atmospheric aerosols. In this case, the phase of the IF signal will exhibit a temporal random walk like behavior. It will be uncorrelated over times greater than the pulse duration as the transmitted pulse samples non-overlapping volumes of scattering centers. Frequency analysis of the IF signal in a window similar to the transmitted pulse envelope will therefore show shot-to-shot frequency deviations on the order of the inverse pulse duration reflecting the random phase rate variations. Like speckle, these deviations arise from the incoherent nature of the scattering process and diminish if the IF signal is averaged over times greater than a single range resolution cell (here the pulse duration). Apart from limiting the high SNR performance of a Doppler lidar, this shot-to-shot variance in velocity estimates has a practical impact on lidar design parameters. In high SNR operation, for example, a lidar's efficiency in obtaining mean wind measurements is determined by its repetition rate and not pulse energy or average power. In addition, this variance puts a practical limit on the shot-to-shot hard target performance required of a lidar.

Mcnicholl, P.↗
NASA NTRS1994

A comparison of GPS broadcast and DMA precise ephemerides

We compare the broadcast ephemerides from Global Positioning Satellites (GPS) to the postprocessed ephemerides from the Defense Mapping Agency (DMA). We find significant energy in the spectrum of the residuals at 1 cycle/day and higher multiples. We estimate the time variance of the residuals and show that the short term residuals, from 15 min, exhibit power law processes with greater low frequency perturbations than white phase modulation. We discuss the significance of these results for the performance of the GPS Kalman filter which estimates the broadcast orbits.

Weiss, Marc A.↗
DOE OSTI2021

Rare Events via Cross-Entropy Population Monte Carlo

Rare events are events that happen with very low frequency. Estimating rare event probabilities using Monte Carlo techniques is computationally expensive, often to the point of intractability, and special methods are required. Importance sampling (IS) is a well known technique that uses a proposal distribution in place of a target distribution to lower the variance of the estimator. Key to the success of IS methods is the choice of a proposal distribution, or the parameters governing the distribution. Adaptive importance sampling improves the parameters of a family or population of proposal distributions iteratively through trials. We present a novel cross-entropy population Monte Carlo algorithm, which adapts the parameters of proposals through the cross-entropy method. The proposed method stands apart from previous work in that we are not optimizing a mixture distribution. Instead, we leverage deterministic mixture weights and optimize the distributions individually through a reinterpretation of the typical derivation of the cross-entropy method. Demonstrations on rare event examples show that the algorithm can outperform existing resampling based population Monte Carlo methods, especially for higher-dimensional problems. Finally, we also demonstrate efficacy on a conjunction analysis problem.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1972

Adaptive filtering with correlated state noise

An adaptive filter which uses a minimum variance criteria to estimate state noise covariance is presented. It is not necessary to assume white state noise in order to implement the filter. Simulation results are given which demonstrate that the filter tracks a satellite in the presence of modeling errors better than a conventional minimum variance filter with state noise. It is also shown that the propagated convariance matrix of the filter is an accurate indicator of the filter's performance.

Argentiero, P.↗
NASA NTRS1999

Multitaper Spectral Analysis and Wavelet Denoising Applied to Helioseismic Data

Estimates of solar normal mode frequencies from helioseismic observations can be improved by using Multitaper Spectral Analysis (MTSA) to estimate spectra from the time series, then using wavelet denoising of the log spectra. MTSA leads to a power spectrum estimate with reduced variance and better leakage properties than the conventional periodogram. Under the assumption of stationarity and mild regularity conditions, the log multitaper spectrum has a statistical distribution that is approximately Gaussian, so wavelet denoising is asymptotically an optimal method to reduce the noise in the estimated spectra. We find that a single m-upsilon spectrum benefits greatly from MTSA followed by wavelet denoising, and that wavelet denoising by itself can be used to improve m-averaged spectra. We compare estimates using two different 5-taper estimates (Stepian and sine tapers) and the periodogram estimate, for GONG time series at selected angular degrees l. We compare those three spectra with and without wavelet-denoising, both visually, and in terms of the mode parameters estimated from the pre-processed spectra using the GONG peak-fitting algorithm. The two multitaper estimates give equivalent results. The number of modes fitted well by the GONG algorithm is 20% to 60% larger (depending on l and the temporal frequency) when applied to the multitaper estimates than when applied to the periodogram. The estimated mode parameters (frequency, amplitude and width) are comparable for the three power spectrum estimates, except for modes with very small mode widths (a few frequency bins), where the multitaper spectra broadened the modest compared with the periodogram. We tested the influence of the number of tapers used and found that narrow modes at low n values are broadened to the extent that they can no longer be fit if the number of tapers is too large. For helioseismic time series of this length and temporal resolution, the optimal number of tapers is less than 10.

Komm, R. W.↗
NASA NTRS1982

A structure function representation theorem with applications to frequency stability estimation

Random processes with stationary nth differences serve as models for oscillator phase noise. A theorem which obtains the structure function (covariance of the nth differences) of such a process in terms of the differences of a single function of one time variable is proven. In turn, this function can easily be obtained from the spectral density of the process. The theorem is used for computing the variance of two estimators of frequency stability.

Greenhall, C. A.↗
DOE OSTI2017

Analyzing the cosmic variance limit of remote dipole measurements of the cosmic microwave background using the large-scale kinetic Sunyaev Zel'dovich effect

Due to cosmic variance we cannot learn any more about large-scale inhomogeneities from the primary cosmic microwave background (CMB) alone. More information on large scales is essential for resolving large angular scale anomalies in the CMB. Here we consider cross correlating the large-scale kinetic Sunyaev Zel'dovich (kSZ) effect and probes of large-scale structure, a technique known as kSZ tomography. The statistically anisotropic component of the cross correlation encodes the CMB dipole as seen by free electrons throughout the observable Universe, providing information about long wavelength inhomogeneities. We compute the large angular scale power asymmetry, constructing the appropriate transfer functions, and estimate the cosmic variance limited signal to noise for a variety of redshift bin configurations. The signal to noise is significant over a large range of power multipoles and numbers of bins. We present a simple mode counting argument indicating that kSZ tomography can be used to estimate more modes than the primary CMB on comparable scales. A basic forecast indicates that a first detection could be made with next-generation CMB experiments and galaxy surveys. This paper motivates a more systematic investigation of how close to the cosmic variance limit it will be possible to get with future observations.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1983

A structure function representation theorem with applications to frequency stability estimation

Random processes with stationary nth differences serve as models for oscillator phase noise. The theorem proved here allows one to obtain the structure function (covariances of the nth differences) of such a process in terms of the differences of a single function of one time variable. In turn, this function can easily be obtained from the spectral density of the process. The theorem is used for computing the variance of two estimators of frequency stability.

Greenhall, C. A.↗
DOE OSTI2018

Optimizing Nuclear Material Accounting and Measurement Systems

The ability to create nuclear weapons from 235 U and 239 Pu makes it imperative to closely account for these materials as they progress through a nuclear fuel cycle. Improved measurement systems provide more accurate estimates of material quantities and material unaccounted for (MUF). This work provides examples of how two safeguards computational toolboxes can optimize and analyze hypothetical nuclear fuel cycle scenarios. The NUclear Measurement System Optimization (NUMSO) toolbox uses operations research techniques to find optimal solutions to safeguards measurement problems based on minimizing the variance of the estimated MUF. The SafeGuards Analysis (SGA) toolbox employs Monte Carlo techniques to analyze a given configuration of measurement methods and material flows to determine the probabilities of Type I (false detection) and Type II (missed detection) errors. Applying these toolboxes to a realistic fuel cycle scenario demonstrates the capability of NUMSO and SGA to address nuclear safeguards problems. Working in tandem, both toolboxes are able to determine how to quickly improve upon an existing safeguards measurement system and to calculate the resulting improvement in the error probabilities of the system. This information shows engineers not only how to develop new measurement systems but also how to improve existing systems in the most efficient manner.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Improved multifidelity Monte Carlo estimators based on normalizing flows and dimensionality reduction techniques

Here, we study the problem of multifidelity uncertainty propagation for computationally expensive models. In particular, we consider the general setting where the high-fidelity and low-fidelity models have a dissimilar parameterization both in terms of number of random inputs and their probability distributions, which can be either known in closed form or provided through samples. We derive novel multifidelity Monte Carlo estimators which rely on a shared subspace between the high-fidelity and low-fidelity models where the parameters follow the same probability distribution, i.e., a standard Gaussian. We build the shared space employing normalizing flows to map different probability distributions into a common one, together with linear and nonlinear dimensionality reduction techniques, active subspaces and autoencoders, respectively, which capture the subspaces where the models vary the most. We then compose the existing low-fidelity model with these transformations and construct modified models with an increased correlation with the high-fidelity model, which therefore yield multifidelity estimators with reduced variance. A series of numerical experiments illustrate the properties and advantages of our approaches.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2020

Multi Model Monte Carlo with Python (MXMCPy)

Multi Model Monte Carlo with Python (\mxmc {}) is a software package developed as a general capability for computing the statistics of outputs from an expensive, high-fidelity model by leveraging faster, low-fidelity models for speedup. Motivated by uncertainty propagation problems where classical Monte Carlo (MC) simulation is computationally intractable, various multi-model MC approaches have recently emerged that yield unbiased estimators with significantly reduced variance relative to MC for the same cost. These existing methods include multi-level Monte Carlo (MLMC), multi-fidelity Monte Carlo (MFMC), and approximate control variates (ACV). Given a fixed computational budget and a collection of models with varying cost/accuracy, each method seeks a sample allocation strategy across the models that results in an estimator with optimal variance reduction. \mxmc {} is a versatile tool that enables convenient access to many existing multi-model MC approaches within one modular and extensible package. With \mxmc {}, users can easily compare existing methods to determine the best choice for their particular problem, while developers have a basis for implementing and sharing new variance reduction approaches. This report introduces the \mxmc {} software, providing a summary of the problem-solving workflow for users as well as a brief overview of the code layout for developers.

Geoffrey F Bomarito↗
DOE OSTI2016

Global sensitivity analysis in stochastic simulators of uncertain reaction networks

Stochastic models of chemical systems are often subjected to uncertainties in kinetic parameters in addition to the inherent random nature of their dynamics. Uncertainty quantification in such systems is generally achieved by means of sensitivity analyses in which one characterizes the variability with the uncertain kinetic parameters of the first statistical moments of model predictions. In this work, we propose an original global sensitivity analysis method where the parametric and inherent variability sources are both treated through Sobol’s decomposition of the variance into contributions from arbitrary subset of uncertain parameters and stochastic reaction channels. The conceptual development only assumes that the inherent and parametric sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. Here, a sampling algorithm is proposed to perform the global sensitivity analysis, and to estimate the partial variances and sensitivity indices characterizing the importance of the various sources of variability and their interactions. The birth-death and Schlögl models are used to illustrate both the implementation of the algorithm and the richness of the proposed analysis method. The output of the proposed sensitivity analysis is also contrasted with a local derivative-based sensitivity analysis method classically used for this type of systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Transmission estimation at the quantum Cramér-Rao bound with macroscopic quantum light

The field of quantum metrology seeks to apply quantum techniques and/or resources to classical sensing approaches with the goal of enhancing the precision in the estimation of a parameter beyond what can be achieved with classical resources. Theoretically, the fundamental minimum uncertainty in the estimation of a parameter for a given probing state is bounded by the quantum Cramér-Rao bound. From a practical perspective, it is necessary to find physical measurements that can saturate this fundamental limit and to show experimentally that it is possible to perform measurements with the required precision to do so. Here we perform experiments that saturate the quantum Cramér-Rao bound for transmission estimation over a wide range of transmissions when probing the system under study with a continuous wave bright two-mode squeezed state. To properly take into account the imperfections in the generation of the quantum state, we extend our previous theoretical results to incorporate the measured properties of the generated quantum state. For our largest transmission level of 84%, we show a 62% reduction over the optimal classical protocol in the variance in transmission estimation when probing with a bright two-mode squeezed state with -8 dB of intensity-difference squeezing. Given that transmission estimation is an integral part of many sensing protocols, such as plasmonic sensing, spectroscopy, calibration of the quantum efficiency of detectors, etc., the results presented promise to have a significant impact on a number of applications in various fields of research.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗