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At least 775 records · Page 43

The gust-front detection and wind-shift algorithms for the Terminal Doppler Weather Radar system

The Federal Aviation Administration's (FAA) Terminal Doppler Weather Radar (TDWR) system was primarily designed to address the operational needs of pilots in the avoidance of low-altitude wind shears upon takeoff and landing at airports. One of the primary methods of wind-shear detection for the TDWR system is the gust-front detection algorithm. The algorithm is designed to detect gust fronts that produce a wind-shear hazard and/or sustained wind shifts. It serves the hazard warning function by providing an estimate of the wind-speed gain for aircraft penetrating the gust front. The gust-front detection and wind-shift algorithms together serve a planning function by providing forecasted gust-front locations and estimates of the horizontal wind vector behind the front, respectively. This information is used by air traffic managers to determine arrival and departure runway configurations and aircraft movements to minimize the impact of wind shifts on airport capacity. This paper describes the gust-front detection and wind-shift algorithms to be fielded in the initial TDWR systems. Results of a quantitative performance evaluation using Doppler radar data collected during TDWR operational demonstrations at the Denver, Kansas City, and Orlando airports are presented. The algorithms were found to be operationally useful by the FAA airport controllers and supervisors.

Hermes, Laurie G.↗

A model for estimating time-variant rainfall infiltration as a function of antecedent surface moisture and hydrologic soil type

Recent research indicates that the use of remote sensing techniques for the measurement of near surface soil moisture could be practical in the not too distant future. Other research shows that infiltration rates, especially for average or frequent rainfall events, are extremely sensitive to the proper definition and consideration of the role of the soil moisture at the beginning of the rainfall. Thus, it is important that an easy to use, but theoretically sound, rainfall infiltration model be available if the anticipated remotely sensed soil moisture data is to be optimally utilized for hydrologic simulation. A series of numerical experiments with the Richards' equation for an array of conditions anticipated in watershed hydrology were used to develop functional relationships that describe temporal infiltration rates as a function of soil type and initial moisture conditions.

Wilkening, H. A.↗

Least-squares sequential parameter and state estimation for large space structures

This paper presents the formulation of simultaneous state and parameter estimation problems for flexible structures in terms of least-squares minimization problems. The approach combines an on-line order determination algorithm, with least-squares algorithms for finding estimates of modal approximation functions, modal amplitudes, and modal parameters. The approach combines previous results on separable nonlinear least squares estimation with a regression analysis formulation of the state estimation problem. The technique makes use of sequential Householder transformations. This allows for sequential accumulation of matrices required during the identification process. The technique is used to identify the modal prameters of a flexible beam.

Thau, F. E.↗

Estimation of finite mixtures using the empirical characteristic function

A problem which occurs in analyzing LANDSAT scenes is the problem of separating the components of a finite mixture of several distinct probability distributions. A review of the literature indicates this is a problem which occurs in many disciplines, such as engineering, biology, physiology and economics. Many approaches to this problem have appeared in the literature; however, most are very restrictive in their assumptions or have met with only a limited degree of success when applied to realistic situations. A proceudre is investigated with combines the k-L procedure of (Feurverger and McDunnough, 1981) with the MAICE procedure of (Akaike, 1974). The feasibility of this approach is being investigated numerically via the development of a computer software package enabling a simulation study and comparison with other procedures.

Anderson, C.↗

Satellite Material Type and Phase Function Determination in Support of Orbital Debris Size Estimation

In performing debris surveys of deep-space orbital regions, the considerable volume of the area to be surveyed and the increased orbital altitude suggest optical telescopes as the most efficient survey instruments; but to proceed this way, methodologies for debris object size estimation using only optical tracking and photometric information are needed. Basic photometry theory indicates that size estimation should be possible if satellite albedo and shape are known. One method for estimating albedo is to try to determine the object's material type photometrically, as one can determine the albedos of common satellite materials in the laboratory. Examination of laboratory filter photometry (using Johnson BVRI filters) on a set of satellite material samples indicates that most material types can be separated at the 1-sigma level via B-R versus R-I color differences with a relatively small amount of required resampling, and objects that remain ambiguous can be resolved by B-R versus B-V color differences and solar radiation pressure differences. To estimate shape, a technique advanced by Hall et al. [1], based on phase-brightness density curves and not requiring any a priori knowledge of attitude, has been modified slightly to try to make it more resistant to the specular characteristics of different materials and to reduce the number of samples necessary to make robust shape determinations. Working from a gallery of idealized debris shapes, the modified technique identifies most shapes within this gallery correctly, also with a relatively small amount of resampling. These results are, of course, based on relatively small laboratory investigations and simulated data, and expanded laboratory experimentation and further investigation with in situ survey measurements will be required in order to assess their actual efficacy under survey conditions; but these techniques show sufficient promise to justify this next level of analysis.

Hejduk, M. D.↗

Model-based prognostics for batteries which estimates useful life and uses a probability density function

This invention develops a mathematical model to describe battery behavior during individual discharge cycles as well as over its cycle life. The basis for the form of the model has been linked to the internal processes of the battery and validated using experimental data. Effects of temperature and load current have also been incorporated into the model. Subsequently, the model has been used in a Particle Filtering framework to make predictions of remaining useful life for individual discharge cycles as well as for cycle life. The prediction performance was found to be satisfactory as measured by performance metrics customized for prognostics for a sample case. The work presented here provides initial steps towards a comprehensive health management solution for energy storage devices.

Saha, Bhaskar↗

The next generation Virgo Cluster Survey. IX. Estimating the efficiency of galaxy formation on the lowest-mass scales

The Next Generation Virgo Cluster Survey has recently determined the luminosity function of galaxies in the core of the Virgo cluster down to unprecedented magnitude and surface brightness limits. Comparing simulations of cluster formation to the derived central stellar mass function, we attempt to estimate the stellar-to-halo-mass ratio (SHMR) for dwarf galaxies, as it would have been before they fell into the cluster. This approach ignores several details and complications, e.g., the contribution of ongoing star formation to the present-day stellar mass of cluster members, and the effects of adiabatic contraction and/or violent feedback on the subhalo and cluster potentials. The final results are startlingly simple, however; we find that the trends in the SHMR determined previously for bright galaxies appear to extend down in a scale-invariant way to the faintest objects detected in the survey. These results extend measurements of the formation efficiency of field galaxies by two decades in halo mass or five decades in stellar mass, down to some of the least massive dwarf galaxies known, with stellar masses of ∼10{sup 5} M{sub ⊙}.

79 ASTRONOMY AND ASTROPHYSICS↗

New Developments in Quaternion Estimation from Vector Observations

This paper contains a critical comparison of estimators minimizing Wahba's loss function. Some new results are presented for the QUaternion ESTimator (QUEST) and EStimators of the Optimal Quaternion (ESOQ and ESOQ2) to avoid the computational burden of sequential rotations in these algorithms. None of these methods is as robust in principle as Davenport's q method or the Singular Value Decomposition (SVD) method, which are significantly slower. Robustness is only an issue for measurements with widely differing accuracies, so the fastest estimators, the modified ESOQ and ESOQ2, are well suited to sensors that track multiple stars with comparable accuracies. More robust forms of ESOQ and ESOQ2 are developed that are intermediate in speed.

Markley, F. Landis↗

Hybrid diversity method utilizing adaptive diversity function for recovering unknown aberrations in an optical system

A method of recovering unknown aberrations in an optical system includes collecting intensity data produced by the optical system, generating an initial estimate of a phase of the optical system, iteratively performing a phase retrieval on the intensity data to generate a phase estimate using an initial diversity function corresponding to the intensity data, generating a phase map from the phase retrieval phase estimate, decomposing the phase map to generate a decomposition vector, generating an updated diversity function by combining the initial diversity function with the decomposition vector, generating an updated estimate of the phase of the optical system by removing the initial diversity function from the phase map. The method may further include repeating the process beginning with iteratively performing a phase retrieval on the intensity data using the updated estimate of the phase of the optical system in place of the initial estimate of the phase of the optical system, and using the updated diversity function in place of the initial diversity function, until a predetermined convergence is achieved.

Dean, Bruce H.↗

Kalman filter estimation of attitude and gyro bias with the QUEST observation model

The loss function for the Wahba attitude estimation problem employs unit vector observations with scalar weights. It is usually associated with the QUEST observation model, where the actual sensor noise is assumed the same for all components of the observed vector, regardless of the position in the field of view. The QUEST model has the great advantage of being sensor-independent except for the scalar parameter that characterizes the sensor errors. Although efficient algorithms for solving the Wahba problem exist, extending these algorithms to estimate gyro biases or sensor alignments has had mixed success. However, it is straightforward to estimate bias and alignment parameters with a Kalman filter. This paper investigates the use of an extended Kalman filter for the attitude and gyro bias that incorporates the QUEST observation model, to be referred to as the Unit Vector Filter (UVF). The UVF results are compared with those from a more conventional filter, the Real-Time Sequential Filter (RTSF), for which the residual is the two-dimensional projection of the unit vector onto the plane perpendicular to the sensor boresight. The RTSF is similar in design to that used by Multimission Modular Spacecraft for onboard attitude determination. An apparent obstacle to the use of unit vectors as measurements is their singular noise covariance matrix. Shuster has shown that this problem should not affect filter performance. The UVF and RTSF are tested using actual flight data from the Extreme Ultraviolet Explorer (EUVE). It is found that these filters generate nearly identical attitude and gyro bias estimates, thus validating the use of unit vectors and the QUEST noise model.

Sedlak, J.↗

Notes on a New Coherence Estimator

This document discusses some interesting features of the new coherence estimator in [1] . The estimator is d erived from a slightly different viewpoint. We discuss a few properties of the estimator, including presenting the probability density function of the denominator of the new estimator , which is a new feature of this estimator . Finally, we present an appr oximate equation for analysis of the sensitivity of the estimator to the knowledge of the noise value. ACKNOWLEDGEMENTS The preparation of this report is the result of an unfunded research and development activity. Sandia National Laboratories is a multi - program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE - AC04 - 94AL85000.

97 MATHEMATICS AND COMPUTING↗

A study of planetary meteorology

Preliminary estimates are prepared of the weighting functions of the infrared bands of methane, ammonia, and hydrogen for the Jovian atmosphere. Together with the infrared spectral emission observations of Jupiter, these weighting functions are used to obtain a rough estimate of the vertical temperature profile in the Jovian atmosphere.

Ohring, G.↗

A Fast Monte Carlo Method for Model-Based Prognostics Based on Stochastic Calculus

This work proposes a fast Monte Carlo method to solve differential equations utilized in model-based prognostics. The methodology is derived from the theory of stochastic calculus, and the goal of such a method is to speed up the estimation of the probability density functions describing the independent variable evolution over time. In the prognostic scenarios presented in this paper, the stochastic differential equations describe variables directly or indirectly related to the degradation of a monitored system. The method allows the estimation of the probability density functions by solving the deterministic equation and approximating the stochastic integrals using samples of the model noise. By so doing, the prognostic problem is solved without the Monte Carlo simulation based on Euler's forward method, which is typically the most time consuming task of the prediction stage. Three different prognostic scenarios are presented as proof of concept: (i) life prediction of electrolytic capacitors, (ii) remaining time to discharge of Lithium-ion batteries, and (iii) prognostic of cracked structures under fatigue loading. The paper shows how the method produces probability density functions that are statistically indistinguishable from the distributions estimated with Euler's forward Monte Carlo simulation. However, the proposed solution is orders of magnitude faster when computing the time-to-failure distribution of the monitored system. The approach may enable complex real-time prognostics and health management solutions with limited computing power.

Corbetta, M.↗

A Fast Monte Carlo Method for Model-Based Prognostics Based on Stochastic Calculus

This work proposes a fast Monte Carlo method to solve differential equations utilized in model-based prognostics. The methodology is derived from the theory of stochastic calculus, and the goal of such a method is to speed up the estimation of the probability density functions describing the independent variable evolution over time. In the prognostic scenarios presented in this paper, the stochastic differential equations describe variables directly or indirectly related to the degradation of a monitored system. The method allows the estimation of the probability density functions by solving the deterministic equation and approximating the stochastic integrals using samples of the model noise. By so doing, the prognostic problem is solved without the Monte Carlo simulation based on Euler's forward method, which is typically the most time consuming task of the prediction stage. Three different prognostic scenarios are presented as proof of concept: (i) life prediction of electrolytic capacitors, (ii) remaining time to discharge of Lithium-ion batteries, and (iii) prognostic of cracked structures under fatigue loading. The paper shows how the method produces probability density functions that are statistically indistinguishable from the distributions estimated with Euler's forward Monte Carlo simulation. However, the proposed solution is orders of magnitude faster when computing the time-to-failure distribution of the monitored system. The approach may enable complex real-time prognostics and health management solutions with limited computing power.

stochastic calculus↗

Accurate shear estimation with fourth-order moments

ABSTRACT As imaging surveys progress in exploring the large-scale structure of the Universe through the use of weak gravitational lensing, achieving sub-per cent accuracy in estimating shape distortions caused by lensing, or shear, is imperative for precision cosmology. In this paper, we extend the Fourier power function shapelets (FPFS) shear estimator using fourth-order shapelet moments and combine it with the original second-order shear estimator to reduce galaxy shape noise. We calibrate this novel shear estimator analytically to a sub-per cent level-accuracy using the AnaCal framework. This higher order shear estimator is tested with realistic image simulations, and after analytical correction for the detection/selection bias and noise bias, the multiplicative shear bias $|m|$ is below $3\times 10^{-3}$ (99.7 per cent confidence interval) for both isolated and blended galaxies. Once combined with the second-order FPFS shear estimator, the shape noise is reduced by $\sim 35~{{\ \rm per\ cent}}$ for isolated galaxies in simulations with Hyper Suprime-Cam and Vera C. Rubin Observatory Legacy Survey of Space and Time observational conditions. However, for blended galaxies, the effective number density does not significantly improve with the combination of the two estimators. Based on these results, we recommend exploration of how this framework can further reduce the systematic uncertainties in shear due to point spread function leakage and modelling error, and potentially provide improved precision in shear inference in high-resolution space-based images.

79 ASTRONOMY AND ASTROPHYSICS↗

Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical discretization error and the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity of the sparse grid. Utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗