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At least 595 records · Page 33

A Comparison of Methods for a Priori Bias Correction in Soil Moisture Data Assimilation

Data assimilation is being increasingly used to merge remotely sensed land surface variables such as soil moisture, snow and skin temperature with estimates from land models. Its success, however, depends on unbiased model predictions and unbiased observations. Here, a suite of continental-scale, synthetic soil moisture assimilation experiments is used to compare two approaches that address typical biases in soil moisture prior to data assimilation: (i) parameter estimation to calibrate the land model to the climatology of the soil moisture observations, and (ii) scaling of the observations to the model s soil moisture climatology. To enable this research, an optimization infrastructure was added to the NASA Land Information System (LIS) that includes gradient-based optimization methods and global, heuristic search algorithms. The land model calibration eliminates the bias but does not necessarily result in more realistic model parameters. Nevertheless, the experiments confirm that model calibration yields assimilation estimates of surface and root zone soil moisture that are as skillful as those obtained through scaling of the observations to the model s climatology. Analysis of innovation diagnostics underlines the importance of addressing bias in soil moisture assimilation and confirms that both approaches adequately address the issue.

Kumar, Sujay V.↗

An approximation theory for nonlinear partial differential equations with applications to identification and control

Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

Banks, H. T.↗

Comparison of U.S. and Russian Slow Crack Growth Data and Models

Both the US and Russian space programs use similar predictive models for design of fused silica windows on the International space station. The Russian model can be derived from the power expression for slow crack growth (SCG) or “static fatigue.” The US uses both power and exponential models. Despite the similarity of models and data fitting approach (linear regression and right censoring), different SCG parameters have been derived by US and Russian parties for the same material (Russian fused silica) tested in a similar manner. The difference appears to be related to the use of short-term strength data along with the longer-term static fatigue data, with the power law parameter n being very sensitive to the conversion of strength data into equivalent static data. This hybrid approach is feasible if strength data is measured with a constant stress rate and is appropriately converted to a static equivalent. More research into the approach is needed. However, because of the nonlinear behavior of fused silica in log(v) – log(K(I) ) space and the sensitivity of parameter estimation to fit range, the exponential model is a better choice regardless of test method. Functions are given to convert parameters from the Russian model to those in the US model. However, accurate conversion is hampered by the lack of inert strength data. When the same test technique is used, US and Russian materials exhibit very similar parameters.

Silica, strength, impact, crack growth, windows, I↗

Multivariate space - time analysis of PRE-STORM precipitation

This paper presents the methodologies and results of the multivariate modeling and two-dimensional spectral and correlation analysis of PRE-STORM rainfall gauge data. Estimated parameters of the models for the specific spatial averages clearly indicate the eastward and southeastward wave propagation of rainfall fluctuations. A relationship between the coefficients of the diffusion equation and the parameters of the stochastic model of rainfall fluctuations is derived that leads directly to the exclusive use of rainfall data to estimate advection speed (about 12 m/s) as well as other coefficients of the diffusion equation of the corresponding fields. The statistical methodology developed here can be used for confirmation of physical models by comparison of the corresponding second-moment statistics of the observed and simulated data, for generating multiple samples of any size, for solving the inverse problem of the hydrodynamic equations, and for application in some other areas of meteorological and climatological data analysis and modeling.

Polyak, Ilya↗

Verifiable Adaptive Control with Analytical Stability Margins by Optimal Control Modification

This paper presents a verifiable model-reference adaptive control method based on an optimal control formulation for linear uncertain systems. A predictor model is formulated to enable a parameter estimation of the system parametric uncertainty. The adaptation is based on both the tracking error and predictor error. Using a singular perturbation argument, it can be shown that the closed-loop system tends to a linear time invariant model asymptotically under an assumption of fast adaptation. A stability margin analysis is given to estimate a lower bound of the time delay margin using a matrix measure method. Using this analytical method, the free design parameter n of the optimal control modification adaptive law can be determined to meet a specification of stability margin for verification purposes.

Nguyen, Nhan T.↗

Aeroelastic Modeling of X-56A Stiff-Wing Configuration Flight Test Data

Aeroelastic stability and control derivatives for the X-56A Multi-Utility Technology Testbed (MUTT), in the stiff-wing configuration, were estimated from flight test data using the output-error method. Practical aspects of the analysis are discussed. The orthogonal phase-optimized multisine inputs provided excellent data information for aeroelastic modeling. Consistent parameter estimates were determined using output error in both the frequency and time domains. The frequency domain analysis converged faster and was less sensitive to starting values for the model parameters, which was useful for determining the aeroelastic model structure and obtaining starting values for the time domain analysis. Including a modal description of the structure from a finite element model reduced the complexity of the estimation problem and improved the modeling results. Effects of reducing the model order on the short period stability and control derivatives were investigated.

Grauer, Jared A.↗

Aircraft System Identification from Multisine Inputs and Frequency Responses

A frequency-domain approach is described for estimating parameters, such as stability and control derivatives, in aircraft flight dynamic models from measured input and output data. The approach uses orthogonal phase-optimized multisines for moving the aircraft control effectors, Fourier analysis for computing multiple-input multiple-output frequency responses, and a maximum likelihood estimator called frequency response error (FRE) for determining values and uncertainties for the model parameters. The approach is demonstrated using flight test data for two subscale airplanes: the T-2 generic transport model and the X-56A aeroelastic demonstrator. Results and comparisons with the output-error method indicated that the approach produced accurate estimates of stability and control derivatives and their uncertainties from flight test data.

Grauer, Jared A.↗

Earth-based navigation capabilities for outer planet missions.

The role of new Earth-based radio metric data types and of advanced estimation algorithms in navigating an outer planet spacecraft in the vicinity of Saturn has been analyzed. The data types included in the study consist of conventional range and range-rate measurements taken from a single station and simultaneous and nearly simultaneous measurements obtained from pairs of stations during overlapping viewing periods. The utility of a third data set that is produced by explicitly differencing the simultaneous points has also been investigated. The data was processed with a conventional least squares batch filter and with a sequential filter that estimated parameters describing small stochastic accelerations (process noise) acting on the spacecraft. It was found that process noise can produce large errors in the estimates obtained from batch filtering conventional and simultaneous data, and that the only batch filtered estimates that were reliable were those obtained from differenced data. The performance of the simultaneous data in the presence of process noise is greatly improved by sequential filtering.

Hildebrand, C. E.↗

GEODYN system support program, volume 4

The GEODYN Orbit Determination and Geodetic Parameter Estimation System consists of a set of computer programs designed to determine and analyze definitive satellite orbits and their associated geodetic and measurement parameters. This manual describes the Support Programs used by the GEODYN System. The mathematics and programming descriptions are detailed. The operational procedures of each program are presented. GEODYN ancillary analysis programs may be grouped into three different categories: (1) orbit comparison - DELTA (2) data analysis using reference orbits - GEORGE, and (3) pass geometry computations - GROUNDTRACK. All of the above three programs use one or more tapes written by the GEODYN program in either a data reduction or orbit generator run.

Mullins, N. E.↗

Noncommunting observables in quantum detection and estimation theory

In quantum detection theory the optimum detection operators must commute; admitting simultaneous approximate measurement of noncommuting observables cannot yield a lower Bayes cost. The lower bounds on mean square errors of parameter estimates predicted by the quantum-mechanical Cramer-Rao inequality can also not be reduced by such means.

Helstrom, C. W.↗

Equivalent GPS measurements for efficient estimation process

Dual-frequency pseudorange and carrier phase data streams can be analytically combined into a single equivalent data stream, reducing the data volume and computing time in the filtering process for parameter estimation by a factor of 2 to 4. The resulting single data stream is that of carrier phase measurements with both data noise and bias uncertainty strictly defined. Based on these analytical formulas the equivalent GPS measurements can be formed by simple and efficient numerical calculations without any degradation in data strength. Formulation for the equivalent GPS measurements and their covariances are given in closed form; and a numerical simulation is performed to demonstrate the validity and effectiveness of the equivalent measurements.

Wu, S. C.↗

Improved calculation of optimum design sensitivity

Optimum design parameter sensitivity analysis has become an important topic in recent years. The principal reasons for obtaining optimum design sensitivity information with respect to various problem parameters are (l) to predict revised optimum designs, associated with specified perturbations of the problem parameters, without re-optimizing the problem and, (2) to provide sensitivity information in multilevel optimization strategies. Methods for calculating these derivatives were proposed by several authors. The most important drawback in estimating parameter sensitivities by the current methods is that they do not allow for changes in the active constraint set. Changes in the active constraint set produce discontinuities in the optimum design sensitivities, and therefore, a correct formulation has to be cast in terms of directional derivatives. Optimum design parameter sensitivity analysis is addressed in terms of directional derivatives so as to include possible discontinuities and it also presents a method for estimating optimum design sensitivities using finite differences.

Sepulveda, Abdon E.↗

Can Neutron Star Tidal Effects Obscure Deviations from General Relativity?

Abstract One of the main goals of gravitational-wave astrophysics is to study gravity in the strong-field regime and constrain deviations from general relativity (GR). Any such deviation affects not only binary dynamics and gravitational-wave emission but also the structure and tidal properties of compact objects. In the case of neutron stars, masses, radii, and tidal deformabilities can all differ significantly between different theories of gravity. Currently, the measurement uncertainties in neutron star radii and tidal deformabilities are quite large. However, much less is known about how the large uncertainty in the nuclear equation of state (EOS) might affect tests of GR using binary neutron star mergers. Conversely, using the wrong theory of gravity might lead to incorrect constraints on the nuclear EOS. Here, we study this problem within scalar–tensor (ST) theory. We apply the recently derived ℓ = 2 tidal Love numbers in this theory to parameter estimation of GW170817. Correspondingly, we test if physics beyond GR could bias measurements of the nuclear EOS and neutron star radii. We find that parameter inference for both the GR and ST cases returns consistent component masses and tidal deformabilities. The radius and the EOS posteriors, however, differ between the two theories, but neither is excluded by current observational limits. This indicates that measurements of the nuclear EOS may be biased and that deviations from GR could go undetected when analyzing current binary neutron star mergers.

79 ASTRONOMY AND ASTROPHYSICS↗

Low Order Equivalent System Identification for the Tu-144LL Supersonic Transport Aircraft

Low order equivalent system models were identified from flight test data for the Tu-144LL supersonic transport aircraft. Flight test maneuvers were executed by Russian and American test Pilots flying the aircraft from Zhukovsky airfield outside Moscow, Russia. Flight tests included longitudinal and lateral / directional maneuvers at supersonic cruise flight conditions. Piloted frequency sweeps and multi-step maneuvers were used to generate data for closed loop low order equivalent system modeling. Model parameters were estimated using a flexible. high accuracy Fourier transform and an equation error / output error (EE/OE) formulation in the frequency domain. Results were compared to parameter estimates obtained using spectral estimation and subsequent least squares fit to frequency response data in Bode plots. Modeling results from the two methods agreed well for both a frequency sweep and multiple concatenated multi-step maneuvers. For a single multi-step maneuvers the EE/OE method gave a better model fit with improved prediction capability. A summary of closed loop low order equivalent system identification results for the Tu-144LL, including estimated parameters, standard errors, and flying qualities level predictions, were computed and tabulated.

Morelli, Eugene A.↗

Low Order Equivalent System for the Tu-144LL Supersonic Transport Aircraft

Low order equivalent system models were identified from flight test data for the Tu- 144LL supersonic transport aircraft. Flight test maneuvers were executed by Russian and American test pilots flying the aircraft from Zhukovsky airfield outside Moscow, Russia. Flight tests included longitudinal and lateral/directional maneuvers at supersonic cruise flight conditions. Piloted frequency sweeps and multi-step maneuvers were used to Generate data for p closed loop low order equivalent system modeling Model parameters were estimated using a flexible, high accuracy Fourier transform and an equation error output error (EE/OE) formulation in the frequency domain. Results were compared to parameter estimates obtained using spectral estimation and subsequent least squares fit to frequency response data in Bode plots. Modeling results from the two methods a-reed well for both a frequency sweep and multiple concatenated multi-step maneuvers. For a single multi-step maneuver, the EE/OE method gave a better model fit with improved prediction capability. A summary of closed loop low order equivalent system identification results for the Tu-144LL. including estimated parameters, standard errors, and flying qualities level predictions, were computed and tabulated.

Morelli, Eugene A.↗

Noncommuting observables in quantum detection and estimation theory

In quantum detection theory, the optimum detection operators must commute; admitting simultaneous approximate measurement of noncommuting observables cannot yield a lower Bayes cost. In addition, the lower bounds on mean square errors of parameter estimates, predicted by the quantum mechanical Cramer-Rao inequality, cannot be reduced by such means.

Helstrom, C. W.↗

Towards constraining cosmological parameters with SPT-3G observations of 25% of the sky

The South Pole Telescope (SPT), using its third-generation camera, SPT-3G, is conducting observations of the cosmic microwave background (CMB) in temperature and polarization across approximately 10 000 deg$^2$ of the sky at 95, 150, and 220 GHz. This comprehensive dataset should yield stringent constraints on cosmological parameters. In this work, we explore its potential to address the Hubble tension by forecasting constraints from temperature, polarization, and CMB lensing on early dark energy (EDE) and the variation in electron mass in spatially flat and curved universes. For this purpose, we investigate first whether analyzing the distinct SPT-3G observation fields independently, as opposed to as a single, unified region, results in a loss of information relevant to cosmological parameter estimation. We develop a realistic temperature and polarization likelihood pipeline capable of analyzing these fields in these two ways, and subsequently forecast constraints on cosmological parameters. Our findings indicate that any loss of constraining power from analyzing the fields separately is primarily concentrated at low multipoles ($\ell$ < 50) and the overall impact on the relative uncertainty on standard $Λ$ cold dark matter parameters is minimal (< 3%). Our forecasts suggest that SPT-3G data should improve by more than a factor of 90 and 190 the figure of merit of the EDE and the varying electron mass models, respectively, when combined with Planck data. The likelihood pipeline developed and used in this work is made publicly available online.

Vitrier, A. [Paris, Inst. Astrophys.]↗