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At least 73 records · Page 4

Optimal Estimation of Clock Values and Trends from Finite Data

We show how to solve two problems of optimal linear estimation from a finite set of phase data. Clock noise is modeled as a stochastic process with stationary dth increments. The covariance properties of such a process are contained in the generalized autocovariance function (GACV). We set up two principles for optimal estimation: with the help of the GACV, these principles lead to a set of linear equations for the regression coefficients and some auxiliary parameters. The mean square errors of the estimators are easily calculated. The method can be used to check the results of other methods and to find good suboptimal estimators based on a small subset of the available data.

stationary increments↗

Lateral control system design for VTOL landing on a DD963 in high sea states

The problem of designing lateral control systems for the safe landing of VTOL aircraft on small ships is addressed. A ship model is derived. The issues of estimation and prediction of ship motions are discussed, using optimal linear linear estimation techniques. The roll motion is the most important of the lateral motions, and it is found that it can be predicted for up to 10 seconds in perfect conditions. The automatic landing of the VTOL aircraft is considered, and a lateral controller, defined as a ship motion tracker, is designed, using optimal control techniqes. The tradeoffs between the tracking errors and the control authority are obtained. The important couplings between the lateral motions and controls are demonstrated, and it is shown that the adverse couplings between the sway and the roll motion at the landing pad are significant constraints in the tracking of the lateral ship motions. The robustness of the control system, including the optimal estimator, is studied, using the singular values analysis. Through a robustification procedure, a robust control system is obtained, and the usefulness of the singular values to define stability margins that take into account general types of unstructured modelling errors is demonstrated. The minimal destabilizing perturbations indicated by the singular values analysis are interpreted and related to the multivariable Nyquist diagrams.

Bodson, M.↗

Estimating regional heat flux from scanning radiometer data

Method using matrix approach to determine best linear estimate of total flux consistent with condition of minimum variance proves useful in meteorological studies. It is useful for researchers studying options in scanner design such as scan pattern, scan rate, and radiometer field-of-view.

Bess, T. D.↗

Application of the Two-Step Filter to Process Ranging Measurements for Relative Navigation in an Elliptical Orbit

This estimator breaks a nonlinear estimation problem into a set of over determined 'first step' states which are linear in the observations and 'second step' states which are ultimately the states of interest. Linear estimation methods are applied to filter the observations and produce the optimal first step state estimate. The 'second step' states are obtained through iterative nonlinear parameter estimation considering the first step states as observations. It has been shown that this process exactly minimizes the least squares cost function for static problems and provides a better solution than the iterated extended Kalman filter (EKF) for dynamic problems. The two step filter is applied in this paper to process range and range rate measurements between the two spacecraft. Details of the application of the two step estimator to this problem will be given, highlighting the use of a test for ill-conditioned covariance estimates that can result from the first order covariance propagation. A comparison will be made between the performance of the two step filter and the IEKF.

Garrison, James L.↗

Hubble Space Telescope Angular Velocity Estimation During the Robotic Servicing Mission

In 2004 NASA began investigation of a robotic servicing mission for the Hubble Space Telescope (HST). Such a mission would require estimates of the HST attitude and rates in order to achieve a capture by the proposed Hubble robotic vehicle (HRV). HRV was to be equipped with vision-based sensors, capable of estimating the relative attitude between HST and HRV. The inertial HST attitude is derived from the measured relative attitude and the HRV computed inertial attitude. However, the relative rate between HST and HRV cannot be measured directly. Therefore, the HST rate with respect to inertial space is not known. Two approaches are developed to estimate the HST rates. Both methods utilize the measured relative attitude and the HRV inertial attitude and rates. First, a non-linear estimator is developed. The nonlinear approach estimates the HST rate through an estimation of the inertial angular momentum. Second, a linearized approach is developed. The linearized approach is a pseudo-linear Kalman filter. Simulation test results for both methods are given. Even though the development began as an application for the HST robotic servicing mission, the methods presented are applicable to any rendezvous/capture mission involving a non-cooperative target spacecraft.

Thienel, Julie K.↗

Ion-temperature- and density-gradient-driven instabilities and turbulence in Wendelstein 7-X close to the stability threshold

Electrostatic gyrokinetic instabilities and turbulence in the Wendelstein 7-X stellarator are studied. Particular attention is paid to the ion-temperature-gradient (ITG) instability and its character close to marginal stability [Floquet-type turbulence (Zocco et al., Phys. Rev. E, vol. 106, 2022, p. L013202) with no electron temperature gradient]. The flux tube version of the δƒ code stella (Barnes et al., J. Comput. Phys., vol. 391, 2019, pp. 365–380) is used to run linear and nonlinear gyrokinetic simulations with kinetic electrons. The nature of the dominant instability depends on the wavelength perpendicular to the magnetic field, and the results are conveniently displayed in stability diagrams that take this dependence into account. This approach highlights the presence of universal instabilities, which are less unstable but have longer wavelengths than other modes. A quasi-linear estimate of the heat flux suggests they are relevant for transport. Close to the stability threshold, the linear eigenmodes and turbulence form highly extended structures along the computational domain if the magnetic shear is small. Numerical experiments and diagnostics are undertaken to assess the resulting radial localisation of the turbulence, which affects the interaction of the latter with zonal flows. Increasing the amplitude of the magnetic shear (e.g.through current drive) has a stabilising effect on the turbulence and, thus, reduces the nonlinear energy transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Sensor Selection for Aircraft Engine Performance Estimation and Gas Path Fault Diagnostics

This paper presents analytical techniques for aiding system designers in making aircraft engine health management sensor selection decisions. The presented techniques, which are based on linear estimation and probability theory, are tailored for gas turbine engine performance estimation and gas path fault diagnostics applications. They enable quantification of the performance estimation and diagnostic accuracy offered by different candidate sensor suites. For performance estimation, sensor selection metrics are presented for two types of estimators including a Kalman filter and a maximum a posteriori estimator. For each type of performance estimator, sensor selection is based on minimizing the theoretical sum of squared estimation errors in health parameters representing performance deterioration in the major rotating modules of the engine. For gas path fault diagnostics, the sensor selection metric is set up to maximize correct classification rate for a diagnostic strategy that performs fault classification by identifying the fault type that most closely matches the observed measurement signature in a weighted least squares sense. Results from the application of the sensor selection metrics to a linear engine model are presented and discussed. Given a baseline sensor suite and a candidate list of optional sensors, an exhaustive search is performed to determine the optimal sensor suites for performance estimation and fault diagnostics. For any given sensor suite, Monte Carlo simulation results are found to exhibit good agreement with theoretical predictions of estimation and diagnostic accuracies.

Gas Turbine Engines↗

Sensor Selection for Aircraft Engine Performance Estimation and Gas Path Fault Diagnostics

This paper presents analytical techniques for aiding system designers in making aircraft engine health management sensor selection decisions. The presented techniques, which are based on linear estimation and probability theory, are tailored for gas turbine engine performance estimation and gas path fault diagnostics applications. They enable quantification of the performance estimation and diagnostic accuracy offered by different candidate sensor suites. For performance estimation, sensor selection metrics are presented for two types of estimators including a Kalman filter and a maximum a posteriori estimator. For each type of performance estimator, sensor selection is based on minimizing the theoretical sum of squared estimation errors in health parameters representing performance deterioration in the major rotating modules of the engine. For gas path fault diagnostics, the sensor selection metric is set up to maximize correct classification rate for a diagnostic strategy that performs fault classification by identifying the fault type that most closely matches the observed measurement signature in a weighted least squares sense. Results from the application of the sensor selection metrics to a linear engine model are presented and discussed. Given a baseline sensor suite and a candidate list of optional sensors, an exhaustive search is performed to determine the optimal sensor suites for performance estimation and fault diagnostics. For any given sensor suite, Monte Carlo simulation results are found to exhibit good agreement with theoretical predictions of estimation and diagnostic accuracies.

Gas Turbine Engines↗

Sensor Selection for Aircraft Engine Performance Estimation and Gas Path Fault Diagnostics

This paper presents analytical techniques for aiding system designers in making aircraft engine health management sensor selection decisions. The presented techniques, which are based on linear estimation and probability theory, are tailored for gas turbine engine performance estimation and gas path fault diagnostics applications. They enable quantification of the performance estimation and diagnostic accuracy offered by different candidate sensor suites. For performance estimation, sensor selection metrics are presented for two types of estimators including a Kalman filter and a maximum a posteriori estimator. For each type of performance estimator, sensor selection is based on minimizing the theoretical sum of squared estimation errors in health parameters representing performance deterioration in the major rotating modules of the engine. For gas path fault diagnostics, the sensor selection metric is set up to maximize correct classification rate for a diagnostic strategy that performs fault classification by identifying the fault type that most closely matches the observed measurement signature in a weighted least squares sense. Results from the application of the sensor selection metrics to a linear engine model are presented and discussed. Given a baseline sensor suite and a candidate list of optional sensors, an exhaustive search is performed to determine the optimal sensor suites for performance estimation and fault diagnostics. For any given sensor suite, Monte Carlo simulation results are found to exhibit good agreement with theoretical predictions of estimation and diagnostic accuracies.

Diagnosis↗

Estimating the Cramer-Rao bound for restored astronomical observations

This work addresses the problem of assigning confidence intervals to estimated photometry data obtained from astronomical observations. The proposed solution is to estimate the Cramer-Rao bound, which is an analytical expression that describes the minimum obtainable mean square error associated with a given estimate of a parameter. This Letter presents a compact and simple form for the bound associated with a linear estimator such as a Wiener filter estimator. A prescription for estimating the variance associated with each element in a restored object was developed using an analytical model for observed data corrupted by either Poisson or Gaussian noise. Both one- and two-dimensional examples are presented.

Zaccheo, T. S.↗

Exploring magnetic anisotropy and robustness of the J eff = 1/2 state under substantial orthorhombic distortion in Sr 2 IrO 4 thin films

Here, we present a comprehensive study revealing the intricate interplay of the magnetic anisotropy and orthorhombic distortion in thin films of Sr 2 IrO 4 through a Ca 3 Ru 2 O 7 substrate. By inducing a pronounced orthorhombic distortion along the direction of oxygen octahedral edges, we effectively modulated the uniaxial magnetic anisotropy in the system. Remarkably divergent responses along the easy and hard magnetic axes were unveiled through x-ray magnetic circular dichroism (XMCD) measurements under magnetic fields. Specifically, the spin flop transition observed when the magnetic field aligns with the hard axis allows us to estimate the magnetic anisotropy energy, which is around 14.2 µeV, close to that estimated from the single magnon peak measured via Raman spectroscopy. The observed anisotropy energy remains notably lower than the linear estimates derived from the strain-anisotropy energy relationship outlined in H.-H. Kim et al., Nat. Commun. 13, 6674 (2022). This underscores the enduring preservation of the isotropic character of the J eff = 1/2 states. This is also supported by the negligible XMCD intensity ratio at the L 2 edge compared to that of the L 3 edge. Furthermore, the branching ratio determined from x-ray absorption spectroscopy shows that the expectation value of the spin-orbit coupling is similar to that of bulk Sr 2 IrO 4 single crystals. Our findings indicate that even under a substantial anisotropic biaxial distortion, Sr 2 IrO 4 remains remarkably proximate to the J eff = 1/2 state. This study not only provides valuable information in understanding the interplay between magnetic anisotropy and strain but also the robustness of the J eff = 1/2 state under octahedral distortion within materials exhibiting emergent quantum phenomena.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Digital phase-lock loop having an estimator and predictor of error

A digital phase-lock loop (DPLL) which generates a signal with a phase that approximates the phase of a received signal with a linear estimator. The effect of a complication associated with non-zero transport delays related to DPLL mechanization is then compensated by a predictor. The estimator provides recursive estimates of phase, frequency, and higher order derivatives, while the predictor compensates for transport lag inherent in the loop.

Statman, Joseph I.↗

Failure detection by pilots during automatic landing - Models and experiments

A model is proposed to describe the pilot as a monitor of automatic landing systems. The failures treated are equivalent to the addition of a dynamic change in the mean of the observation process. The failure detection model of the pilot consists of two stages: a linear estimator (Kalman filter) and a decision mechanism based on sequential analysis. The filter equations are derived from a simplified version of the linearized dynamics of the airplane and the control loop. The perceptual observation noise is modified to include the effects of allocation of attention among the several instruments. The final result is a simple model consisting of a high-pass filter to produce the observation residuals and a decision function which is a pure integration of the residuals minus a bias term. The dynamics of a Boeing 707 were used to simulate the fully coupled final approach in a fixed-base simulator. Observers monitored the approaches and detected the failures; their performance was compared with the predictions of the model.

Gai, E. G.↗

GMLS-Nets: A Framework for Learning from Unstructured Data

Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gaining benefits from weight sharing and invariances. We generalize CNNs by introducing methods for data on unstructured point clouds based on Generalized Moving Least Squares (GMLS). GMLS is a nonparametric technique for estimating linear bounded functionals from scattered data, and has recently been used in the literature for solving partial differential equations. By parameterizing the GMLS estimator, we obtain learning methods for operators with unstructured stencils. In GMLS-Nets the necessary calculations are local, readily parallelizable, and the estimator is supported by a rigorous approximation theory. We show how the framework may be used for unstructured physical data sets to perform functional regression to identify associated differential operators and to regress quantities of interest. The results suggest the architectures to be an attractive foundation for data-driven model development in scientific machine learning applications.

42 ENGINEERING↗

Surface and aerosol models for use in radiative transfer codes

Absolute reflectance-based radiometric calibrations of Landsat-5 Thematic Mapper (TM) are improved with the inclusion of a method to invert optical-depth measurements to obtain aerosol-particle size distributions, and a non-Lambertian surface reflectance model. The inverted size distributions can predict radiances varying from the previously assumed jungian distributions by as much as 5 percent, though the reduction in the estimated error is less than one percent. Comparison with measured diffuse-to-global ratios show that neither distribution consistently predicts the ratio accurately, and this is shown to be a large contributor to calibration uncertainties. An empirical model for the surface reflectance of White Sands, using a two-degree polynomial fit as a function of scattering angle, was employed. The model reduced estimated errors in radiance predictions by up to one percent. Satellite calibrations dating from October, 1984 were reprocessed using the improved methods and linear estimations of satellite counts per unit radiance versus time since launch were determined which showed a decrease over time for the first four bands.

Hart, Quinn J.↗

GMLS-Nets: Scientific Machine Learning Methods for Unstructured Data

Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gaining benefits from weight sharing and invariances. We generalize CNNs by introducing methods for data on unstructured point clouds based on Generalized Moving Least Squares (GMLS). GMLS is a nonparametric technique for estimating linear bounded functionals from scattered data, and has recently been used in the literature for solving partial differential equations. By parameterizing the GMLS estimator, we obtain learning methods for operators with unstructured stencils. In GMLS-Nets the necessary calculations are local, readily parallelizable, and the estimator is supported by a rigorous approximation theory. We show how the framework may be used for unstructured physical data sets to perform functional regression to identify associated differential operators and to regress quantities of interest. The results suggest the architectures to be an attractive foundation for data-driven model development in scientific machine learning applications

97 MATHEMATICS AND COMPUTING↗