We consider a class of interpolation algorithms, including the least-squares optimal Yen interpolator, and we derive a closed-form expression for the interpolation error for interpolators of this type. The error depends on the eigenvalue distribution of a matrix which is specified for each set of sampling points. The error expression can be used to prove that the Yen interpolator is optimal. The implementation of the Yen algorithm suffers from numerical ill-conditioning, forcing the use of a regularized, approximate solution. We suggest a new, approximate solution, consisting of a sinc-kernel interpolator with specially chosen weighting coefficients. The newly designed sinc-kernel interpolator is compared with the usual sinc interpolator using Jacobian (area) weighting, through numerical simulations. We show that the sinc interpolator with Jacobian weighting works well only when the sampling is nearly uniform. The newly designed sinc-kernel interpolator is shown to perform better than ...

Air traffic automation depends on accurate trajectory predictions. Flight tests show that wind errors are a large source of error. Wind-field accuracy is sufficient on average, but large errors occasionally exist that cause significant errors in trajectory-prediction. A year long study was conducted to better understand the wind-prediction errors, to establish metrics for quantifying large errors, and to validate two approaches to improve wind prediction accuracy. Three methods are discussed for quantifying large errors: percentage of point errors that exceed 10 m/s, probability distribution of point errors, and the number of hourly time periods with a high number of large errors. The baseline wind-prediction system evaluated for this study is the Rapid Update Cycle (RUC). Two approaches to improving the original RUC wind predictions are examined. The first approach is to enhance RUC in terms of increased model resolution, enhancement of the model physics, and increased observational input data. The second method is to augment the RUC output, in near-real time, through an optimal-interpolation scheme that incorporates the latest aircraft reports received since the last RUC update. Both approaches are shown to greatly reduce the occurrence of large wind errors.

This paper also proposed another reconstruction method based on a direct approximation of the Fourier inversion formula using a twodimensional (2-D) trapezoidal rule. In addition, the possibility of reconstruction from a concentric-squares raster was discussed. Numerous simple interpolators have been tried in DF reconstruction with the results compared with CBP [33]. In [34] and [35], the concept of angular bandlimiting was used to interpolate the polar data onto a Cartesian grid. In [36], a DF reconstruction using bilinear interpolation for diffraction tomography provided image quality that was comparable to that produced by the CBP algorithm. Very good reconstruction quality was obtained in [37] and [38] using a spline interpolator, or a hybrid type of spline interpolator. The notion of "gridding" was introduced in [39] as a method of obtaining optimal inversion of Fourier data. An optimal gridding function was proposed, and successful results were obtained when applied to the tomographic reconstruction problem. In [40], several different gridding functions were tried for DF reconstruction, and the performances were compared. In [41, 42], the linogram reconstruction method was proposed as a form of DF reconstruction. The data collection grid in the linogram method is the same as in the concentric-squares sampling scheme. The inversion of the Fourier data in [41, 42] was accomplished by first applying the chirp-z transform in one direction and then computing FFTs in the other direction. In CT, many of these attempts at DF reconstruction have given a poorer result than the CBP algorithm, due to the error incurred in the process of the polar-to-Cartesian interpolation. The attraction of DF reconstruction, however, is that it is thought to require less computation than ...

. The on-line or adaptive identification of parameters in abstract linear and nonlinear infinite-dimensional dynamical systems is considered. An estimator in the form of an infinitedimensional linear evolution system having the state and parameter estimates as its states is defined. Convergence of the state estimator is established via a Lyapunov estimate. The finite-dimensional notion of a plant being su#ciently rich or persistently excited is extended to infinite dimensions. Convergence of the parameter estimates is established under the additional assumption that the plant is persistently excited. A finite-dimensional approximation theory is developed, and convergence results are established. Numerical results for examples involving the estimation of both constant and functional parameters in one-dimensional linear and nonlinear heat or di#usion equations and the estimation of sti#ness and damping parameters in a one-dimensional wave equation with Kelvin--Voigt viscoelastic damping ...

In many face recognition systems, the input is a video sequence consisting of one or more faces. It is necessary to track each face over this video sequence so as to extract the information that will be processed by the recognition system. Tracking is also necessary for 3D model-based recognition systems where the 3D model is estimated from the input video. Face tracking can be divided along different lines depending upon the method used, e.g., head tracking, feature tracking, image-based tracking, model-based tracking. The output of the face tracker can be the 2D position of the face in each image of the video (2D tracking), the 3D pose of the face (3D tracking), or the location of features on the face. Some trackers are able to output other parameters related to lighting or expression. The major challenges encountered by face tracking systems are robustness to pose changes, lighting variations, and facial deformations due to changes of expression, occlusions of the face to be tracked and clutter in the scene that makes it difficult to distinguish the face from the other objects. Main Body Text

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The National Aeronautics and Space Administration (NASA) is developing the Center–TRA-