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NASA NTRS1985

Navigation systems

The elements of the measurement and communications network comprising the global deep space navigation system (DSN) for NASA missions are described. Among the measurement systems discussed are: VLBI, two-way Doppler and range measurements, and optical measurements carried out on board the spacecraft. Processing of navigation measurement is carried out using two modules: an N-body numerical integration of the trajectory (and state transition partial derivatives) based on pre-guessed initial conditions; and partial derivatives of simulated observables corresponding to each actual observation. Calculations of velocity correction parameters is performed by precise modelling of all physical phenomena influencing the observational measurements, including: planetary motions; tracking station locations, gravity field structure, and transmission media effects. Some of the contributions to earth-relative orbit estimate errors for the Doppler/range system on board Voyager are discussed in detail. A line drawing of the DSN navigation system is provided.

Jordan, J. F.↗

NASA NTRS1986

Ultraviolet extinction toward five open clusters, and the accuracy of IUE extinction measurements

The UV extinction curves of 33 main-sequence B stars in five open clusters are presented and analyzed. An analytic fitting function is introduced which represents the observed curves and codifies the structure of the 2175 A extinction bump. A set of extinction parameters are also defined which describe the shape of the far-UV extinction. These data are first used to determine whether the extinction toward any of the clusters is uniform, i.e., whether it can be represented by a single curve for the cluster. This is accomplished by comparing the observed scatter of the far-UV extinction measurements toward a given cluster with that predicted by an error model. The extinction toward four of the five clusters is found to be uniform. The extinction data for those clusters with uniform extinction are then used to determine the observational uncertainties in other extinction parameters for which a priori error estimates cannot be made. With one exception, all of the parameters which describe the shapes of UV extinction curves differ significantly from cluster to cluster. The exception is the central position of the UV extinction bump, which has the same value for all of the cluster extinction curves. Applications and interpretation of the results are given elsewhere.

Massa, D.↗

NASA NTRS1985

Verification of L-band SAR calibration

Absolute calibration of a digital L-band SAR system to an accuracy of better than 3 dB has been verified. This was accomplished with a calibration signal generator that produces the phase history of a point target. This signal relates calibration values to various SAR data sets. Values of radar cross-section (RCS) of reference reflectors were obtained using a derived calibration relationship for the L-band channel on the ERIM/CCRS X-C-L SAR system. Calibrated RCS values were compared to known RCS values of each reference reflector for verification and to obtain an error estimate. The calibration was based on the radar response to 21 calibrated reference reflectors.

Larson, R. W.↗

NASA NTRS1985

Kalman-like estimation for static distributed systems Antenna shape from radiation measurements

This paper advances an approach to the determination of shape of static distributed systems. It also illustrates the application of the approach to the problems of surface diagnosis of large parabolic reflectors. The estimation methods developed combine in an optimal sense the information from an elliptic model of the structure and from measurements of the structural deflection and of the far-field pattern changes due to the structural deformation. The estimators have a predictor-corrector structure, quite similar to that of a Kalman filter. The system model is first used to obtain a predicted estimate. A correction term is then added to the prediction to obtain the final state estimate. The relative weighting between prediction and correction terms is determined by an estimator gain. As in a Kalman filter, the estimator gain can be expressed in terms of the state estimation error covariance.

Rodriguez, G.↗

NASA NTRS1986

Total absorption and photoionization cross sections of water vapor between 100 and 1000 A

Absolute photoabsorption and photoionization cross sections of water vapor are reported at a large number of discrete wavelengths between 100 and 1000 A with an estimate error of + or - 3 percent in regions free from any discrete structure. The double ionization chamber technique utilized is described. Recent calculations are shown to be in reasonable agreement with the present data.

Haddad, G. N.↗

NASA NTRS1986

Landsat D Thematic Mapper image dimensionality reduction and geometric correction accuracy

To characterize and quantify the performance of the Landsat thematic mapper (TM), techniques for dimensionality reduction by linear transformation have been studied and evaluated and the accuracy of the correction of geometric errors in TM images analyzed. Theoretical evaluations and comparisons for existing methods for the design of linear transformation for dimensionality reduction are presented. These methods include the discrete Karhunen Loeve (KL) expansion, Multiple Discriminant Analysis (MDA), Thematic Mapper (TM)-Tasseled Cap Linear Transformation and Singular Value Decomposition (SVD). A unified approach to these design problems is presented in which each method involves optimizing an objective function with respect to the linear transformation matrix. From these studies, four modified methods are proposed. They are referred to as the Space Variant Linear Transformation, the KL Transform-MDA hybrid method, and the First and Second Version of the Weighted MDA method. The modifications involve the assignment of weights to classes to achieve improvements in the class conditional probability of error for classes with high weights. Experimental evaluations of the existing and proposed methods have been performed using the six reflective bands of the TM data. It is shown that in terms of probability of classification error and the percentage of the cumulative eigenvalues, the six reflective bands of the TM data require only a three dimensional feature space. It is shown experimentally as well that for the proposed methods, the classes with high weights have improvements in class conditional probability of error estimates as expected.

Ford, G. E.↗

NASA NTRS1987

Galerkin/Runge-Kutta discretizations for semilinear parabolic equations

A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for semilinear parabolic initial boundary value problems. Unlike any classical counterpart, this class offers arbitrarily high, optimal order convergence. In support of this claim, error estimates are proved, and computational results are presented. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.

Keeling, Stephen L.↗

NASA NTRS1986

Laser fringe anemometry for aero engine components

Advances in flow measurement techniques in turbomachinery continue to be paced by the need to obtain detailed data for use in validating numerical predictions of the flowfield and for use in the development of empirical models for those flow features which cannot be readily modelled numerically. The use of laser anemometry in turbomachinery research has grown over the last 14 years in response to these needs. Based on past applications and current developments, the key issues which are involved when considering the application of laser anemometry to the measurement of turbomachinery flowfields are discussed. Aspects of laser fringe anemometer optical design which are applicable to turbomachinery research are briefly reviewed. Application problems which are common to both laser fringe anemometry (LFA) and laser transit anemometry (LTA) such as seed particle injection, optical access to the flowfield, and measurement of rotor rotational position are covered. The efficiency of various data acquisition schemes is analyzed and issues related to data integrity and error estimation are addressed. Real-time data analysis techniques aimed at capturing flow physics in real time are discussed. Finally, data reduction and analysis techniques are discussed and illustrated using examples taken from several LFA turbomachinery applications.

Strazisar, Anthony J.↗

NASA NTRS1987

Combined optimization of image-gathering and image-processing systems for scene feature detection

The relationship between the image gathering and image processing systems for minimum mean squared error estimation of scene characteristics is investigated. A stochastic optimization problem is formulated where the objective is to determine a spatial characteristic of the scene rather than a feature of the already blurred, sampled and noisy image data. An analytical solution for the optimal characteristic image processor is developed. The Wiener filter for the sampled image case is obtained as a special case, where the desired characteristic is scene restoration. Optimal edge detection is investigated using the Laplacian operator x G as the desired characteristic, where G is a two dimensional Gaussian distribution function. It is shown that the optimal edge detector compensates for the blurring introduced by the image gathering optics, and notably, that it is not circularly symmetric. The lack of circular symmetry is largely due to the geometric effects of the sampling lattice used in image acquisition. The optimal image gathering optical transfer function is also investigated and the results of a sensitivity analysis are shown.

Halyo, Nesim↗

NASA NTRS1987

A new linear quadratic optimal controller for the 34-meter high efficiency antenna position loop

The design of a new position loop controller for the 34-meter High Efficiency Deep Space antennas using linear quadratic (LQ) optimal control techniques is discussed. The LQ optimal control theory is reviewed, and model development and verification are discussed. Families of optimal gain vectors are generated by varying weight parameters. Performance specifications were used to select a final gain vector. Estimator dynamics were selected and the corresponding gain vectors were computed. Final estimator selection was based on position, commanded rate, and estimator error responses.

Nickerson, J. A.↗

NASA NTRS1987

Galerkin/Runge-Kutta discretizations for parabolic equations with time dependent coefficients

A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for linear parabolic initial boundary value problems with time dependent coefficients. Unlike any classical counterpart, this class offers arbitrarily high order convergence while significantly avoiding what has been called order reduction. In support of this claim, error estimates are proved, and computational results are presented. Additionally, since the time stepping equations involve coefficient matrices changing at each time step, a preconditioned iterative technique is used to solve the linear systems only approximately. Nevertheless, the resulting algorithm is shown to preserve the original convergence rate while using only the order of work required by the base scheme applied to a linear parabolic problem with time independent coefficients. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.

Keeling, Stephen L.↗

NASA NTRS1985

Thematic Mapper Image Processing System - Geometric correction performance for Landsat-5

Geometric correction performance data are presented for the Landsat-5 Thematic Mapper and the Thematic Mapper Image Processing System. Temporal registration and geodetic rectification results are displayed in the form of 90 percent errors. Both error estimation and direct measurements demonstrate that the instrument and system meet performance requirements.

Brooks, J.↗

NASA NTRS1986

An exterior Poisson solver using fast direct methods and boundary integral equations with applications to nonlinear potential flow

A general method is developed combining fast direct methods and boundary integral equation methods to solve Poisson's equation on irregular exterior regions. The method requires O(N log N) operations where N is the number of grid points. Error estimates are given that hold for regions with corners and other boundary irregularities. Computational results are given in the context of computational aerodynamics for a two-dimensional lifting airfoil. Solutions of boundary integral equations for lifting and nonlifting aerodynamic configurations using preconditioned conjugate gradient are examined for varying degrees of thinness.

Young, D. P.↗

NASA NTRS1986

Combined optimization of image-gathering optics and image-processing algorithm for edge detection

This paper investigates the relationships between the image-gathering and image-processing systems for minimum mean-squared error estimation of scene characteristics. A stochastic optimization problem is formulated in which the objective is to determine a spatial characteristic of the scene rather than a feature of the already blurred, sampled, and noisy image data. The Wiener filter for the sampled image case is obtained as a special case, where the desired characteristics is scene restoration. Optimal edge detection is investigated. It is shown that the optimal edge detector compensates for the blurring introduced by the image-gathering optics, and, notably, that it is not circularly symmetric. The lack of circular symmetry is largely due to the geometric effects of the sampling lattice used in image acquisition.

Halyo, N.↗

NASA NTRS1986

An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in one space variable

The present adaptive FEM technique for convection-dominated problems is based on a Petrov-Galerkin scheme for spatial approximation, whose typical time-step employs test functions chosen to yield an approximate solution coinciding with the exact solutions at the finite element grid nodes. The derivation of truly local a posteriori error estimates is made possible by this procedure, which is also shown to be a very effective solver by the numerical examples presented.

Demkowicz, L.↗

NASA NTRS1986

Stability regions for multiloop LQ-regulated systems with state estimators

This note investigates the closed-loop stability of linear, time-invariant systems controlled by linear-quadratic-Gaussian (LQG) type controllers, when the actuators have nonlinearities. The nonlinearities N(sigma) are assumed to violate the standard LQ robustness condition either for values of sigma away from sigma = 0, or in a neighborhood of sigma = 0. The cases with an exponentially stable state estimator, and an estimator with ultimately bounded estimation error are considered, and expressions are obtained for the regions of attraction and ultimate boundedness.

Joshi, S. M.↗

NASA NTRS1986

Carrier tracking by smoothing filter improves symbol SNR

The potential benefit of using a smoothing filter to estimate carrier phase over use of phase locked loops (PLL) is determined. Numerical results are presented for the performance of three possible configurations of the deep space network advanced receiver. These are residual carrier PLL, sideband aided residual carrier PLL, and finally sideband aiding with a Kalman smoother. The average symbol signal to noise ratio (SNR) after losses due to carrier phase estimation error is computed for different total power SNRs, symbol rates and symbol SNRs. It is found that smoothing is most beneficial for low symbol SNRs and low symbol rates. Smoothing gains up to 0.4 dB over a sideband aided residual carrier PLL, and the combined benefit of smoothing and sideband aiding relative to a residual carrier loop is often in excess of 1 dB.

Pomalaza-Raez, Carlos A.↗

NASA NTRS1987

A further analysis for the minimum-variance deconvolution filter performance

Chi and Mendel (1984) analyzed the performance of minimum-variance deconvolution (MVD). In this correspondence, a further analysis of the performance of the MVD filter is presented. It is shown that the MVD filter performs like an inverse filter and a whitening filter as SNR goes to infinity, and like a matched filter as SNR goes to zero. The estimation error of the MVD filter is colored noise, but it becomes white when SNR goes to zero. This analysis also conects the error power-spectral density of the MVD filter with the spectrum of the causal-prediction error filter.

Chi, Chong-Yung↗