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NASA NTRS1986

Aerodynamics of Engine-Airframe Interaction

The report describes progress in research directed towards the efficient solution of the inviscid Euler and Reynolds-averaged Navier-Stokes equations for transonic flows through engine inlets, and past complete aircraft configurations, with emphasis on the flowfields in the vicinity of engine inlets. The research focusses upon the development of solution-adaptive grid procedures for these problems, and the development of multi-grid algorithms in conjunction with both, implicit and explicit time-stepping schemes for the solution of three-dimensional problems. The work includes further development of mesh systems suitable for inlet and wing-fuselage-inlet geometries using a variational approach. Work during this reporting period concentrated upon two-dimensional problems, and has been in two general areas: (1) the development of solution-adaptive procedures to cluster the grid cells in regions of high (truncation) error;and (2) the development of a multigrid scheme for solution of the two-dimensional Euler equations using a diagonalized alternating direction implicit (ADI) smoothing algorithm.

Caughey, D. A.↗

NASA NTRS1975

Use of known landmarks for satellite navigation

The use of known landmark measurements along with an onboard attitude reference system for estimation of both the ephemeris and attitude of an earth orbiting satellite is discussed. Simulation results are presented which show that, although known landmarks alone do not provide sufficient information to bound the uncertainty in attitude and ephemeris, they are useful in combination with other navigation aids, such as star tracking, ground tracking, or satellite tracking. An extended Kalman filter is used for optimal estimation. The result of using a smoothing algorithm is also shown.

White, R. L.↗

NASA NTRS1977

ALTKAL: An optimum linear filter for GEOS-3 altimeter data

ALTKAL is a computer program designed to smooth sea surface height data obtained from the GEOS 3 altimeter, and to produce minimum variance estimates of sea surface height and sea surface slopes, along with their standard derivations. The program operates by processing the data through a Kalman filter in both the forward and backward directions, and optimally combining the results. The sea surface height signal is considered to have a geoid signal, modeled by a third order Gauss-Markov process, corrupted by additive white noise. The governing parameters for the signal and noise processes are the signal correlation length and the signal-to-noise ratio. Mathematical derivations of the filtering and smoothing algorithms are presented. The smoother characteristics are illustrated by giving the frequency response, the data weighting sequence and the transfer function of a realistic steady-state smoother example. Based on nominal estimates for geoidal undulation amplitude and correlation length, standard deviations for the estimated sea surface height and slope are 12 cm and 3 arc seconds, respectively.

Fang, B. T.↗

NASA NTRS1979

Acceleration of transonic potential flow calculations on arbitrary meshes by the multiple grid method

A multiple grid method for transonic flow calculations is developed. The proposed scheme incorporates a generalized alternating direction method as the smoothing algorithm. Numerical experiments indicate that this multigrid alternating direction method converges rapidly and reliably for a range of cases typical of the cruising regime up to the onset of drag rise. It also appears that the method can be readily generalized to treat three-dimensional flows.

Jameson, A.↗

NASA NTRS1980

Analysis of urban area land cover using SEASAT Synthetic Aperture Radar data

Digitally processed SEASAT synthetic aperture raar (SAR) imagery of the Denver, Colorado urban area was examined to explore the potential of SAR data for mapping urban land cover and the compatability of SAR derived land cover classes with the United States Geological Survey classification system. The imagery is examined at three different scales to determine the effect of image enlargement on accuracy and level of detail extractable. At each scale the value of employing a simplistic preprocessing smoothing algorithm to improve image interpretation is addressed. A visual interpretation approach and an automated machine/visual approach are employed to evaluate the feasibility of producing a semiautomated land cover classification from SAR data. Confusion matrices of omission and commission errors are employed to define classification accuracies for each interpretation approach and image scale.

Henderson, F. M.↗

NASA NTRS1982

Precipitating electron energy flux and auroral zone conductances - An empirical model

Data from the low energy electron (LEE) experiments on the Atmosphere Explorer C and D satellites have been used to determine the average global distribution of the energy flux of precipitating auroral electrons and their average energy for different levels of geomagnetic activity. Measurements from the Atmosphere Explorer unified abstract file (15-s resolution) have been binned according to invariant latitude (in the range 50-90 deg), magnetic local time, and geomagnetic activity as measured by the Kp and auroral electrojet (AE) indices, separately. Bin-averaged values of precipitating energy flux and average energy have been calculated, and a smoothing algorithm used to reduce stochastic variations in the raw data. The results indicate that, for the parameters studied, the AE inces does a superior job of ordering the data with regard to geomagnetic activity. The global distribution of the auroral enhancement porition of the Pedersen and Hall conductances were inferred from the data by means of an empirical fit to detailed energy deposition calculations.

Spiro, R. W.↗

NASA NTRS1982

Estimating planetary terrain slopes from range measurements using a two dimensional spline smoothing technique

A new scanning scheme is presented for implementation for terrain slope estimation on a Martian exploratory rover. The rover will be equipped with a laser rangefinder as a principal sensing device for distance in its navigational equipment. A scan of the horizontal terrain from 5-50 m is indicated, and calculations are devised for quantifying the range errors. A constant incremental pointing angle is ruled out and a set of three pointing angles for different sub-areas of scan are defined. A two-dimensional smoothing algorithm is described for estimating slopes. The resultant scanning scheme involves the use of the characteristic curves derived from the relationships between the incremental elevation angle and the horizontal data spacing and the slope error index. A simulation was run and wavy terrain was produced from noise corrupted range measurements.

Kim, C. S.↗

NASA NTRS1983

A mathematical model for efficient estimation of aircraft motions

In the usual formulation of the aircraft state-estimation problem, motions along a flight trajectory are represented by a plant consisting of nonlinear state and measurement models. Problem solution using this formulation requires that both state- and measurement-dependent Jacobian matrices be evaluated along any trajectory. In this paper it is shown that a set of state variables can be chosen to realize a linear state model of very simple form, such that all nonlinearities appear in the measurement model. The potential advantage of the new formulation is computational: the Jacobian matrix corresponding to a linear state model is constant, a feature that should outweigh the fact that the measurement model is more complicated than in the conventinal formulation. To compare the modeling methods, aircraft motions from typical flight-test and accident data were estimated, using each formulation with the same off-line (smoothing) algorithm. The results of these experiments, reported in the paper, demonstrate clearly the computational superiority of the linear state-variable formulation. The procedure advocated here may be extended to other nonlinear estimation problems, including on-line (filtering) applications.

Bach, R. E., Jr.↗

NASA NTRS1984

A Method for Measuring the Effective Throughput Time Delay in Simulated Displays Involving Manual Control

The advent and widespread use of the computer-generated image (CGI) device to simulate visual cues has a mixed impact on the realism and fidelity of flight simulators. On the plus side, CGIs provide greater flexibility in scene content than terrain boards and closed circuit television based visual systems, and they have the potential for a greater field of view. However, on the minus side, CGIs introduce into the visual simulation relatively long time delays. In many CGIs, this delay is as much as 200 ms, which is comparable to the inherent delay time of the pilot. Because most GCIs use multiloop processing and smoothing algorithms and are linked to a multiloop host computer, it is seldom possible to identify a unique throughput time delay, and it is therefore difficult to quantify the performance of the closed loop pilot simulator system relative to the real world task. A method to address these issues using the critical task tester is described. Some empirical results from applying the method are presented, and a novel technique for improving the performance of GCIs is discussed.

Jewell, W. F.↗

NASA NTRS1986

Transformation of two and three-dimensional regions by elliptic systems

Efforts in transferring computational work from the LRC computer to the IRIS Graphics Workstation at MSU are reported and the computation of a conservative solution of a simple hyperbolic equation on an overlapping grid is discussed. Several conclusions concerning computations on overlapping grids are apparent. Problems only occur when there is a major difference in grid spacing on the individual component grids. In the case of hyperbolic equations, it is necessary that both interpolation and extrapolation be applied at the grid boundaries. When interpolated values are used at outflow boundary points, excessive oscillations in the numerical solution may be the result. The same conclusions would be valid for more complicated systems of hyperbolic equations such as the Euler equations for inviscid flow. Some of the solution values would be extrapolated at the overlap boundary, the exact number depending on the number of characteristics pointing out of the overlap region. It is also possible that similar boundary conditions may be needed for some parabolic equations such as high Reynolds number viscous flow equations. Efforts were also expended on the development of three-dimensional conservative interpolation procedures. Finally, the investigation of grid smoothing procedures were initiated during this reporting period. It was decided that the first grid smoothing algorithms will be based on the concepts of variational grid generation.

Mastin, C. W.↗

NASA NTRS1987

Fixed lag smoothers for carrier phase and frequency tracking

The application of fixed lag smoothing algorithms are presented for the problem of estimation of the phase and frequency of a sinusoidal carrier received in the presence of process noise and additive observation noise. A suboptimal structure consists of a phase-locked loop (PLL) followed by a post loop correction to the phase and frequency estimates. When the PLL is operating under a high signal-to-noise ratio, the phase detector is approximately linear, and the smoother equations then correspond to the optimal linear equations for an equivalent linear signal model. The performance of such a smoother can be predicted by the linear filtering theory. However, if the PLL is operating near the threshold region of the signal to noise ratio, the phase detector cannot be assumed to be linear. Then the actual performance of the smoother can significantly differ from that predicted by linear filtering theory. Both the theoretical and simulated performance of such smoothers derived on the basis of various models for the phase of frequency processes are presented.

Kumar, R.↗

NASA NTRS1987

Optimum filters and smoothers design for carrier phase and frequency tracking

The report presents the application of fixed lag smoothing algorithms to the problem of estimation of the phase and frequency of a sinusoidal carrier received in the presence of process noise and additive observation noise. A suboptimal structure consists of a phase-locked loop (PLL) followed by post-loop correction to the phase and frequency estimates. When the PLL is operating under high signal-to-noise ratio, the phase detector is approximately linear, and the smoother equations then correspond to the optimal linear equations for an equivalent linear signal model. The performance of such a smoother can be predicted by linear filtering theory. However, if the PLL is operating near the threshold region of the signal-to-noise ratio, the phase detector cannot be assumed to be linear. Then the actual performance of the smoother can significantly differ from that predicted by linear theory. In this report we present both the theoretical and simulated performance of such smoothers derived on the basis of various models for the phase and frequency processes.

Kumar, Rajendra↗

NASA NTRS1989

Multigrid calculation of three-dimensional turbomachinery flows

Research was performed in the general area of computational aerodynamics, with particular emphasis on the development of efficient techniques for the solution of the Euler and Navier-Stokes equations for transonic flows through the complex blade passages associated with turbomachines. In particular, multigrid methods were developed, using both explicit and implicit time-stepping schemes as smoothing algorithms. The specific accomplishments of the research have included: (1) the development of an explicit multigrid method to solve the Euler equations for three-dimensional turbomachinery flows based upon the multigrid implementation of Jameson's explicit Runge-Kutta scheme (Jameson 1983); (2) the development of an implicit multigrid scheme for the three-dimensional Euler equations based upon lower-upper factorization; (3) the development of a multigrid scheme using a diagonalized alternating direction implicit (ADI) algorithm; (4) the extension of the diagonalized ADI multigrid method to solve the Euler equations of inviscid flow for three-dimensional turbomachinery flows; and also (5) the extension of the diagonalized ADI multigrid scheme to solve the Reynolds-averaged Navier-Stokes equations for two-dimensional turbomachinery flows.

Caughey, David A.↗

NASA NTRS1988

Applications of square-root information filtering and smoothing in spacecraft orbit determination

The JPL (Jet Propulsion Laboratory) Orbit Determination Software System is a set of computer programs developed for the primary purpose of determining the flight path of deep-space mission spacecraft in NASA's Planetary Program and highly elliptical orbiting spacecraft in Earth orbit. The filtering processes available within the JPL Orbit Determination Software are discussed, and several examples are presented. In particular, solutions obtained by the Square Root Information Filter (SRIF) using Bierman's Estimation Subroutine Library (ESL) are discussed and compared with the solutions obtained by the singular value decomposition (SVD) technique. It is concluded that the SRIF filtering and smoothing algorithms are efficient and numerically stable for well-conditioned systems. The use of Bierman's ESL simplifies the task of maintaining the orbit determination software by providing efficient, tested filtering tools. For solving a large well-conditioned system (rank higher than 120), SRIF is approximately four times faster than SVD; however, for solving an ill-conditioned system, SVD is recommended.

Wang, Tseng-Chan↗

NASA NTRS1990

More About Fixed-Lag Smoothers For Tracking Carriers

Performance in presence of fades improved. Report amplifies and extends subject matter of "Performance of Fixed-Lag Phase-Smoothing Algorithms" (NPO-17202). Fixed-lag smoothers also used to mitigate effects of short, deep fades, including multipath effects, in mobile or fixed terrestrial receivers of frequency- or phase-modulated signals.

Kumar, Rajendra↗

NASA NTRS1993

Comparative mapping of Pluto's sub-Charon hemisphere - Three least squares models based on mutual event lightcurves

Observations of Charon transits are used here to derive preliminary maps of Pluto's sub-Charon hemisphere. Three models are used to describe the brightness of Pluto's surface as functions of latitude and longitude. Mapping results are presented using spherical harmonic functions, polynomial functions, and finite elements. A smoothing algorithm applied to the maps is described and the validity and resolution of the maps is tested by reconstruction from synthetic data. A preliminary finding from the maps is that the south polar region has the highest albedo of any location on the planet.

Young, Eliot F.↗

NASA NTRS1998

LAPS Lidar Measurements at the ARM Alaska Northslope Site (Support to FIRE Project)

This report consists of data summaries of the results obtained during the May 1998 measurement period at Barrow Alaska. This report does not contain any data interpretation or analysis of the results which will follow this activity. This report is forwarded with a data set on magnetic media which contains the reduced data from the LAPS lidar in 15 minute intervals. The data was obtained during the period 15-30 May 1998. The measurement period overlapped with several aircraft flights conducted by NASA as part of the FIRE project. The report contains a summary list of the data obtained plus figures that have been prepared to help visualize the measurement periods. The order of the presentation is as follows: Section 1. A copy of the Statement of Work for the planned activity of the second measurement period at the ARM Northslope site is provided. Section 2. A list of the data collection periods shows the number of one minute data records stored during each hour of operation and the corresponding size (Mbytes) of the one hour data folders. The folder and file names are composed from the year, month, day, hour and minute. The date/time information is given in UTC for easier comparison with other data sets. Section 3. A set of 4 comparisons between the LAPS lidar results and the sondes released by the ARM scientists from a location nearby the lidar. The lidar results show the +/- 1 sigma statistical error on each of the independent 75 m altitude bins of the data. This set of 4 comparisons was used to set and validate the calibration value which was then used for the complete data set. Section 4. A set of false color figures with up to 10 hours of specific humidity measurements are shown in each graph. Two days of measurements are shown on each page. These plots are crude representations of the data and permit a survey which indicates when the clouds were very low or where interesting events may occur in the results. These plots are prepared using the real time sequence plot program which has no smoothing in either the altitude or time (except that you are allowed to pick the integration time and time step. All of these plots were prepared with 15 minute integration and 5 minute time step. Section 5. A set of time sequence data for all of the extended observation periods are shown with a smoothing algorithm from the Matlab plotting library. Most of these data are integrated for 5 minutes and stepped at I minute intervals but several plots are shown with both 15 minute integration and 5 minute steps. The upper level on these data was selected and converted to the white background where the error in the specific humidity reached 25%. Section 6. The set of one hour integrated plots shown with up to 4 hours per page are provided- from the real time analysis snapshot program. The only difference in these plots and the real time display is that the plots are stopped at an altitude where the error appears to be too large for the data to contain any meaningful information.

Philbrick, C. Russell↗

NASA NTRS1997

Analysis of Texture Using the Fractal Model

Properties such as the fractal dimension (FD) can be used for feature extraction and classification of regions within an image. The FD measures the degree of roughness of a surface, so this number is used to characterize a particular region, in order to differentiate it from another. There are two basic approaches discussed in the literature to measure FD: the blanket method, and the box counting method. Both attempt to measure FD by estimating the change in surface area with respect to the change in resolution. We tested both methods but box counting resulted computationally faster and gave better results. Differential Box Counting (DBC) was used to segment a collage containing three textures. The FD is independent of directionality and brightness so five features were used derived from the original image to account for directionality and gray level biases. FD can not be measured on a point, so we use a window that slides across the image giving values of FD to the pixel on the center of the window. Windowing blurs the boundaries of adjacent classes, so an edge-preserving, feature-smoothing algorithm is used to improve classification within segments and to make the boundaries sharper. Segmentation using DBC was 90.8910 accurate.

Navas, William↗