NASA Scientific and Technical Aerospace Reports

and unfavorable responses for a particular control design but also to search for controls while favoring the values of the
parameters with higher chance of occurrence. In this manner, robust optimality is achieved while the characteristic
conservatism of conventional robust control methods is eliminated. Examples that admit closed form expressions for the
probabilistic metrics of the output are used to elucidate the nature of the problem at hand and validate the proposed
formulations.
Author
Stochastic Processes; Control Systems Design; Optimization; Robustness (Mathematics); Probability Theory; Uncertain
Systems
20040074324 Old Dominion Univ., Norfolk, VA, USA
An Investigation of Wave Propagations in Discontinuous Galerkin Method
Hu, Fang Q.; 2004; 4 pp.; In English; 7th AIAA/CEAS Aeroacoustics Conference, 2001, Maastricht, Netherlands
Contract(s)/Grant(s): NAG1-01044; No Copyright; Avail: CASI; A01, Hardcopy
Analysis of the discontinuous Galerkin method has been carried out for one- and two-dimensional system of hyperbolic
equations. Analytical, as well as numerical, properties of wave propagation in a DGM scheme are derived and verified with
direct numerical simulations. In addition to a systematic examination of the dissipation and dispersion errors, behaviours of
a DG scheme at an interface of two different grid topologies are also studied. Under the same framework, a quantitative
discrete analysis of various artificial boundary conditions is also conducted. Progress has been made in numerical boundary
condition treatment that is closely related to the application of DGM in aeroacoustics problems. Finally, Fourier analysis of
DGM for the Convective diffusion equation has also be studied in connection with the application of DG schemes for the
Navier-Stokes equations. This research has resulted in five(5) publications, plus one additional manuscript in preparation,
four(4) conference presentations, and three(3) departmental seminars, as summarized in part II. Abstracts of papers are given
in part 111 of this report.
Author
Wave Propagation; Galerkin Method; Two Dimensional Models; Numerical Analysis
65
STATISTICS AND PROBABILITY
Includes data sampling and smoothing; Monte Carlo method; time series analysis; and stochastic processes.
20040073593 Duke Univ., Durham, NC
Moving Target Depth Estimation for Passive Sonar, Using Sequential Resampling Techniques
Kraut, Shawn; Krolik, Jeffrey; Mar. 14, 2001; 7 pp.; In English; Original contains color illustrations
Contract(s)/Grant(s): F19628-00-C-0002
Report No.(s): AD-A422437; No Copyright; Avail: CASI; A02, Hardcopy
In this paper, the authors investigate an approach of joint estimation of range-rate and depth in a littoral environment,
rather than range and depth. Range-rate provides another dimension with which to discriminate targets against interfering
sources (such as moving ships). In addition, discrimination based on range-rate is more robust with respect to environmental
uncertainties as verified by simulations, and with respect to associated uncertainties in the horizontal wave numbers of the
channel modes used for the matched-field target response. Using this approach, the complex amplitudes of the modes are
treated as nuisance parameters, which comprise a hidden, first-order Markov state process. In lieu of an analytic expression
of the updated likelihood, they have investigated a technique of sequential resampling or particle filtering. They compare its
performance with the conventional matched-field processor (MFP), which localizes in depth and range. The limitations of this
particular technique seem to be its ability to compensate for low signal-to-noise ratio by integrating over many snapshots. It
should be emphasized, however, that this is a limitation of the particle-filter implementation investigated here and not a
limitation of the basic state-model approach of localizing with respect to range- rate and depth, rather than range and depth.
Future work will be focused on implementations that more effectively exploit the entire data history. (8 figures, 10 refs.)
DTIC
Depth; Depth Measurement; Regions; Sonar; Sound Ranging; Targets
224