212 research outputs found
The Three-Dimensional Mass Distribution in NGC 1700
A variety of modeling techniques is used with surface photometry from the
literature and recently acquired high-accuracy stellar kinematic data to
constrain the three-dimensional mass distribution in the luminous cuspy
elliptical galaxy NGC 1700. First, we model the radial velocity field and
photometry, and, using a Bayesian technique, estimate the triaxiality T and
short-to-long axis ratio c in five concentric annuli between approximately 1
and 3 effective radii. The results are completely consistent with T being
constant inside about 2.5 r_e (36 arcsec; 6.7/h kpc). Adding an assumption of
constant T as prior information gives an upper limit of T < 0.16 (95%
confidence); this relaxes to T < 0.22 if it is also assumed that there is
perfect alignment between the angular momentum and the galaxy's intrinsic short
axis. Near axisymmetry permits us then to use axisymmetric models to constrain
the radial mass profile. Using the Jeans (moment) equations, we demonstrate
that 2-integral, constant-M/L models cannot fit the data; but a 2-integral
model in which the cumulative enclosed M/L increases by a factor of roughly 2
from the center out to 12/h kpc can. Three-integral models constructed by
quadratic programming show that, in fact, no constant-M/L model is consistent
with the kinematics. Anisotropic 3-integral models with variable M/L, while not
uniquely establishing a minimum acceptable halo mass, imply, as do the moment
models, a cumulative M/L_B approximately 10 h at 12/h kpc. We conclude that NGC
1700 represents the best stellar dynamical evidence to date for dark matter in
elliptical galaxies.Comment: 26 pages, Latex, AASTeX v4.0, with 11 eps figures. To appear in The
Astronomical Journal, January 1999. Figures 1 and 3 are color but are
readable in b/
Multitarget tracking and terrain-aided navigation using square-root consider filters
Filtering is a term used to describe methods that estimate the values of partially observed states, such as the position, velocity, and attitude of a vehicle, using current observations that are corrupted due to various sources, such as measurement noise, transmission dropouts, and spurious information. The study of filtering has been an active focus of research for decades, and the resulting filters have been the cornerstone of many of humankind\u27s greatest technological achievements. However, these achievements are enabled principally by the use of specialized techniques that seek to, in some way, combat the negative impacts that processor roundoff and truncation error have on filtering.
Two of these specialized techniques are known as square-root filters and consider filters. The former alleviates the fragility induced from estimating error covariance matrices by, instead, managing a factorized representation of that matrix, known as a square-root factor. The latter chooses to account for the statistical impacts a troublesome system parameter has on the overall state estimate without directly estimating it, and the result is a substantial reduction in numerical sensitivity to errors in that parameter. While both of these techniques have found widespread use in practical application, they have never been unified in a common square-root consider framework. Furthermore, consider filters are historically rooted to standard, vector-valued estimation techniques, and they have yet to be generalized to the emerging, set-valued estimation tools for multitarget tracking.
In this dissertation, formulae for the square-root consider filter are derived, and the result is extended to finite set statistics-based multitarget tracking tools. These results are used to propose a terrain-aided navigation concept wherein data regarding a vehicle\u27s environment is used to improve its state estimate, and square-root consider techniques provide the numerical stability necessary for an onboard navigation application. The newly developed square-root consider techniques are shown to be much more stable than standard formulations, and the terrain-aided navigation concept is applied to a lunar landing scenario to illustrate its applicability to navigating in challenging environments --Abstract, page iii
The Equity Premium and Structural Breaks
A long return history is useful in estimating the current equity premium even if the historical distribution has experienced structural breaks. The long series helps not only if the timing of breaks is uncertain but also if one believes that large shifts in the premium are unlikely or that the premium is associated, in part, with volatility. Our framework incorporates these features along with a belief that prices are likely to move opposite to contemporaneous shifts in the premium. The estimated premium since 1834 fluctuates between four and six percent and exhibits its sharpest drop in the last decade.
GREAT3 results I: systematic errors in shear estimation and the impact of real galaxy morphology
We present first results from the third GRavitational lEnsing Accuracy
Testing (GREAT3) challenge, the third in a sequence of challenges for testing
methods of inferring weak gravitational lensing shear distortions from
simulated galaxy images. GREAT3 was divided into experiments to test three
specific questions, and included simulated space- and ground-based data with
constant or cosmologically-varying shear fields. The simplest (control)
experiment included parametric galaxies with a realistic distribution of
signal-to-noise, size, and ellipticity, and a complex point spread function
(PSF). The other experiments tested the additional impact of realistic galaxy
morphology, multiple exposure imaging, and the uncertainty about a
spatially-varying PSF; the last two questions will be explored in Paper II. The
24 participating teams competed to estimate lensing shears to within systematic
error tolerances for upcoming Stage-IV dark energy surveys, making 1525
submissions overall. GREAT3 saw considerable variety and innovation in the
types of methods applied. Several teams now meet or exceed the targets in many
of the tests conducted (to within the statistical errors). We conclude that the
presence of realistic galaxy morphology in simulations changes shear
calibration biases by per cent for a wide range of methods. Other
effects such as truncation biases due to finite galaxy postage stamps, and the
impact of galaxy type as measured by the S\'{e}rsic index, are quantified for
the first time. Our results generalize previous studies regarding sensitivities
to galaxy size and signal-to-noise, and to PSF properties such as seeing and
defocus. Almost all methods' results support the simple model in which additive
shear biases depend linearly on PSF ellipticity.Comment: 32 pages + 15 pages of technical appendices; 28 figures; submitted to
MNRAS; latest version has minor updates in presentation of 4 figures, no
changes in content or conclusion
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