3,249 research outputs found
The Recursive Form of Error Bounds for RFS State and Observation with Pd<1
In the target tracking and its engineering applications, recursive state
estimation of the target is of fundamental importance. This paper presents a
recursive performance bound for dynamic estimation and filtering problem, in
the framework of the finite set statistics for the first time. The number of
tracking algorithms with set-valued observations and state of targets is
increased sharply recently. Nevertheless, the bound for these algorithms has
not been fully discussed. Treating the measurement as set, this bound can be
applied when the probability of detection is less than unity. Moreover, the
state is treated as set, which is singleton or empty with certain probability
and accounts for the appearance and the disappearance of the targets. When the
existence of the target state is certain, our bound is as same as the most
accurate results of the bound with probability of detection is less than unity
in the framework of random vector statistics. When the uncertainty is taken
into account, both linear and non-linear applications are presented to confirm
the theory and reveal this bound is more general than previous bounds in the
framework of random vector statistics.In fact, the collection of such
measurements could be treated as a random finite set (RFS)
An improved method to test the Distance--Duality relation
Many researchers have performed cosmological-model-independent tests for the
distance duality (DD) relation. Theoretical work has been conducted based on
the results of these tests. However, we find that almost all of these tests
were perhaps not cosmological-model-independent after all, because the distance
moduli taken from a given type Ia supernovae (SNe Ia) compilation are dependent
on a given cosmological model and Hubble constant. In this Letter, we overcome
these defects and by creating a new cosmological-model-independent test for the
DD relation. We use the original data from the Union2 SNe Ia compilation and
the angular diameter distances from two galaxy cluster samples compiled by De
Filippis et al. and Bonamente et al. to test the DD relation. Our results
suggest that the DD relation is compatible with observations, and the spherical
model is slightly better than the elliptical model at describing the intrinsic
shape of galaxy clusters if the DD relation is valid. However, these results
are different from those of previous work.Comment: 5 pages, 2 figures, published on ApJ
Cosmological constraints from Radial Baryon Acoustic Oscillation measurements and Observational Hubble data
We use the Radial Baryon Acoustic Oscillation (RBAO) measurements, distant
type Ia supernovae (SNe Ia), the observational data (OHD) and the Cosmic
Microwave Background (CMB) shift parameter data to constrain cosmological
parameters of CDM and XCDM cosmologies and further examine the role of
OHD and SNe Ia data in cosmological constraints. We marginalize the likelihood
function over by integrating the probability density to obtain the best fitting results and the confidence regions
in the plane.With the combination analysis for
both of the {\rm }CDM and XCDM models, we find that the confidence
regions of 68.3%, 95.4% and 99.7% levels using OHD+RBAO+CMB data are in good
agreement with that of SNe Ia+RBAO+CMB data which is consistent with the result
of Lin et al's work. With more data of OHD, we can probably constrain the
cosmological parameters using OHD data instead of SNe Ia data in the future.Comment: 8 pages, 6 figures, 2 tables, accepted for publication in Physics
Letters
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