391,128 research outputs found
Ergodicity and Accuracy of Optimal Particle Filters for Bayesian Data Assimilation
Data assimilation refers to the methodology of combining dynamical models and observed data with the objective of improving state estimation. Most data assimilation algorithms are viewed as approximations of the Bayesian posterior (filtering distribution) on the signal given the observations. Some of these approximations are controlled, such as particle filters which may be refined to produce the true filtering distribution in the large particle number limit, and some are uncontrolled, such as ensemble Kalman filter methods which do not recover the true filtering distribution in the large ensemble limit. Other data assimilation algorithms, such as cycled 3DVAR methods, may be thought of as controlled estimators of the state, in the small observational noise scenario, but are also uncontrolled in general in relation to the true filtering distribution. For particle filters and ensemble Kalman filters it is of practical importance to understand how and why data assimilation methods can be effective when used with a fixed small number of particles, since for many large-scale applications it is not practical to deploy algorithms close to the large particle limit asymptotic. In this paper, the authors address this question for particle filters and, in particular, study their accuracy (in the small noise limit) and ergodicity (for noisy signal and observation) without appealing to the large particle number limit. The authors first overview the accuracy and minorization properties for the true filtering distribution, working in the setting of conditional Gaussianity for the dynamics-observation model. They then show that these properties are inherited by optimal particle filters for any fixed number of particles, and use the minorization to establish ergodicity of the filters. For completeness we also prove large particle number consistency results for the optimal particle filters, by writing the update equations for the underlying distributions as recursions. In addition to looking at the optimal particle filter with standard resampling, they derive all the above results for (what they term) the Gaussianized optimal particle filter and show that the theoretical properties are favorable for this method, when compared to the standard optimal particle filter
Robust failure detection filters
The robustness of detection filters applied to the detection of actuator failures on a free-free beam is analyzed. This analysis is based on computer simulation tests of the detection filters in the presence of different types of model mismatch, and on frequency response functions of the transfers corresponding to the model mismatch. The robustness of detection filters based on a model of the beam containing a large number of structural modes varied dramatically with the placement of some of the filter poles. The dynamics of these filters were very hard to analyze. The design of detection filters with a number of modes equal to the number of sensors was trivial. They can be configured to detect any number of actuator failure events. The dynamics of these filters were very easy to analyze and their robustness properties were much improved. A change of the output transformation allowed the filter to perform satisfactorily with realistic levels of model mismatch
A Class of Mean-field LQG Games with Partial Information
The large-population system consists of considerable small agents whose
individual behavior and mass effect are interrelated via their state-average.
The mean-field game provides an efficient way to get the decentralized
strategies of large-population system when studying its dynamic optimizations.
Unlike other large-population literature, this current paper possesses the
following distinctive features. First, our setting includes the partial
information structure of large-population system which is practical from real
application standpoint. Specially, two cases of partial information structure
are considered here: the partial filtration case (see Section 2, 3) where the
available information to agents is the filtration generated by an observable
component of underlying Brownian motion; the noisy observation case (Section 4)
where the individual agent can access an additive white-noise observation on
its own state. Also, it is new in filtering modeling that our sensor function
may depend on the state-average. Second, in both cases, the limiting
state-averages become random and the filtering equations to individual state
should be formalized to get the decentralized strategies. Moreover, it is also
new that the limit average of state filters should be analyzed here. This makes
our analysis very different to the full information arguments of
large-population system. Third, the consistency conditions are equivalent to
the wellposedness of some Riccati equations, and do not involve the fixed-point
analysis as in other mean-field games. The -Nash equilibrium
properties are also presented.Comment: 19 page
Ergodicity and Accuracy of Optimal Particle Filters for Bayesian Data Assimilation
Data assimilation refers to the methodology of combining dynamical models and observed data with the objective of improving state estimation. Most data assimilation algorithms are viewed as approximations of the Bayesian posterior (filtering distribution) on the signal given the observations. Some of these approximations are controlled, such as particle filters which may be refined to produce the true filtering distribution in the large particle number limit, and some are uncontrolled, such as ensemble Kalman filter methods which do not recover the true filtering distribution in the large ensemble limit. Other data assimilation algorithms, such as cycled 3DVAR methods, may be thought of as controlled estimators of the state, in the small observational noise scenario, but are also uncontrolled in general in relation to the true filtering distribution. For particle filters and ensemble Kalman filters it is of practical importance to understand how and why data assimilation methods can be effective when used with a fixed small number of particles, since for many large-scale applications it is not practical to deploy algorithms close to the large particle limit asymptotic. In this paper, the authors address this question for particle filters and, in particular, study their accuracy (in the small noise limit) and ergodicity (for noisy signal and observation) without appealing to the large particle number limit. The authors first overview the accuracy and minorization properties for the true filtering distribution, working in the setting of conditional Gaussianity for the dynamics-observation model. They then show that these properties are inherited by optimal particle filters for any fixed number of particles, and use the minorization to establish ergodicity of the filters. For completeness we also prove large particle number consistency results for the optimal particle filters, by writing the update equations for the underlying distributions as recursions. In addition to looking at the optimal particle filter with standard resampling, they derive all the above results for (what they term) the Gaussianized optimal particle filter and show that the theoretical properties are favorable for this method, when compared to the standard optimal particle filter
A numerical study of the alpha model for two-dimensional magnetohydrodynamic turbulent flows
We explore some consequences of the ``alpha model,'' also called the
``Lagrangian-averaged'' model, for two-dimensional incompressible
magnetohydrodynamic (MHD) turbulence. This model is an extension of the
smoothing procedure in fluid dynamics which filters velocity fields locally
while leaving their associated vorticities unsmoothed, and has proved useful
for high Reynolds number turbulence computations. We consider several known
effects (selective decay, dynamic alignment, inverse cascades, and the
probability distribution functions of fluctuating turbulent quantities) in
magnetofluid turbulence and compare the results of numerical solutions of the
primitive MHD equations with their alpha-model counterparts' performance for
the same flows, in regimes where available resolution is adequate to explore
both. The hope is to justify the use of the alpha model in regimes that lie
outside currently available resolution, as will be the case in particular in
three-dimensional geometry or for magnetic Prandtl numbers differing
significantly from unity. We focus our investigation, using direct numerical
simulations with a standard and fully parallelized pseudo-spectral method and
periodic boundary conditions in two space dimensions, on the role that such a
modeling of the small scales using the Lagrangian-averaged framework plays in
the large-scale dynamics of MHD turbulence. Several flows are examined, and for
all of them one can conclude that the statistical properties of the large-scale
spectra are recovered, whereas small-scale detailed phase information (such as
e.g. the location of structures) is lost.Comment: 22 pages, 20 figure
The Initial Mass Function of the Orion Nebula Cluster across the H-burning limit
We present a new census of the Orion Nebula Cluster (ONC) over a large field
of view (>30'x30'), significantly increasing the known population of stellar
and substellar cluster members with precisely determined properties. We develop
and exploit a technique to determine stellar effective temperatures from
optical colors, nearly doubling the previously available number of objects with
effective temperature determinations in this benchmark cluster. Our technique
utilizes colors from deep photometry in the I-band and in two medium-band
filters at lambda~753 and 770nm, which accurately measure the depth of a
molecular feature present in the spectra of cool stars. From these colors we
can derive effective temperatures with a precision corresponding to better than
one-half spectral subtype, and importantly this precision is independent of the
extinction to the individual stars. Also, because this technique utilizes only
photometry redward of 750nm, the results are only mildly sensitive to optical
veiling produced by accretion. Completing our census with previously available
data, we place some 1750 sources in the Hertzsprung-Russel diagram and assign
masses and ages down to 0.02 solar masses. At faint luminosities, we detect a
large population of background sources which is easily separated in our
photometry from the bona fide cluster members. The resulting initial mass
function of the cluster has good completeness well into the substellar mass
range, and we find that it declines steeply with decreasing mass. This suggests
a deficiency of newly formed brown dwarfs in the cluster compared to the
Galactic disk population.Comment: 16 pages, 18 figures. Accepted for publication in The Astrophysical
Journa
Optimizing weak lensing mass estimates for cluster profile uncertainty
Weak lensing measurements of cluster masses are necessary for calibrating
mass-observable relations (MORs) to investigate the growth of structure and the
properties of dark energy. However, the measured cluster shear signal varies at
fixed mass M_200m due to inherent ellipticity of background galaxies,
intervening structures along the line of sight, and variations in the cluster
structure due to scatter in concentrations, asphericity and substructure. We
use N-body simulated halos to derive and evaluate a weak lensing circular
aperture mass measurement M_ap that minimizes the mass estimate variance <(M_ap
- M_200m)^2> in the presence of all these forms of variability. Depending on
halo mass and observational conditions, the resulting mass estimator improves
on M_ap filters optimized for circular NFW-profile clusters in the presence of
uncorrelated large scale structure (LSS) about as much as the latter improve on
an estimator that only minimizes the influence of shape noise. Optimizing for
uncorrelated LSS while ignoring the variation of internal cluster structure
puts too much weight on the profile near the cores of halos, and under some
circumstances can even be worse than not accounting for LSS at all. We briefly
discuss the impact of variability in cluster structure and correlated
structures on the design and performance of weak lensing surveys intended to
calibrate cluster MORs.Comment: 11 pages, 5 figures; accepted by MNRA
LOW AREA AND DELAY IMPLEMENTATION OF ERROR CORRECTING AND ERROR DETECTING CODE USING REVERSIBLE GATE
Digital filters are widely used in signal processing and communication systems. In some cases, the reliability of those systems is critical, and fault tolerant filter implementations are needed. Over the years, many techniques that exploit the filters’ structure and properties to achieve fault tolerance have been proposed. As technology scales, it enables more complex systems that incorporate many filters. In those complex systems, it is common that some of the filters operate in parallel, for example, by applying the same filter to different input signals. Recently, a simple technique that exploits the presence of parallel filters to achieve fault tolerance has been presented. In this brief, that idea is generalized to show that parallel filters can be protected using error correction codes (ECCs) in which each filter is the equivalent of a bit in a traditional ECC. This new scheme allows more efficient protection when the number of parallel filters is large. The technique is evaluated using a case study of parallel finite impulse response filters showing the effectiveness in terms of protection and implementation cost
- …