2,202 research outputs found
Telescoping Recursive Representations and Estimation of Gauss-Markov Random Fields
We present \emph{telescoping} recursive representations for both continuous
and discrete indexed noncausal Gauss-Markov random fields. Our recursions start
at the boundary (a hypersurface in , ) and telescope inwards.
For example, for images, the telescoping representation reduce recursions from
to , i.e., to recursions on a single dimension. Under
appropriate conditions, the recursions for the random field are linear
stochastic differential/difference equations driven by white noise, for which
we derive recursive estimation algorithms, that extend standard algorithms,
like the Kalman-Bucy filter and the Rauch-Tung-Striebel smoother, to noncausal
Markov random fields.Comment: To appear in the Transactions on Information Theor
Finding Non-overlapping Clusters for Generalized Inference Over Graphical Models
Graphical models use graphs to compactly capture stochastic dependencies
amongst a collection of random variables. Inference over graphical models
corresponds to finding marginal probability distributions given joint
probability distributions. In general, this is computationally intractable,
which has led to a quest for finding efficient approximate inference
algorithms. We propose a framework for generalized inference over graphical
models that can be used as a wrapper for improving the estimates of approximate
inference algorithms. Instead of applying an inference algorithm to the
original graph, we apply the inference algorithm to a block-graph, defined as a
graph in which the nodes are non-overlapping clusters of nodes from the
original graph. This results in marginal estimates of a cluster of nodes, which
we further marginalize to get the marginal estimates of each node. Our proposed
block-graph construction algorithm is simple, efficient, and motivated by the
observation that approximate inference is more accurate on graphs with longer
cycles. We present extensive numerical simulations that illustrate our
block-graph framework with a variety of inference algorithms (e.g., those in
the libDAI software package). These simulations show the improvements provided
by our framework.Comment: Extended the previous version to include extensive numerical
simulations. See http://www.ima.umn.edu/~dvats/GeneralizedInference.html for
code and dat
Completely-Positive Non-Markovian Decoherence
We propose an effective Hamiltonian approach to investigate decoherence of a
quantum system in a non-Markovian reservoir, naturally imposing the complete
positivity on the reduced dynamics of the system. The formalism is based on the
notion of an effective reservoir, i.e., certain collective degrees of freedom
in the reservoir that are responsible for the decoherence. As examples for
completely positive decoherence, we present three typical decoherence processes
for a qubit such as dephasing, depolarizing, and amplitude-damping. The effects
of the non-Markovian decoherence are compared to the Markovian decoherence.Comment: 8 pages, 1 figur
Processing of GPS Data using Accuracy Enhancement Techniques for Sag Monitoring Device
The paper describes an experimental set up used to collect GPS data in real time. The effect of weather of particular location is also considered in the paper. The major problems in GPS measurements may be due to tall buildings, high mountains, overhead foliage etc. The positioning data provided directly by the satellites are subject to variety of error sources such as thermal noise, tropospheric delays, multipath error, ephemeris errors, satellite clock errors and ionospheric delays before they are processed into position and time solution in the GPS receiver. The paper discusses DSP techniques such as Bad Data identification and modification and Kalman filter used to enhance the accuracy of GPS altitude measurements. Results obtained demonstrate that Kalman filter after Bad Data identification and modification technique significantly reduced the errors in GPS altitude measurements
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