9,925 research outputs found
Data assimilation in the low noise regime with application to the Kuroshio
On-line data assimilation techniques such as ensemble Kalman filters and
particle filters lose accuracy dramatically when presented with an unlikely
observation. Such an observation may be caused by an unusually large
measurement error or reflect a rare fluctuation in the dynamics of the system.
Over a long enough span of time it becomes likely that one or several of these
events will occur. Often they are signatures of the most interesting features
of the underlying system and their prediction becomes the primary focus of the
data assimilation procedure. The Kuroshio or Black Current that runs along the
eastern coast of Japan is an example of such a system. It undergoes infrequent
but dramatic changes of state between a small meander during which the current
remains close to the coast of Japan, and a large meander during which it bulges
away from the coast. Because of the important role that the Kuroshio plays in
distributing heat and salinity in the surrounding region, prediction of these
transitions is of acute interest. Here we focus on a regime in which both the
stochastic forcing on the system and the observational noise are small. In this
setting large deviation theory can be used to understand why standard filtering
methods fail and guide the design of the more effective data assimilation
techniques. Motivated by our analysis we propose several data assimilation
strategies capable of efficiently handling rare events such as the transitions
of the Kuroshio. These techniques are tested on a model of the Kuroshio and
shown to perform much better than standard filtering methods.Comment: 43 pages, 12 figure
Inverse Problems and Data Assimilation
These notes are designed with the aim of providing a clear and concise
introduction to the subjects of Inverse Problems and Data Assimilation, and
their inter-relations, together with citations to some relevant literature in
this area. The first half of the notes is dedicated to studying the Bayesian
framework for inverse problems. Techniques such as importance sampling and
Markov Chain Monte Carlo (MCMC) methods are introduced; these methods have the
desirable property that in the limit of an infinite number of samples they
reproduce the full posterior distribution. Since it is often computationally
intensive to implement these methods, especially in high dimensional problems,
approximate techniques such as approximating the posterior by a Dirac or a
Gaussian distribution are discussed. The second half of the notes cover data
assimilation. This refers to a particular class of inverse problems in which
the unknown parameter is the initial condition of a dynamical system, and in
the stochastic dynamics case the subsequent states of the system, and the data
comprises partial and noisy observations of that (possibly stochastic)
dynamical system. We will also demonstrate that methods developed in data
assimilation may be employed to study generic inverse problems, by introducing
an artificial time to generate a sequence of probability measures interpolating
from the prior to the posterior
A particle filtering approach for joint detection/estimation of multipath effects on GPS measurements
Multipath propagation causes major impairments to Global
Positioning System (GPS) based navigation. Multipath results in biased GPS measurements, hence inaccurate position estimates. In this work, multipath effects are considered as abrupt changes affecting the navigation system. A multiple model formulation is proposed whereby the changes are represented by a discrete valued process. The detection of the errors induced by multipath is handled by a Rao-Blackwellized particle filter (RBPF). The RBPF estimates the indicator process jointly with the navigation states and multipath biases. The interest of this approach is its ability to integrate a priori constraints about the propagation environment. The detection is improved by using information from near future GPS measurements at the particle filter (PF) sampling step. A computationally modest delayed sampling is developed, which is based on a minimal duration assumption for multipath effects. Finally, the standard PF resampling stage is modified to include an hypothesis test based decision step
A Randomized Greedy Algorithm for Near-Optimal Sensor Scheduling in Large-Scale Sensor Networks
We study the problem of scheduling sensors in a resource-constrained linear
dynamical system, where the objective is to select a small subset of sensors
from a large network to perform the state estimation task. We formulate this
problem as the maximization of a monotone set function under a matroid
constraint. We propose a randomized greedy algorithm that is significantly
faster than state-of-the-art methods. By introducing the notion of curvature
which quantifies how close a function is to being submodular, we analyze the
performance of the proposed algorithm and find a bound on the expected mean
square error (MSE) of the estimator that uses the selected sensors in terms of
the optimal MSE. Moreover, we derive a probabilistic bound on the curvature for
the scenario where{\color{black}{ the measurements are i.i.d. random vectors
with bounded norm.}} Simulation results demonstrate efficacy of the
randomized greedy algorithm in a comparison with greedy and semidefinite
programming relaxation methods
A Randomized Greedy Algorithm for Near-Optimal Sensor Scheduling in Large-Scale Sensor Networks
We study the problem of scheduling sensors in a resource-constrained linear
dynamical system, where the objective is to select a small subset of sensors
from a large network to perform the state estimation task. We formulate this
problem as the maximization of a monotone set function under a matroid
constraint. We propose a randomized greedy algorithm that is significantly
faster than state-of-the-art methods. By introducing the notion of curvature
which quantifies how close a function is to being submodular, we analyze the
performance of the proposed algorithm and find a bound on the expected mean
square error (MSE) of the estimator that uses the selected sensors in terms of
the optimal MSE. Moreover, we derive a probabilistic bound on the curvature for
the scenario where{\color{black}{ the measurements are i.i.d. random vectors
with bounded norm.}} Simulation results demonstrate efficacy of the
randomized greedy algorithm in a comparison with greedy and semidefinite
programming relaxation methods
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