3,741 research outputs found
An Empirical Bayes Approach for Distributed Estimation of Spatial Fields
In this paper we consider a network of spatially distributed sensors which
collect measurement samples of a spatial field, and aim at estimating in a
distributed way (without any central coordinator) the entire field by suitably
fusing all network data. We propose a general probabilistic model that can
handle both partial knowledge of the physics generating the spatial field as
well as a purely data-driven inference. Specifically, we adopt an Empirical
Bayes approach in which the spatial field is modeled as a Gaussian Process,
whose mean function is described by means of parametrized equations. We
characterize the Empirical Bayes estimator when nodes are heterogeneous, i.e.,
perform a different number of measurements. Moreover, by exploiting the
sparsity of both the covariance and the (parametrized) mean function of the
Gaussian Process, we are able to design a distributed spatial field estimator.
We corroborate the theoretical results with two numerical simulations: a
stationary temperature field estimation in which the field is described by a
partial differential (heat) equation, and a data driven inference in which the
mean is parametrized by a cubic spline
Signal tracking beyond the time resolution of an atomic sensor by Kalman filtering
We study causal waveform estimation (tracking) of time-varying signals in a
paradigmatic atomic sensor, an alkali vapor monitored by Faraday rotation
probing. We use Kalman filtering, which optimally tracks known linear Gaussian
stochastic processes, to estimate stochastic input signals that we generate by
optical pumping. Comparing the known input to the estimates, we confirm the
accuracy of the atomic statistical model and the reliability of the Kalman
filter, allowing recovery of waveform details far briefer than the sensor's
intrinsic time resolution. With proper filter choice, we obtain similar
benefits when tracking partially-known and non-Gaussian signal processes, as
are found in most practical sensing applications. The method evades the
trade-off between sensitivity and time resolution in coherent sensing.Comment: 15 pages, 4 figure
Signal tracking beyond the time resolution of an atomic sensor by Kalman filtering
We study causal waveform estimation (tracking) of time-varying signals in a
paradigmatic atomic sensor, an alkali vapor monitored by Faraday rotation
probing. We use Kalman filtering, which optimally tracks known linear Gaussian
stochastic processes, to estimate stochastic input signals that we generate by
optical pumping. Comparing the known input to the estimates, we confirm the
accuracy of the atomic statistical model and the reliability of the Kalman
filter, allowing recovery of waveform details far briefer than the sensor's
intrinsic time resolution. With proper filter choice, we obtain similar
benefits when tracking partially-known and non-Gaussian signal processes, as
are found in most practical sensing applications. The method evades the
trade-off between sensitivity and time resolution in coherent sensing.Comment: 15 pages, 4 figure
Distributing the Kalman Filter for Large-Scale Systems
This paper derives a \emph{distributed} Kalman filter to estimate a sparsely
connected, large-scale, dimensional, dynamical system monitored by a
network of sensors. Local Kalman filters are implemented on the
(dimensional, where ) sub-systems that are obtained after
spatially decomposing the large-scale system. The resulting sub-systems
overlap, which along with an assimilation procedure on the local Kalman
filters, preserve an th order Gauss-Markovian structure of the centralized
error processes. The information loss due to the th order Gauss-Markovian
approximation is controllable as it can be characterized by a divergence that
decreases as . The order of the approximation, , leads to a lower
bound on the dimension of the sub-systems, hence, providing a criterion for
sub-system selection. The assimilation procedure is carried out on the local
error covariances with a distributed iterate collapse inversion (DICI)
algorithm that we introduce. The DICI algorithm computes the (approximated)
centralized Riccati and Lyapunov equations iteratively with only local
communication and low-order computation. We fuse the observations that are
common among the local Kalman filters using bipartite fusion graphs and
consensus averaging algorithms. The proposed algorithm achieves full
distribution of the Kalman filter that is coherent with the centralized Kalman
filter with an th order Gaussian-Markovian structure on the centralized
error processes. Nowhere storage, communication, or computation of
dimensional vectors and matrices is needed; only dimensional
vectors and matrices are communicated or used in the computation at the
sensors
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