By using di?®erent but non-zero, positive weights w
tain convexity), we can assign levels of importance to nodes in the network.
4 Sampling of Parametrized Fields
problem using logarithmic utility functions can be reduced to finding the opti-
2D plane, the resulting optimal utility function can be calculated numerically,
based on Closed-form Information Measures
p (c (r ) ??’ y ))
Chapter 2 Algorithms for Robotic Deployment of WSN
(a)
(b)
Fig. 2. Link capacity as a function of its distance with ?® = 2, rzone = 8, rmin = 2
(a), and the optimization problem for a simple four-link network configuration (b).
be the case, for example, with a bottom profile or systematic variations in temperature
or salinity, the field estimation can be integrated with localization in
order to improve these estimates. Given uncertainty models for the field measurements
and the location where the samples are taken, determining optimal
sampling points can be based on minimizing information measures. An example
of such measures is the state covariance estimates of the Kalman Filter.
Furthermore, certain simple assumptions, such as that the field distribution
41
Dan O. Popa and Frank L. Lewis
model with =2, rmin=2, rzone=8.
is linear in a given region, further allow us to compute a closed form solution
to determine the unknown coe?±cients of the 3D plane that describes the field
variable, given a known localization uncertainty described by the robot dynamic
model.
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