7 DISCUSSION & CONCLUSION
An approach for the decentralized estimation of the
motion of a spatio-temporal field with a WSN has
been presented. The performance of the algorithm
has been illustrated by examples of a simulated
dynamic field and sensor network. In the following,
possible extensions of the proposed algorithm are
discussed.
Sensor Network: Currently, stationary sensors and
time-synchronized sampling is assumed, since this is
considered the base case and eases the equations.
However, moving sensors monitoring spatio-
temporal fields, such as cars for measuring rainfall
(Fitzner et al., 2013); (Haberlandt and Sester, 2010),
exist and provide interesting possibilities for
extension. Further, the approach uses single-hop
communication and therefore assumes local
translational motion within the sensor neighborhood.
If motion is assumed to be constant over larger
neighborhoods, motion estimation accuracy could be
improved by multi-hop communication.
Accuracy of Gradient Constraint: Currently, the
accuracy of a gradient constraint is solely
determined by spatial configuration of the
neighborhood generating the constraint. However, it
is clear and already discussed in early work on
optical flow such as (Lucas et al., 1981) that field
properties such as the magnitude of the first or
second derivative are indicators of the accuracy.
Including these as well as weighting measures based
on spatial distance is planned for future extensions.
Kalman Filter: The kalman filter proposed in this
work comprises the motion vector only and
therefore, constant motion over time is assumed.
Possible motion changes are solely modeled by the
prediction error variance, which is larger zero and
hence, allows for state changes over time. A more
realistic assumption is motion change constancy that
could be implemented by adding motion change
variables to the kalman state. Further, the kalman
filter assumes white gaussian noise for both,
prediction and measurement, a requirement that has
to be tested in a real deployment of the algorithm. In
addition, the values for the kalman filter noise
parameters and have been set rather arbitrarily
based on a visual evaluation of the motion
estimation results. In future work, methods for
estimating these from the data will be investigated.
ACKNOWLEDGEMENTS
We gratefully acknowledge the financial support of
the German Research Foundation (DFG, SE645/8-
2).
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