  Technological advances have made wireless sensors cheap and reliable enough
to be brought into industrial use. A major challenge arises from the fact that
wireless channels introduce random packet dropouts. Power control and coding
are key enabling technologies in wireless communications to ensure efficient
communications. In the present work, we examine the role of power control and
coding for Kalman filtering over wireless correlated channels. Two estimation
architectures are considered: In the first, the sensors send their measurements
directly to a single gateway. In the second scheme, wireless relay nodes
provide additional links. The gateway decides on the coding scheme and the
transmitter power levels of the wireless nodes. The decision process is carried
out on-line and adapts to varying channel conditions in order to improve the
trade-off between state estimation accuracy and energy expenditure. In
combination with predictive power control, we investigate the use of
multiple-description coding, zero-error coding and network coding and provide
sufficient conditions for the expectation of the estimation error covariance
matrix to be bounded. Numerical results suggest that the proposed method may
lead to energy savings of around 50 %, when compared to an alternative scheme,
wherein transmission power levels and bit-rates are governed by simple logic.
In particular, zero-error coding is preferable at time instances with high
channel gains, whereas multiple-description coding is superior for time
instances with low gains. When channels between the sensors and the gateway are
in deep fades, network coding improves estimation accuracy significantly
without sacrificing energy efficiency.
