  Decentralized state estimation in a communication-constrained sensor network
is considered. The exchanged estimates are dimension-reduced to reduce the
communication load using a linear mapping to a lower-dimensional space. The
mean squared error optimal linear mapping depends on the particular estimation
method used. Several dimension-reducing algorithms are proposed, where each
algorithm corresponds to a commonly applied decentralized estimation method.
All except one of the algorithms are shown to be optimal. For the remaining
algorithm, we provide a convergence analysis where it is theoretically shown
that this algorithm converges to a stationary point and numerically shown that
the convergence rate is fast. A message-encoding solution is proposed that
allows for efficient communication when using the proposed dimension reduction
techniques. We also derive different properties from the proposed framework and
show its superiority in relation to baseline methods. The applicability of the
different algorithms is demonstrated using a simple fusion example and a more
realistic target tracking scenario.
