Decentralized State Estimation In A Dimension-Reduced Linear Regression

Decentralized state estimation in a communication constrained sensor network is considered. To reduce the communication load only dimension-reduced estimates are exchanged between the networking agents. The considered dimension-reduction is restricted to be a linear mapping from a higher-dimensional space to a lower-dimensional space. The optimal, in the mean square error sense, linear mapping depends on the particular estimation method used. Several dimension-reducing algorithms are therefore 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. Applicability of the different algorithms is illustrated by a numerical evaluation.