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Distributed State Estimation With Dimension Reduction Preprocessing

System state estimation relies heavily on the measurements. With the advance of sensing technology, the ability to measure is no longer a bottleneck in many systems, and more and more researchers now focus on the rich-information setting, i.e., big data. However, although information never hurts, it does not help unconditionally. How to make the most of it depends on whether we can process the data efficiently. In some systems, the inherent constraint such as the bandwidth and cost makes it necessary to reduce the dimension of the measurement before further processing. The problem that the raw measurements are first preprocessed to reduce size and then used for estimation is addressed in this paper. It is shown that there is a lower bound on the size of the preprocessed data such that if the size is beyond the bound, there exists a closed-form estimator design that the linear minimum mean-square estimation can be obtained. Moreover, we propose an algorithm that is guaranteed to converge to a stationary point to design an estimator in the conditions that the lower bound cannot be reached. Besides convergence, the proposed algorithm guarantees bounded performance loss compared with the global optimal solution under some additional conditions. Finally, simulation results in three different applications are shown to demonstrate the effectiveness of the proposed algorithm.