A distributed estimation method over network based on compressed sensing

This article presents a distributed estimation method called compressed-combine-reconstruct-adaptive to estimate an unknown sparse parameter of interest from noisy measurement over networks based on compressed sensing. It is useful in some distributed networks where the robustness and low consumption are desired features. The compressed sensing theory is introduced in the distributed estimation to further reduce the communication load as the unknown parameter of interest is sparse in many situations. With the proposed method, each node compresses its estimation in a compressed dimension form. The nodes only exchange their compressed estimations to reduce the communication load over the network. Next, each node combines the compressed estimations of neighbors with its own compressed estimation using combination coefficients depend on the topology of the network. Then, the compressed estimations are reconstructed in full dimension form with a reconstruction algorithm. At last, the nodes update their estimations with normalized least mean square algorithm. The stability analysis of the proposed compressed-combine-reconstruct-adaptive method is illustrated in this article. Our method is compared with standard diffusion methods and communication reduced methods in simulations. The results show that the compressed-combine-reconstruct-adaptive method achieves nearly the same performance as the standard diffusion methods while reducing the communication load significantly, and with a better performance (network mean square error), network mean square error, steady-state mean-square deviation and steady-state mean-square deviation) than other communication reduced methods.