Distributed Recursive State Estimation Over Sensor Networks With Compress-and-Forward Relays: A Compressed Sensing Strategy

Abstract

This article addresses the distributed recursive state estimation problem for wireless sensor networks operating under stringent energy, bandwidth, and computational constraints. A compress-and-forward relay architecture integrated with compressed sensing is proposed to reduce the transmission burden while preserving the information required for reliable estimation. Within the proposed framework, sensor measurements are compressed at the relay and reconstructed at the remote estimator from low-dimensional observations. To account for the uncertainty induced by wireless transmission, the effects of channel fading and channel noise on the compressed-sensing reconstruction process are analyzed, and a corresponding reconstruction error model is established by exploiting channel statistical characteristics. On this basis, a distributed recursive state estimator is developed to mitigate channel-induced distortion. An upper bound on the estimation error covariance is then derived in the presence of reconstruction error, and the estimator gains are determined by minimizing this bound. Simulation studies based on an unmanned surface vehicle (USV) mooring-assisted dynamic positioning system demonstrate that the proposed method can maintain satisfactory estimation accuracy and robustness while significantly reducing communication overhead.