Analysis of Optimal Reconstruction Methods Based on Incomplete Information From Sensor Nodes Using Kalman Filter

In order to reduce the communication cost of wireless sensor nodes, many methods have been proposed to reduce the transmission rate and reconstruct the signal based on incomplete information. Among them, Kalman filter (KF)-based methods provide the optimal reconstruction for the monitoring of linear systems with Gaussian noise. They require sensor nodes to intermittently transmit either the raw data or the preprocessed data mainly depending on nodes' processing capabilities. However, it is unclear whether the improvement of the reconstruction quality after using local processing is significant enough to compensate the energy overhead. To solve this question, this work studies three KF-based reconstruction solutions under different transmission strategies, considering the measurement noise, the transmission rate reduction and the packet loss. The reconstruction quality of each method is formulated with the help of Markov chain and a set of algebraic Riccati equations (AREs); the corresponding energy cost of the sensor node is further measured by the physical implementation. The results indicate that the advantage of using local processing is very sensitive to some parameters, e.g., the packet size. In addition, the three KF-based methods are compared with compressive sensing. Both simulation and experimental results demonstrate the superiority of the KF-based approaches for the analyzed linear systems.