Abstract: Aiming at the situation that the inter-node correlation is weak but the inner-node correlation is strong, an adaptive compressed sensing algorithm based on Kalman predictor is proposed. In a system model with relays, each sensing node selects Kalman prediction to decide whether to be active, so that the number of active nodes decreases and is sparse in the spatial domain. Morever, a sequential reconstruction algorithm which chooses the number of relays adaptively is proposed in the fusion center to reduse the energy consumption of the relays. Simulation results demonstrate that, compared with other compressed sensing algorithm based on predictors, the calculation complexity of the sensing nodes and the energy consumption of the relays of the proposed algorithm are much lower without any additional error.