Distributed consensus state estimation (DCSE) is an effective fusion method in sensor networks. For the DCSE problem with asymmetrical topology, a four-layer functional model which describes the main flow of consistency state estimation technology is firstly proposed from the perspective of information processing, interaction and fusion. And then, considering the network topology of asymmetrical consistency of slow convergence rate, an adaptive assignment algorithm for consensus-rate factor based on dynamic topology information is designed according to the importance of communication links between nodes, and a Kalman consensus filter named adaptive weighted Kalman consensus filter (AW-KCF) is proposed based on the adaptive consistency rate factor. Finally, the simulation results indicate that AW-KCF outperforms KCF with faster convergence rate in sparse networks with asymmetrical topology.