Due to the battery energy exhausted, sensor node becomes invalid and gets out of use, hence researching on energy efficiency query processing algorithms plays a significant role in the area of sensor networks. The results returned by the Top-k queries provide k largest (or smallest) sensed values and their locations, which are very useful for detecting abnormal events happened in the monitored region. Existing algorithms focus on returning either exact results or approximate results, which brings about higher communication consumption. To overcome the shortcomings of the existing Top-k queries and improve the energy efficiency, filter based Top-k monitoring algorithm is proposed in this paper, which aims at minimizing the expectation of communication overhead. Firstly, the robustness of filters guaranteeing the correctness and high energy efficiency is proposed, and then the communication overhead model is presented. Based on the essence of expectation and sensed data correlation, the probability of filter failure is derived. Finally, minimizing the expectation of communication overhead as an optimization objective, optimal filter threshold is proved and filter based Top-k monitoring algorithm (FTM) is proposed. Real dataset based experiments are carried out to evaluate the efficiency and effectiveness of the proposed algorithm. The theoretical analysis and performance evaluation demonstrate the accuracy and energy efficiency of the proposed algorithm.