Cryptographic approaches are vulnerable to impersonation attacks when nodes become compromised. Meanwhile, trust-based judgment and confirmation of cluster heads in WSN imposes higher communication cost. Trust management and authentication on cluster heads in WSN are essential in research on the mechanisms of secure data aggregation at present. In this paper, an energy attenuation model is adopted to describe event sensing in a kind of WSNs. Approximate evaluation on distance between occurring event and nodes within a cluster is achieved in case the location of the event is not known. Distribution properties of data points with clustering characteristics based on fitting curve construction are theoretically analyzed. In addition, the mechanism on trust authentication on cluster heads is also refined. Experimental results show that the proposed mechanism has much better performance on fitting accuracy and malicious CH recognition than previous works.