Distributed estimation has proven to be suitable for many multiagent system (MAS) applications, yet it relies heavily on information exchange via a costly and vulnerable communication network. This paper proposes a sensing-based distributed estimation algorithm that enables a local monitoring agent to expand its estimation capabilities beyond its sensing range without needing communication overhead. The key to expanding the limited sensing range is to incorporate the MAS's cooperative control protocol, allowing the monitoring agent to infer the state of out-of-range agents from the behavior of in-range agents that may interact with them. Then, the state estimation for out-of-range agents is performed through a Bayesian approach that considers the correlation of state estimates between in-range and out-of-range agents. This approach of only taking sensor measurements of local monitoring agents without interagent communications can successfully compensate for the existing communication-based distributed estimation methods. The performance of the proposed sensing-based distributed estimation algorithm is theoretically verified and demonstrated with numerical simulations of a multivehicle formation flight example.