Heterogeneous communication networks with their variety of application demands, time-varying load, and mixture of wired and wireless links pose several challenging problems in modeling and control. This paper focuses on estimation of the round trip time which is important for the transport layer because it impacts the throughput of TCP and allows efficient development of congestion control techniques for multimedia applications. An algorithm that combines expanding and fading memory polynomials to predict a future value of the round trip time from previously recorded values is proposed. Comparison using real data collected when streaming a video over the Internet proves that a composite filter of degree zero provides better start-up estimations than the round trip time estimator currently used in TCP. Additionally, the paper provides an algorithm of a composite polynomial filter of degree 3 and illustrates its ability in tracking the instant value of the round trip time.