We present a distributed projection algorithm for system identification of spatiotemporally invariant systems. Each subsystem communicates only with its immediate neighbor to share its current estimate along with a cumulative improvement index. Based on the cumulative improvement index, the best estimate available is picked in order to carry out the next iterate. For small estimation error, the scheme switches over to a "smart" averaging routine. The proposed algorithm guarantees to bring the local estimates arbitrarily close to one another. We demonstrate that the proposed scheme has a clear advantage over the standard projection algorithm and is amenable to indirect distributed adaptive control of spatiotemporally invariant systems. Our proposed algorithm is also suitable to address the estimation problem in distributed networks that arise in a variety of applications, such as environment monitoring, target localization and potential sensor network problems.