We consider the distributed estimation problem, where a set of nodes is required to collectively estimate some parameter vector of interest with unknown or variable tap-length. In practice, a sufficiently large filter length is utilized in such contexts to avoid a large excess mean square error at steady state, thereby resulting in slower convergence rate and increased computations. In this work we motivate and propose a new diffusion-based variable tap-length algorithm, which is able to track tap-length changes during the convergence process.

Theoretical analyses are provided in terms of steady-state performance and convergence performance, which are verified by simulation results. Some general criteria for parameter selections are also given according to the performance analyses. Numerical simulations demonstrate the efficiency of the proposed algorithm as compared with existing techniques, and robustness to parameter settings provided the parameter choice guidelines are satisfied.