Consensus-based Distributed Total Least-squares Estimation Using Parametric Semidefinite Programming

We propose a new distributed algorithm to solve the total least-squares (TLS) problem when data are distributed over a multi-agent network. To develop the proposed algorithm, named distributed ADMM TLS (DA-TLS), we reformulate the TLS problem as a parametric semidefinite program and solve it using the alternating direction method of multipliers (ADMM). Unlike the existing consensus-based approaches to distributed TLS estimation, DA-TLS does not require careful tuning of any design parameter. Numerical experiments demonstrate that the DA-TLS converges to the centralized solution significantly faster than the existing consensus-based TLS algorithms.