Power iteration-based distributed total least squares estimation in ad hoc sensor networks

In this paper, we revisit the distributed total least squares (D-TLS) algorithm, which operates in an ad hoc sensor network where each node has access to a subset of the equations of an overdetermined set of linear equations. The D-TLS algorithm computes the total least squares (TLS) solution of the full set of equations in a fully distributed fashion (without fusion center). We modify the D-TLS algorithm to eliminate the large computational complexity due to an eigenvalue decomposition (EVD) at every node and in each iteration. In the modified algorithm, a single power iteration (PI) is performed instead of a full EVD computation, which significantly reduces the computational complexity. Since the nodes then do not exchange their true eigenvectors, the theoretical convergence results of the original D-TLS algorithm do not hold anymore. Nevertheless, we find that this PI-based D-TLS algorithm still converges to the network-wide TLS solution, under certain assumptions, which are often satisfied in practice. We provide simulation results to demonstrate the convergence of the algorithm, even when some of these assumptions are not satisfied.