Distributed Total Least Squares estimation over networks

We consider Total Least Squares (TLS) estimation in a network in which each node has access to a subset of equations of an overdetermined linear system. Previous distributed approaches require that the number of equations at each node be larger than the dimension L of the unknown parameter. We present novel distributed TLS estimators which can handle as few as a single equation per node. In the first scheme, the network computes an extended correlation matrix via standard iterative average consensus techniques, and the TLS estimate is extracted afterwards by means of an eigenvalue decomposition (EVD). The second scheme is EVD-free, but requires that a linear system of size L be solved at each iteration by each node. Replacing this step by a single Gauss-Seidel subiteration is shown to be an effective means to reduce computational cost without sacrificing performance.