  This paper aims at distributed algorithms for solving a system of linear
algebraic equations. Different from most existing formulations for this
problem, we assume that the local data at each node is not accurately measured
but subject to some disturbances. To be specific, the local measurement
consists of two parts: a nominal value and a multiple sinusoidal disturbance.
By introducing an identifier-enhanced observer to estimate the disturbance, we
present a novel distributed least squares solver for the linear equations using
noisy measurements. The proposed solver is proven to be able to recover the
least squares solution to the linear equations associated with the nominal
values irrespective of any multi-sinusoidal disturbance even with unknown
frequencies. We also show the robustness of the distributed solvers under
standard conditions against unstructured perturbations. The effectiveness of
our design is verified by a numerical example.
