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This paper aims at distributed algorithms for solving a system of linearalgebraic equations. Different from most existing formulations for thisproblem, we assume that the local data at each node is not accurately measuredbut subject to some disturbances. To be specific, the local measurementconsists of two parts: a nominal value and a multiple sinusoidal disturbance.By introducing an identifier-enhanced observer to estimate the disturbance, wepresent a novel distributed least squares solver for the linear equations usingnoisy measurements. The proposed solver is proven to be able to recover theleast squares solution to the linear equations associated with the nominalvalues irrespective of any multi-sinusoidal disturbance even with unknownfrequencies. We also show the robustness of the distributed solvers understandard conditions against unstructured perturbations. The effectiveness ofour design is verified by a numerical example.

On Measurement Disturbances in Distributed Least Squares Solvers for Linear Equations