Solving Linear Equations with Disturbance Rejection

This paper aims to solve a system of linear equations with measurement noises. Different from existing noise-free or stochastic formulations, we assume the noisy data is subject to some deterministic and periodic disturbances. We develop an observer-based dynamic to estimate and reject these disturbances. This combined with some optimization method is proven to be able to recover the least squares solution to the nominal linear equations in both centralized and distributed settings. The effectiveness of this design is verified by a numerical example.