  Blind system identification is known to be a hard ill-posed problem and
without further assumptions, no unique solution is at hand. In this
contribution, we are concerned with the task of identifying an ARX model from
only output measurements. Driven by the task of identifying systems that are
turned on and off at unknown times, we seek a piecewise constant input and a
corresponding ARX model which approximates the measured outputs. We phrase this
as a rank minimization problem and present a relaxed convex formulation to
approximate its solution. The proposed method was developed to model power
consumption of electrical appliances and is now a part of a bigger energy
disaggregation framework. Code will be made available online.
