Blind system identification is known to be an 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. We phrase
this as a constrained rank minimization problem and present a relaxed convex formulation to approximate its solution. To make the problem well posed we assume that the sought input lies in some known linear subspace.
Provided an arbitrary nonintrusive load monitoring (NILM) algorithm, we seek bounds on the probability of distinguishing between scenarios, given an aggregate power consumption signal. We introduce a framework for studying a general NILM algorithm, a
nd analyze the theory in the general case. Then, we specialize to the case where the error is Gaussian. In both cases, we are able to derive upper bounds on the probability of distinguishing scenarios. Finally, we apply the results to real data to derive bounds on the probability of distinguishing between scenarios as a function of the measurement noise, the sampling rate, and the device usage.
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.
