Identification of linear systems with binary outputs using short independent experiments

Abstract

This paper considers the identification of linear systems based on binary measurements of the output. In contrast to existing techniques with strict requirements on the excitation signals, the identification is performed based on a sequence of short and independent measurements. The linear systems are represented using Finite Impulse Response (FIR) models, whose parameters are estimated by exploiting the known characteristics of the binary measurement. Two different methods are derived, both yielding convex parameter estimation problems that can be solved with standard software. The first achieves a high prediction accuracy but yields constrained optimization problems. A second alternative is therefore derived with a slightly worse performance but without constraints, such that solutions can be found more quickly. The identification procedure for both is illustrated on a simulation model.