Identification of linear systems with binary output measurements using short independent experiments

Abstract

This paper presents a novel identification technique for linear systems based on binary measurements of an analog output signal of the device under test. This type of measurement arises when the output signal is not measured directly with a high resolution sensor but it is only known whether its value exceeds a given threshold or not. The presented technique performs the estimation using a combination of many short and independent low resolution measurement runs, each of which contains only a limited amount of information. This is a significant difference with respect to the existing techniques, whose practical usefulness can be limited due to the associated requirements for long and/or periodic excitation signals. The knowledge about the binary measurement׳s characteristics is exploited to adapt standard prediction error minimisation techniques. This is done for both Rational Transfer Function (RTF) and Finite Impulse Response (FIR) model representations of the linear system. Simulation results are included to illustrate the identification procedure, and an experimental validation is provided to demonstrate the practical usefulness of the proposed methods.