Identification of systems using binary sensors via Support Vector Machines

In this paper, we consider the identification of systems based on binary measurements of the output. The linear part of the system is parameterized by a Finite Impulse Response filter and the binary sensor is parameterized by a threshold. The idea is to formulate the identification problem as a classification problem. This formulation allows the use of supervised learning algorithm such as Support Vector Machines (SVM). Simulation examples are given to illustrate the performance of the presented method.

I. Introduction

The system identification process is the process that extracts a mathematical model based on measurements of the input and output of the system. For some systems, it is not possible to have high-resolution on the output signal, the only available information are binary measurements. The cause of this loss of information may be economic or technical. There are many examples of systems using binary sensors, such as chemical process sensors for monitoring pressure or liquid levels, another example is a binary sensor used in communication systems to indicate a traffic conditions in the asynchronous transmission mode (ATM) networks [13]. (For more details on these examples and others, see [13] and reference therein). In such situations, the output sensor acts as a switch: if the output of the system is above a characteristic threshold, the switch is open; if the output of the system is below the threshold, the switch is closed. In this context, the identification of the dynamical behavior of the system is a challenging problem.