Identification of a gain system with binary input and output measurements

This paper studies the identification problem of a gain system using both input and output quantized data. Specifically, the system input and the output are separately quantized into one bit before sent to a remote estimator, which generates a recursive algorithm to identify the system. If the random input is an independent and identical Gaussian process, we develop the identification algorithms respectively by using the empirical measure and the maximum likelihood estimation, which is given in a recursive form by the EM and quasi-Newton iterations. Finally, simulations are included to validate theoretical results.