Parameter Estimation with Binary Observations of Input and Output Signals

Abstract

This papers considers parameter estimation of a constant gain system with only binary measurements of the input and output signals available. It is assumed that the thresholds of the binary quantizers can be adapted. Depending on the prior information about the stochastic nature of the input signal and the presence of output noise, several estimation schemes based on empirical measures and stochastic approximation algorithms are proposed and analysed. It is shown that the algorithms converge almost surely to the true gain of the system, and the algorithms are illustrated in simulation examples.