Impulse response identification from input/output binary measurements

In this paper, we study the identification of Finite Impulse Response systems in a particular context: data on the input and the output are obtained with one-bit quantizers, the thresholds of quantizers can be different from zero. A three-step identification algorithm is proposed from these binary-valued measurements. This algorithm is based on the normal distribution of the input and noises. The algorithm is appropriately analyzed: it is shown to be asymptotically unbiased, its asymptotic variance is also expressed. Numerical simulations are provided to demonstrate the effectiveness of the proposed algorithm even in presence of noise and to validate the analysis.