Identification of Hammerstein Systems with Quantized Observations

Abstract

This chapter concerns the identification of Hammerstein systems whose outputs are measured by quantized sensors. The system consists of a memoryless nonlinearity that is polynomial and possibly noninvertible, followed by a linear subsystem. The parameters of linear and nonlinear parts are unknown but have known orders.We present input design, identification algorithms, and their essential properties under the assumptions that the distribution function of the noise and the quantization thresholds are known. Also introduced is the concept of strongly scaled full-rank signals to capture the essential conditions under which the Hammerstein system can be identified with quantized observations. Then under strongly scaled full-rank conditions, we construct an algorithm and demonstrate its consistency and asymptotic efficiency.