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A Recursive Nonlinear System Identification Method Based on Binary Measurements

An online approach to nonlinear system identiﬁcation based on binary observations is presented in this paper. This recursive method is a nonlinear extension of the LMS-like (least-mean-squares) basic identiﬁcation method using binary observations (LIMBO). It can be applied in the case of weakly nonlinear Dufﬁng oscillator coupled with a linear system characterized by a ﬁnite impulse response. It is then possible to estimate both Dufﬁng and impulse response coefﬁcients knowing only the system input and the sign of the system output. The impulse response is identiﬁed up to a positive multiplicative constant. The proposed method is compared in terms of convergence speed and estimation quality with the usual LMS approach, which is not based on binary observations.