Binary-Valued Identification of Nonlinear Wiener–Hammerstein Systems Using Adaptive Scheme

Abstract

In the field of instrumentation and measurement science, quantized system identification based on sophisticated sensors has greatly reduced the cost of regular sensors. Although existing identification techniques are available, an identification algorithm with a novel-framework and high estimation performance is required for new applications. This report is concerned with the system identification of a nonlinear Wiener-Hammerstein system with binary-valued measurements. In quantized system identification communities, stochastic approximation type scheme is a main direction of research by directly constructing an effective identification algorithm based on the error learning feedback principle. To overcome the difficulty in constructing the estimator by using the data directly related to parameter estimation (e.g., estimation error information, initial error information), this report aims to introduce a method to utilize the estimation error information, and to establish an adaptive estimator by combining the parameter initial error information. A novel-structured adaptive filter is introduced to improve the estimation bias phenomenon. By use of auxiliary vectors and matrices, an estimation error representation is established. Then, the estimation error data with the conversion operator and initial error data with a smoothing factor are merged to derive the identifier, in which the time-varying gain is also provided. Theoretical analysis shows that the estimate reaches the true value of the parameter in the sense of almost surely. Numerical results and practical applications are supplied to clarify and verify the theoretical findings.