Identification of Wiener Systems with Binary-Valued Observations

Abstract

AbstractThis chapter studies the identification of Wiener systems whose outputs are measured by binary-valued sensors. The system consists of a linear FIR (finite impulse response) subsystem of known order, followed by a nonlinear function with a known parameterization structure. The parameters of both linear and nonlinear parts are unknown. Input design, identification algorithms, and their essential properties are presented under the assumptions that the distribution function of the noise is known and the nonlinearity is continuous and invertible. We show that under scaled periodic inputs, the identification of Wiener systems can be decomposed into a finite number of core identification problems. The concept of joint identifiability of the core problem is introduced to capture the essential conditions under which the Wiener system can be identified with binary-valued observations. Under scaled full-rank conditions and joint identifiability, a strongly convergent algorithm is constructed. The algorithm is shown to be asymptotically efficient for the core identification problem, hence achieving asymptotic optimality in its convergence rate. For computational simplicity, recursive algorithms are also developed.KeywordsFull RankRecursive AlgorithmNonlinear PartCore ProblemCirculant MatrixThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.