Identification of Wiener models using optimal local linear models

Identification of a Wiener model using optimal local linear models (LLMs) is presented. The model consists of a discrete-time transfer function and piece-wise linear functions. Parameter estimation as well as partitioning of the LLMs is simultaneously accomplished by the algorithm. The optimality is threefold: first, each local model is linear in the parameters, thus leading to an optimal solution. Second, the model size of each LLM is adaptively optimized using a chi-squared criterion, explicitly incorporating the measurement noise level. Third, the resulting model has a minimum of parameters for a given performance. Simulation results document that the output noise is balanced with the systems nonlinearity.