An identification algorithm for parallel Wiener-Hammerstein systems

Block-oriented nonlinear models such as Wiener and Hammerstein models have the advantage that they are quite simple to understand and easy to use. Hammerstein and Wiener models can be extended to models containing extra blocks in a series connection such as Wiener-Hammerstein models. To further increase the modeling power of block-oriented models a parallel connection of Wiener-Hammerstein branches is considered. This paper presents a parametric identification algorithm for parallel Wiener-Hammerstein systems in discrete time starting from input-output data only. First, the overall dynamics of the system are estimated in least squares sense at different operating points of the system. Second, these dynamics are decomposed over the parallel branches, and partitioned into the front and back linear time invariant (LTI) blocks, giving an estimate of the LTI blocks. Finally, the static nonlinearities are estimated using a linear least squares estimator.