Efficient pole optimization of nonlinear laguerre filter models

The problem of identifying nonlinear dynamic systems with one or more inputs and one output (SISO/MISO) is considered. The properties of orthonormal basis functions (OBF) as inputs for a nonlinear approximator are compared to the common ARX structure which possesses both, delayed input and output values, entering the nonlinearity. The disadvantage of optimizing the pole in the OBF context is overcompensated by the advantages which arise especially in the nonlinear MISO case. The key idea of this paper is the optimization of the OBF pole while fixing the nonlinear model structure, here called Fixed Structure Optimization (FSO). In the SISO case the computational effort can be decreased dramatically. For the MISO case, the increasing complexity of the pole search is tackled with a staggered optimization approach. The reliability is underlined by demonstrating the low correlation between the OBF poles for uncorrelated inputs. The combination of the proposed repeated fixed structure optimization (FSO) with a staggered optimization for the multivariate extension yields many benefits compared to conventional optimization procedures.