Identification of a noiseless nonlinear system by gradient method

When a system containing nonlinearity is noiseless and its composite structure is known a priori, we propose the use of a gradient method for system identification to replace the usual Volterra series approach. The identifier system in the gradient method is a composite replica to the nonlinear system to be identified, while in the Volterra series approach, the identifier system is an extended FIR filter. As a result, the number of unknowns (filter weight coefficients) in the identifier system when using the gradient method is largely reduced as compared to the Volterra method. This can alleviate computational and implementation difficulties. As we shall see, the complexity of a gradient algorithm will largely depend on the complexity of the composite structure of the system to be identified. To demonstrate, we derive the gradient algorithm applied to a linear-nonlinear-linear system (LNL). Computer simulation results with varying parameters such as the order of the nonlinearity and lengths of linear filter parts are presented with discussions on algorithm adaptation speed and adaptation step size.