An affine projection-based algorithm for identification of nonlinear Hammerstein systems

There are parametric and non-parametric methods for adaptive Hammerstein system identification. The most commonly used method is the non-parametric. In reality, the linear subsystem of a Hammerstein system is not of finite impulse response and non-parametric adaptive algorithms require large matrices and therefore increase computational complexity.The objectives of this paper are to identify the Hammerstein system adaptively based on the affine projection criterion using a parametric algorithm. We also develop a bound for control of step size of the proposed algorithm and derive an expression for its mean square error performance. The error surface of the nonlinear Hammerstein filter was determined by examining the non-quadratic nature and the global and local minima of the mean square error cost function. A bound was determined for the adaptive step size and an expression was derived for the mean square error convergence based on energy conservation theory. Simulations of system identification applications showed that convergence speed of the proposed algorithm was faster and the convergence was superior to previously existing Hammerstein algorithms. Applying the new algorithm to the identification of the human muscles stretch reflex dynamics showed good convergence results. The proposed algorithm is of practical value in real life situations.