The robust multi-innovation estimation algorithm for Hammerstein non-linear systems with non-Gaussian noise

The characteristic of the external noise has significant influences on system modelling and identification, and the assumption that the noise follows the Gaussian distribution may be invalid due to realistic reasons. This paper discusses the identification issue of Hammerstein non-linear systems with non-Gaussian noise and presents a robust gradient algorithm. The algorithm is derived based on the logarithmic cost function of continuous mixed p-norm of prediction errors, which takes into account each p-norm of errors for 1 <= p <= 2. The gain at each recursive step adapts to the data quality so that the algorithm has good robustness to non-Gaussian noise. To improve the estimation accuracy, a robust multi-innovation gradient algorithm is proposed by using the multi-innovation identification theory. Two examples are provided to exhibit the validity of the proposed algorithms.