Weighted multi‐innovation parameter estimation for a time‐varying Volterra–Hammerstein system with colored noise

Abstract This article considers the parameter estimation problems of a time‐varying Volterra–Hammerstein (V–H) system with colored noise. We derive a weighted multi‐innovation forgetting factor gradient algorithm by applying the multi‐innovation identification with the weight matrix to adjust the weights of the innovation vector. In order to simplify the identification algorithm and improve the parameter estimation accuracy, the original V–H system with colored noise is separated into two sub‐systems by the hierarchical identification theory. A weighted hierarchical multi‐innovation forgetting factor gradient algorithm is presented for two sub‐systems. Numerical simulation examples test the effectiveness of the proposed algorithms.