Data filtering‐based recursive identification for an exponential autoregressive moving average model by using the multi‐innovation theory

This study employs the data filtering technique to investigate the recursive identification problems for a non‐linear exponential autoregressive model with moving average noise, i.e. the ExpARMA model. Whitening the ExpARMA model by a linear filter, the original identification model is divided into a filtered identification model and a coloured noise model, then a filtering‐based extended stochastic gradient algorithm is derived. In order to improve the parameter estimation accuracy, the multi‐innovation identification theory is used to develop a filtering‐based multi‐innovation extended stochastic gradient algorithm for the ExpARMA model. A simulation example is given to demonstrate the superiority of the proposed filtering‐based multi‐innovation algorithm over the existing algorithms.