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.