Adaptive identification of non-stationary systems with multiple forgetting factors

Recently much attentions have been paid to the use of adaptive forgetting factor related to the level of system alertness to estimate the parameters in nonstationary stochastic systems. The approaches are, however, generally complex to apply. We propose, in this paper, an adaptive identification method called multiple forgetting factors (MMF) method for nonstationary linear stochastic systems with time-varying parameters. The parameter estimates are constructed as a weighted sum of the estimates obtained by multiple recursive least squares methods operating in parallel with constant but different forgetting factors and the weights for each weighted least squares method are adjusted to fit the time variation of the parameters. The identification method has a simple structure and is quite easy to implement. Simulation experiments show that the proposed method works well not only for systems with abruptly changing parameters but also for systems with gradually changing ones.