Identification of time-varying systems using multi-scale radial basis function

A time-varying autoregressive model with time-varying coefficients was investigated to identify linear system parameters from nonstationary time series. The basis function of multi-scale radial basis function (MRBF) was employed, and the identification of nonstationary modeling problem was then simplified to a linear time-invariant modeling problem. Particle swarm optimization (PSO) algorithm was applied to search the optimal RBF scales for the estimation of time-varying system parameters. The basis functions of RBF can better estimate time-varying parameters with a variety of dynamic process because optimal different RBF scales with good local properties can be effectively adjusted by the PSO algorithm. One simulation example of second-order time-varying autoregressive model with time-varying parameters involved different waveform was presented to show the effectiveness of the proposed method. Compared with classical approaches of time-varying parametric estimations such as recursive least square algorithms and the expansion approach of Legendre polynomial basis function, the identification results of time-varying parameters can be more accurately estimated which validates the effectiveness of the proposed time-varying modeling method.