Abstract: Complexity pursuit is an extension of projection pursuit to time series data and the method is closely related to blind separation of timedependent source signals and independent component analysis (ICA). In this paper， we consider the estimation of the data model of ICA when Gaussian noise is present and the components are time dependent. The separation result is affected because existing blind source separation algorithms do not give the method to estimate the autoregressive coefficients. A novel algorithm for noisy complexity pursuit is proposed. The algorithm gives the method to estimate autoregressive coefficients. Computer stimulations with natural images and artificial signals indicate the validity of the proposed algorithm. Moreover， comparisons with existing blind source separation algorithms further show the better performance of the proposed algorithm.