Modeling of nonlinear colored noise in stable distribution environments
Daifeng Zha, Tianshuang Qiu, Wenqiang Guo, Ying Guo · 2005
Stable processes can better model the impulsive random signals and noises in physical observations. This paper briefly introduces the statistical characteristics of a stable distribution, describes its spectral representation, proposes a new different spectral density from power spectrum density of second order processes, thus we can get a new concept of stable white noise based on a covariation sequence and covariation spectrum, which generalizes the conventional Gaussian white noise based on second order statistics. In addition, we propose a new technique for the estimation of the parameters of PAR (polynomial autoregressive) nonlinear colored noise processes with stable white noise innovations in PAR nonlinear systems.