Autoregressive models with multiple roots of the characteristic equations

It is proposed to use autoregressive processes with multiple roots of the characteristic equations generated by dynamic systems as models describing real-time signals and noises with smooth realizations. Correlation functions and parameters of autoregressive processes are found. Special attention is paid to the case of characteristic equation with root multiplicity equal to 2. Generalization for causal models of images on multidimensional grids with properties close to isotropic random fields is considered. Algorithms of Kalman filtering of autoregressive sequences observed against additive noise background are presented.