Partial realization of random systems

Consider a vector-valued stationary random process {Yk}∞-∞, from which the estimates, R0, R1, ..., RN, of the covariance matrices EYkY′k-i, i=0, 1, 1, ..., N, can be made. The three matrices, (G(N), F(N), H(N)) are said to form a minimal partial realization of the process {Yk}∞-∞ if we can write. {A figure is presented}. {A figure is presented}. In the paper an algorithm is described for recursively calculating the minimal partial repreentations for the sequences R0, ..., RN, N=0, 1, ..., taken as inputs to the algorithm.