Generalized least squares innovation representation
The paper gives a unified approach to the stochastic realization problem of finite dimensional discrete-time stochastic systems. If y(t)\(\in R\) m is a discrete weakly stationary stochastic process, then using different bases in the spaces of its future - generated by y(0), y(1),... and its past - generated by y(-1), y(-2),... - we can define different algorithms for the matrices in its innovation representation. The essence of these algorithms is: (i) compose a Hankel matrix based on the covariances of some random variables generating the future and the past, respectively; (ii) factor the elements of this Hankel-matrix using the Ho-Kalman algorithm; (iii) using some Riccati equations to obtain the required matrices. Using the unnormalized forward and backward innovations of y(t) as bases in the future and the past we get Faurre's algorithm, using normalized innovations we get the Desai-Pal algorithm, using unnormalized innovations in the future space and normalized innovations in the past space we get the algorithm which is discussed in the paper and called GLS IR algorithm.
finite dimensional discrete-time stochastic systems
scientific article; zbMATH DE number 4066764