An extension of the split Levinson algorithm and its relatives to the joint process estimation problem

It is shown that the split Levinson algorithm, the split Schur algorithm, and the split lattice algorithm to compute the reflection coefficients of the optimal linear prediction filter for a discrete-time stationary stochastic process can be extended to the more general case of the joint process estimation problem. The new algorithms are essentially based on well-defined recurrence relations for symmetric prediction filters and symmetric estimation filters. They are more economical than the standard methods in terms of storage space and number of arithmetic operations