Orthogonality of oblique projections and lattice-form models

A recursive biorthogonalization procedure, which forms the basis for the derivation of lattice recursions for the instrumental variable algorithm is presented. We show that the basis for this procedure is an orthogonal decomposition of non-orthogonal (oblique) projections. Furthermore, we show that the orthogonality principle, which underlies the well-known Gram-Schmidt procedure also extends to the above-mentioned recusive biorthogonalization procedure. Applications to the construction of instrumental variable lattice recursions are briefly described.