Lattice Implementation of the Instrumental Variable Method: Shift and Delta Operator Formulations

摘要

The lattice forms of the Instrumental Variable (IV) method is derived, for the standard shift operator. The extension to the delta operator formulation, for cases where high sampling rates cause numerical difficulties, is also discussed. For the sake of brevity, however, some of the routine technical details are omitted. The derivation yields the complete multi-channel and vector-channel (or multi-experiment) lattice algorithms. The overall approach is based on the non-orthogonal projections, and employs some of the techniques used in the lattice derivation of the least-square problem, where the projections are orthogonal. Complete algorithms, with appropriate end conditions, are presented, as well as an example to compare the estimates obtained from the basic least square methods to those from the instrumental variable method.