Necessary and sufficient convergence conditions of the instrumental variable method for identification

The consistency of the instrumental variable method is considered for a system driven by independent identically distributed input signals with zero mean. Necessary and sufficient conditions for convergence are developed with respect to the given model structure. The sufficient and necessary conditions are established for cases with and without data prefiltering. In this paper we extend on existing results such that the requirements on the degree of the instrumental variables can be relaxed. Numerical examples supporting the theoretical results are provided.