Generalized Diagram for Various Parameter Estimation Methods; the Coherence in Pseudo-Linear Regression Schemes

摘要

The relationships between recursive estimation schemes for single-input single-output systems are established by presenting a general diagram of which well-known estimators are special cases (least-squares, generalized least squares, extended matrix method, instrumental variable method, approximated maximum likelihood, implicit quasi-linearization, filtered instrumental variable estimator, (sub) optimal instrumental variable estimator and the instrumental variable variant of the extended matrix method). In the diagram, three important operations can be distinguished: noise filtering, model extension, and instrumental variable generation. It is shown that by proper combination of these three main operations, all the mentioned estimators can be constructed.