Synthesis Identification Analysis for Closed Loop EIV System

This new paper combines errors-in-variable (EIV) system with closed loop situation to consider a more complex closed loop EIV system. Consider the identification problem for closed loop EIV system, synthesis analysis is completed from the point of system identification field. Firstly, the reason about why closed loop EIV system is useful in academy and practice is explained in detail. Secondly, to identify that unknown plant, existing in closed loop EIV system with the measurement and process noise simultaneously, nonparametric estimate is proposed to be one plant estimate through our own mathematical derivation. Then statistical analysis above nonparametric estimate is studied to show the unbiased property. Thirdly, for the rational transfer function as the unknown plant, parameterized by one unknown parameter vector, the plant identification is transferred into one parameter estimate, so after reformulating the parameterized input-output relation for closed loop EIV system, least squares solution is derived to be biased. To avoid this explicit biased term, bias compensated estimate and an iterative least squares estimate are proposed to improve the overall identification performance. Finally, one practical example is to show the existence of our considered closed loop EIV system, and the detailed numerical results prove our proposed identification strategies.