Abstract

Motivated by an application in metrology for speed up of measurement devices, the following problem is considered: given output observations of a stable linear time-invariant system with known dc gain, generated by a step input, find the input. If a model of the data generating process is available, the input estimation problem is solved as an equivalent state estimation problem for an autonomous system. Otherwise, the input estimation problem is reduced to standard system identification problems: (1) identification from step response data and (2) autonomous system identification. The link to autonomous system identification suggests a data-driven solution, i.e., an algorithm for computation of the input value without identifying a representation of the system. The data-driven algorithm is a structured low rank approximation problem.

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