Abstract: We consider the problem of reconstructing the initial states of an ensemble of linear systems from output measurements that are anonymized in the sense that the association between output measurements and systems in the ensemble is lost. Building on our previous works, in this paper we consider the situation in which there are couplings between the different systems in the ensemble. We demonstrate that for a particular class of coupled ensembles, the coupled problem can be efficiently reduced to the well-established uncoupled case. This class consists of groups of homogeneous linear systems that are coupled through all-to-all diffusive coupling. By virtue of the reduction to the uncoupled case, we are able to formulate non-pathological sampling results for the specific coupled case. Furthermore, we illustrate the theoretical techniques by means of a practical simulation example.
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