Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the problem of reconstructing the initial states of a finite group of structurally identical linear systems in the situation that output measurements of the individual systems are received at discrete time steps and in an anonymized manner: While  do know all output measurements of the individual systems in the group,  do not know which output measurement corresponds to which system. This state estimation problem addresses the essence of state estimation problems for populations, in which the output measurements of the individual systems are given only as statistics.  adopt a measure theoretical approach in which the group is modelled by an LTI system describing the structure of the individual systems and an initial state which is expressed by a discrete measure. In this framework  derive a geometric characterization for the state estimation to admit a unique solution, which combined with a result on the observability of linear systems under irregular sampling, yields a sufficient condition for the sampled observability of discrete ensembles. As a supplement to our theoretical findings,  provide illustrations by means of simulation examples. Furthermore  consider the practical state estimation problem under noisy output measurements.
['Shen Zeng', 'Hideaki Ishii', 'Frank Allgöwer']
I am writing a research paper on a idea Sampled Observability and State Estimation of Linear Discrete Ensembles
[{"from": "human", "value": "I am writing a research paper on a idea Sampled Observability and State Estimation of Linear Discrete Ensembles"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the problem of reconstructing the initial states of a finite group of structurally identical linear systems in the situation that output measurements of the individual systems are received at discrete time steps and in an anonymized manner: While  do know all output measurements of the individual systems in the group,  do not know which output measurement corresponds to which system. This state estimation problem addresses the essence of state estimation problems for populations, in which the output measurements of the individual systems are given only as statistics.  adopt a measure theoretical approach in which the group is modelled by an LTI system describing the structure of the individual systems and an initial state which is expressed by a discrete measure. In this framework  derive a geometric characterization for the state estimation to admit a unique solution, which combined with a result on the observability of linear systems under irregular sampling, yields a sufficient condition for the sampled observability of discrete ensembles. As a supplement to our theoretical findings,  provide illustrations by means of simulation examples. Furthermore  consider the practical state estimation problem under noisy output measurements."}]