This paper introduces a novel model-free approach to synthesize virtual sensors for the estimation of dynamical quantities that are unmeasurable at runtime but are available for design purposes on test benches. After collecting a dataset of measurements of such quantities, together with other variables that are also available during on-line operations, the virtual sensor is obtained using machine learning techniques by training a predictor whose inputs are the measured variables and the features extracted by a bank of linear observers fed with the same measures. The approach is applicable to infer the value of quantities such as physical states and other time-varying parameters that affect the dynamics of the system. The proposed virtual sensor architecture — whose structure can be related to the Multiple Model Adaptive Estimation framework — is conceived to keep computational and memory requirements as low as possible, so that it can be efficiently implemented in embedded hardware platforms. The effectiveness of the approach is shown in different numerical examples, involving the estimation of the scheduling parameter of a nonlinear parameter-varying system, the reconstruction of the mode of a switching linear system, and the estimation of the state of charge (SoC) of a lithium-ion battery.
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