  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.
