  We apply a model-independent reconstruction method to experimental data in
order to identify complex poles of overlapping resonances. The algorithm is
based on the Schlessinger Point Method where data points are interpolated using
a continued-fraction expression. Statistical uncertainties of the experimental
data are propagated with resampling. In order to demonstrate the feasibility of
this method, we apply it to the $S$-wave $J/\psi \to \gamma \pi^0\pi^0$ decay.
We benchmark the method on known analytic models, which allows us to estimate
the deviation from the true value. We then perform the pole extraction from
BESIII data, and identify the $f_0(1500)$, $f_0(1710)$, and $f_0(2020)$ scalar
states. Our results are in reasonable agreement with recent results, which
suggests the proposed method as a promising model-independent alternative for
the determination of resonance poles that is solely based on available
experimental data.
