We performed a more comprehensive test of a new NPF parameter estimator published recently. The estimator considers measurements as test data and automatically adjusts the values of its physical control parameters according to the criterion of best fit. The parameters estimated within this procedure include nucleation rate, particle growth rate, birth size of nanoparticles etc. We analyzed all new particle formation events recorded during a measurement campaign at Hyytiala, Finland. The results show a good performance in reproducing the time series of the concentrations of small air ions and aerosol nanoparticles in the diameter interval of 2.8-8.6 nm. The numerically estimated values of the parameters are in accordance with the results known from certain other studies carried out at Hyytiala. We conclude the new method may appear useful in the analysis of several air ion and atmospheric aerosol measurements during new particle formation events.