Solar activity is a determining factor for space climate of the Solar system. Thus, predicting the magnetic activity of the Sun is very important. However, our incomplete knowledge about the dynamo processes of generation and transport of magnetic fields inside Sun does not allow us to make an accurate forecast. For predicting the solar cycle properties use the Ensemble Kalman Filter (EnKF) to assimilate the sunspot data into a simple dynamo model. This method takes into account uncertainties of both the dynamo model and the observed sunspot number series. The method has been tested by calculating predictions of the past cycles using the observed annual sunspot numbers only until the start of these cycles, and showed a reasonable agreement between the predicted and actual data. After this, we have calculated a prediction for the upcoming solar cycle 24, and found that it will be approximately 30% weaker than the previous one, confirming some previous expectations. In addition, we have investigated the properties of the dynamo model during the solar minima, and their relationship to the strength of the following solar cycles. The results show that prior the weak cycles, 20 and 23, and the upcoming cycle, 24, the vector-potential of the poloidal component of magnetic field and the magnetic helicity substantial decrease. The decrease of the poloidal field corresponds to the well-known correlation between the polar magnetic field strength at the minimum and the sunspot number at the maximum. However, the correlation between the magnetic helicity and the future cycle strength is new, and should be further investigated.