In this paper, a review of lithium-ion secondary battery technologies is given, along with the advantages and disadvantages of the individual electrochemical compositions present on the market. In this context, the characteristics of lithium-titanate batteries are highlighted, which are an attractive choice for many application areas. Further in the paper, the relevant types of battery models are briefly explained, with an emphasis on the model of the equivalent circuit of the battery cell, and the derivation of transfer functions in all forms required for carrying out further steps. A review of the parameters obtained experimentally for the lithium titanate battery is also given, as well as a review of the model in the form of a block diagram. After all the necessary information has been provided at the battery model level, the design of the battery parameter estimator is continued. First, a theoretical review of the Kalman filter is given in basic and extended form, with all the necessary expressions for its implementation in the MATLAB/Simulink environment. Then, simulation results are shown using a nonlinear battery model with and without parameter maps. The same was repeated for the parameter estimator based on the concept of the adaptive process model, with the difference that it used exclusively the battery model that contains parameter maps. Such an estimator was then integrated into the battery charging system model and simulation results are shown for different charging currents and for different initial values of the battery state of charge.