The paper considers solving the problem of localization of players in virtual soccer. The authors use the RoboCup 2D Soccer Simulation League international competition platform as a medium for conducting experiments. The location information of objects in the field is important for deciding–it is necessary to find players in conditions of both complete and insufficient information. Using previous states and predicting actions for recently hidden objects can improve the accuracy of the projected growth of the situation in the field.

The authors reviewed existing solutions for the localization of players and developed a new algorithm.
If the initial information suffices to calculate the player's coordinates, we use the Kalman filter, and if the information is insufficient, we use the inertial navigation algorithm based on known previous states. The paper describes an approach to predicting the players' location that has recently disappeared from view, considers the mathematical model of the algorithm, and designs the architecture of the software solution. Several actual players in the virtual soccer environment tested the developed solution. We show the results as graphs of mathematical expectation and dispersion and confirm the predictability of the location of recently disappeared objects, calculating the coordinates of the player in various conditions.

The obtained results determine the directions for further research on forecasting based not only on previous states but also on the logic of players' decisions. The next step is to integrate the developed program into the decision-making system for joint verification during the competition.