The aim of my thesis is to estimate the position and the mobility of a subscriber in 4G mobile communication networks. These estimations facilitate the execution of location-dependent services and the measurements of quality and coverage periodically, according to the estimated position. The first task was to explore the actual positioning and mobility estimating methods applied in mobile networks. After being acquainted with these methods, I created my own distance and angle measurement based positioning algorithms and received power and positioning based mobility estimation algorithms. The ultimate aim is to predict the handover mechanism and thus save network traffic and avoid occurrent network unavailability. We could not presume to have a GPS-receiver or to use other navigation systems, because in many mobile phones it is not available and between buildings and indoor it is inaccurate and furthermore it can be unreachable. Presuming devices the positioning procedure can estimate the position with three algorithms. The procedure choose one of them as a function of the number of the available base stations (eNodeBs) and the capabilities of those. Also using the estimated position and the received power from base stations (eNodeBs) the procedure can predict handover with four algorithms. I implemented the positioning and handover prediction algorithms into a C++ based LTE Simulator, and finally I analysed parameter-dependency of the accuracy of the algorithms with changing input parameters.