In an elevator installation, an elevator car is movably arranged alongside guide rails and the elevator car is equipped with a brake system with preferably two safety brakes. A movement monitoring system monitors the movement parameters of the elevator car and triggers corresponding warnings or safety measures, if permissible threshold values are exceeded or it provides determined adjusted movement parameters to an elevator control. The movement monitoring system determines a first movement parameter in a time interval and detects an acceleration of the elevator car. The movement monitoring system determines the time interval for determining the adjusted movement parameter as a function of the detected acceleration.