A gimbal system, including components and methods of use, configured to track moving targets. More specifically, the disclosed system may be configured to orient and maintain the line of sight (“los”) of the gimbal system toward a target, as the target and, in some cases, the platform supporting the gimbal system are moving. The system also may be configured to calculate an estimated target velocity based on user input, and to compute subsequent target positions from previous positions by integrating the estimated target velocity over time. A variety of filters and other mechanisms may be used to enable a user to input information regarding a target velocity into a gimbal controller.