Algorithm for object tracking
assuming you have a relative high frame rate video (the object is moving relatively slow between two consecutive images) some standard tracking algorithms can be applied.

Mean shift [Wikepedia - Mean shift]
Use some template of the object you are tracking to create a likelihood function for the object location and track the object.


if you need more advanced method that can be more robust, e.g. object occlusions you can use more advanced methods:

kalman filter [Wikipedia - Kalman filter]
In short kalman filter uses a dynamic model that is composed of
prediction step and update step to track an object in an unsertain
enviroment.


More advanced option you can consider, if you have couple of objects you want to track at the same time is particle filter