Moving horizon estimation is a way for a computer to figure out the best course of action based on changing data. Imagine you have a robot driving along a path. It has a sensor that can measure how far it is away from the path. With moving horizon estimation, the robot can keep track of how far away it is and update its actions so it can get back on path. It runs the computation again and again, each time looking at the most up-to-date data and adjusting its path when needed.