In simple words, **When is it used?** to estimate system states, extract state information especially from a noisy measurement. **Why called moving horizon?** The measurement slot changes..or at each sample, a fixed window of past measurements is used to estimate the current state of the system. Usually the estimation of state is used along with the model to forecast the future process behavior for a fixed time-window.
**Estimation and control** With the help of available data in each window (measurement slot) dynamic optimization computes the optimal sequence of manipulable variables (inputs to the process) such that the predicted process behavior is as desirable as possible subject to the physical and operational constraints of the system. This is when control comes into picture with the estimated state information.