• estimation
• fast gradient
• kalman filter
• MHE
• moving horizon estimation
• nesterov
• optimization

The Moving Horizon Estimation (MHE) is a technique that allows to estimate the states
of a system considering constraints, either when they are effected by noise or are not
measured. This method can be associated with control techniques such as Model Predictive
Control.
The core of the mathematics formulation of MHE consists of an optimization problem
that can easily become huge as the horizon and the number of states of the system
increase. This leads inevitably to a large computational time that makes dicult the
implementation of the algorithm for on-line purpose. In this work we show through
several simulations on linear random systems that if we assume box constraints on
the states and output noises, we can eciently apply the Nesterov's Fast Gradient
method for solving the optimization problem faster than using the standard optimization
algorithms such as Interior Point Method or Active Set Method.