Recursive Elimination Method for Moving Horizon Estimation of Discrete-Time Polynomial Systems

This paper proposes an algebraic method to solve optimal filtering problems for discrete-time polynomial systems. Most of the computation in the proposed method can be performed off-line using symbolic computation based on mathematical tools from algebraic geometry. Therefore, the computational time required in the on-line part of this method is significantly reduced; this property is suitable for moving horizon estimation, where a certain optimal filtering problem is solved at each time step for different observed outputs. A numerical example is provided to show the efficiency of the proposed method.