Iteratively Preconditioned Gradient-Descent Approach for Moving Horizon Estimation Problems

Moving horizon estimation (MHE) is a state estimation method that has been extensively studied. The state estimates for the MHE problem are obtained by solving an approximation nonlinear optimization problem. This optimization process is known to be computationally challenging. This paper explores the idea of iteratively preconditioned gradient-descent (IPG) to solve the MHE issue to outperform the current solution methods in light of this limitation. To our knowledge, the preconditioning technique is employed for the first time in this research to speed up the critical MHE optimization stage and lower the computing cost. For a class of MHE problems, the proposed iterative approach's convergence guarantee is shown. Sufficient conditions for the MHE problem to be convex are also derived. Finally, the proposed method is implemented on a unicycle localization example. The simulation results demonstrate that the proposed approach can improve accuracy with reduced computational costs.