Iteratively Preconditioned Gradient-Descent Approach for Moving Horizon Estimation Problems

TL;DR

This paper introduces an iterative preconditioning method for moving horizon estimation that reduces computational costs and improves accuracy, with proven convergence and applicability to convex problems.

Contribution

It is the first to apply preconditioning in MHE to enhance computational efficiency and convergence, providing theoretical guarantees and practical validation.

Findings

Reduced computational cost in MHE optimization

Improved estimation accuracy in simulations

Convergence guarantees for the iterative method

Abstract

Moving horizon estimation (MHE) is a widely studied state estimation approach in several practical applications. In the MHE problem, the state estimates are obtained via the solution of an approximated nonlinear optimization problem. However, this optimization step is known to be computationally complex. Given this limitation, this paper investigates the idea of iteratively preconditioned gradient-descent (IPG) to solve MHE problem with the aim of an improved performance than the existing solution techniques. To our knowledge, the preconditioning technique is used for the first time in this paper to reduce the computational cost and accelerate the crucial optimization step for MHE. The convergence guarantee of the proposed iterative approach for a class of MHE problems is presented. Additionally, 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 achieve better accuracy with reduced computational costs.