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.

翻译：移动时域估计（MHE）是一种在实际应用中广泛研究的状态估计方法。在MHE问题中，状态估计通过求解一个近似非线性优化问题获得。然而，这一优化步骤已知计算复杂度较高。鉴于这一局限性，本文研究了迭代预条件梯度下降（IPG）方法以解决MHE问题，旨在比现有求解技术获得更优性能。据我们所知，本文首次采用预条件技术来降低计算成本并加速MHE中的关键优化步骤。针对一类MHE问题，给出了所提迭代方法的收敛性保证。此外，还推导了MHE问题为凸的充分条件。最后，将所提方法应用于单轮定位示例。仿真结果表明，该方法能在降低计算成本的同时获得更优的精度。