Receding Horizon Recursive Location Estimation

TL;DR

This paper introduces a recursive approach to moving horizon estimation for nonlinear systems, establishing conditions for equivalence with EKF, and explores its connection to factor graph optimization, with applications in GNSS localization.

Contribution

It provides a recursive formulation of MHE, links it to EKF and FGO, and demonstrates its effectiveness in GNSS localization tasks.

Findings

Recursive MHE is equivalent to EKF under certain conditions.

The approach improves localization accuracy in GNSS datasets.

Theoretical and empirical validation supports the method's effectiveness.

Abstract

This paper presents a recursive solution to the receding or moving horizon estimation (MHE) problem for nonlinear time-variant systems. We provide the conditions under which the recursive MHE is equivalent to the extended Kalman filter (EKF), regardless of the horizon size. Theoretical and empirical evidence is also provided. Moreover, we clarify the connection between MHE and factor graph optimization (FGO). We apply the recursive MHE to GNSS localization and evaluate its performance using publicly available datasets. The paper is based on the deterministic least squares framework.