A Transformation-based Consistent Estimation Framework: Analysis, Design and Applications

TL;DR

This paper introduces a transformation-based framework to ensure consistent state estimation in nonlinear systems, addressing observability mismatch issues and demonstrating improved accuracy and efficiency in various applications.

Contribution

The paper develops a theoretical foundation for observability matching, introduces transformation-based estimators, and validates their effectiveness in multiple nonlinear system scenarios.

Findings

Achieves state-of-the-art accuracy and consistency

Reduces computational complexity in nonlinear estimation

Validates methods on multi-robot and visual-inertial systems

Abstract

In this paper, we investigate the inconsistency problem arising from observability mismatch that frequently occurs in nonlinear systems such as multi-robot cooperative localization and simultaneous localization and mapping. For a general nonlinear system, we discover and theoretically prove that the unobservable subspace of the EKF estimator system is independent of the state and belongs to the unobservable subspace of the original system. On this basis, we establish the necessary and sufficient conditions for achieving observability matching. These theoretical findings motivate us to introduce a linear time-varying transformation to achieve a transformed system possessing a state-independent unobservable subspace. We prove the existence of such transformations and propose two design methodologies for constructing them. Moreover, we propose two equivalent consistent transformation-based EKF estimators, referred to as T-EKF 1 and T-EKF 2, respectively. T-EKF 1 employs the transformed system for consistent estimation, whereas T-EKF 2 leverages the original system but ensures consistency through state and covariance corrections from transformations. To validate our proposed methods, we conduct experiments on several representative examples, including multi-robot cooperative localization, multi-source target tracking, and 3D visual-inertial odometry, demonstrating that our approach achieves state-of-the-art performance in terms of accuracy, consistency, computational efficiency, and practical realizations.