arXiv subjects

Chungeng Tian

Publications and source records attributed to Chungeng Tian.

6 recordsLinked to original sources

arXiv2026

Equivariant Filter Transformations for Consistent and Efficient Visual--Inertial Navigation

This paper presents an equivariant filter (EqF) transformation approach for visual--inertial navigation. By establishing analytical links between EqFs with different symmetries, the proposed approach enables systematic consistency design and efficient implementation. First, we formalize the mapping from the global system state to the local error-state and prove that it induces a nonsingular linear transformation between the error-states of any two EqFs. Second, we derive transformation laws for the associated linearized error-state systems and unobservable subspaces. These results yield a general consistency design principle: for any unobservable system, a consistent EqF with a state-independent unobservable subspace can be synthesized by transforming the local coordinate chart, thereby avoiding ad hoc symmetry analysis. Third, to mitigate the computational burden arising from the non-block-diagonal Jacobians required for consistency, we propose two efficient implementation strategies. These strategies exploit the Jacobians of a simpler EqF with block-diagonal structure to accelerate covariance operations while preserving consistency. Extensive Monte Carlo simulations and real-world experiments validate the proposed approach in terms of both accuracy and runtime.

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arXiv2025

Unobservable Subspace Evolution and Alignment for Consistent Visual-Inertial Navigation

The inconsistency issue in the Visual-Inertial Navigation System (VINS) is a long-standing and fundamental challenge. While existing studies primarily attribute the inconsistency to observability mismatch, these analyses are often based on simplified theoretical formulations that consider only prediction and SLAM correction. Such formulations fail to cover the non-standard estimation steps, such as MSCKF correction and delayed initialization, which are critical for practical VINS estimators. Furthermore, the lack of a comprehensive understanding of how inconsistency dynamically emerges across estimation steps has hindered the development of precise and efficient solutions. As a result, current approaches often face a trade-off between estimator accuracy, consistency, and implementation complexity. To address these limitations, this paper proposes a novel analysis framework termed Unobservable Subspace Evolution (USE), which systematically characterizes how the unobservable subspace evolves throughout the entire estimation pipeline by explicitly tracking changes in its evaluation points. This perspective sheds new light on how individual estimation steps contribute to inconsistency. Our analysis reveals that observability misalignment induced by certain steps is the antecedent of observability mismatch. Guided by this insight, we propose a simple yet effective solution paradigm, Unobservable Subspace Alignment (USA), which eliminates inconsistency by selectively intervening only in those estimation steps that induce misalignment. We design two USA methods: transformation-based and re-evaluation-based, both offering accurate and computationally lightweight solutions. Extensive simulations and real-world experiments validate the effectiveness of the proposed methods.

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arXiv2025

T-ESKF: Transformed Error-State Kalman Filter for Consistent Visual-Inertial Navigation

This paper presents a novel approach to address the inconsistency problem caused by observability mismatch in visual-inertial navigation systems (VINS). The key idea involves applying a linear time-varying transformation to the error-state within the Error-State Kalman Filter (ESKF). This transformation ensures that \textrr{the unobservable subspace of the transformed error-state system} becomes independent of the state, thereby preserving the correct observability of the transformed system against variations in linearization points. We introduce the Transformed ESKF (T-ESKF), a consistent VINS estimator that performs state estimation using the transformed error-state system. Furthermore, we develop an efficient propagation technique to accelerate the covariance propagation based on the transformation relationship between the transition and accumulated matrices of T-ESKF and ESKF. We validate the proposed method through extensive simulations and experiments, demonstrating better (or competitive at least) performance compared to state-of-the-art methods. The code is available at github.com/HITCSC/T-ESKF.

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arXiv2025

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

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.

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arXiv2024

Consistent Distributed Cooperative Localization: A Coordinate Transformation Approach

This paper addresses the consistency issue of multi-robot distributed cooperative localization. We introduce a consistent distributed cooperative localization algorithm conducting state estimation in a transformed coordinate. The core idea involves a linear time-varying coordinated transformation to render the propagation Jacobian independent of the state and make it suitable for a distributed manner. This transformation is seamlessly integrated into a server-based distributed cooperative localization framework, in which each robot estimates its own state while the server maintains the cross-correlations. The transformation ensures the correct observability property of the entire framework. Moreover, the algorithm accommodates various types of robot-to-robot relative measurements, broadening its applicability. Through simulations and real-world dataset experiments, the proposed algorithm has demonstrated better performance in terms of both consistency and accuracy compared to existing algorithms.

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arXiv2023

KD-EKF: A Consistent Cooperative Localization Estimator Based on Kalman Decomposition

In this paper, we revisit the inconsistency problem of EKF-based cooperative localization (CL) from the perspective of system decomposition. By transforming the linearized system used by the standard EKF into its Kalman observable canonical form, the observable and unobservable components of the system are separated. Consequently, the factors causing the dimension reduction of the unobservable subspace are explicitly isolated in the state propagation and measurement Jacobians of the Kalman observable canonical form. Motivated by these insights, we propose a new CL algorithm called KD-EKF which aims to enhance consistency. The key idea behind the KD-EKF algorithm involves perform state estimation in the transformed coordinates so as to eliminate the influencing factors of observability in the Kalman observable canonical form. As a result, the KD-EKF algorithm ensures correct observability properties and consistency. We extensively verify the effectiveness of the KD-EKF algorithm through both Monte Carlo simulations and real-world experiments. The results demonstrate that the KD-EKF outperforms state-of-the-art algorithms in terms of accuracy and consistency.

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