arXiv subjects

Changwu Liu

Publications and source records attributed to Changwu Liu.

4 recordsLinked to original sources

arXiv2025

Global Observer Design for a Class of Linear Observed Systems on Groups

Linear observed systems on groups encode the geometry of a variety of practical state estimation problems. In this paper, we propose an observer framework for a class of linear observed systems by restricting a bi-invariant system on a Lie group to its normal subgroup. This structural property enables a system embedding of the original system into a linear time-varying system. An observer is constructed by first designing a Kalman-like observer for the embedded system and then reconstructing the group-valued state via optimization. Under an extrinsic observability rank condition, global exponential stability (GES) is achieved provided that one global optimum of the reconstruction optimization is found, reflecting the topological difficulties inherent to the non-Euclidean state space. Semi-global stability is guaranteed when input biases are jointly estimated. The theory is applied to the GES observer design for two-frame systems, capable of modeling a family of navigation problems. Simulations are provided to illustrate the implementation details.

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arXiv2024

Classification of Linear Observed Systems on Multi-Frame Groups via Automorphisms

Many navigation problems can be formulated as observer design on linear observed systems with a two-frame group structure, on which an invariant filter can be implemented with guaranteed consistency and stability. It's still unclear how this could be generalized to simultaneous estimation of the poses of multiple frames and the general forms of the linear observed systems involving multiple frames remain unknown. In this letter, we propose a multi-frame group structure by semi-direct product using the two-frame group as building blocks, covering all natural extensions. More importantly, we give a systematic direct calculation to classify all possible forms of linear observed systems including process ODEs and algebraic observations on such multi-frame group through its automorphism structure, in comparison to the existing classification on two-frame groups relying on ingenious construction. Depth-camera inertial odometry with online extrinsics calibration is provided as an application.

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arXiv2024

On the Existence of Linear Observed Systems on Manifolds with Connection

Linear observed systems on manifolds are a special class of nonlinear systems whose state spaces are smooth manifolds but possess properties similar to linear systems. Such properties can be characterized by preintegration and exact linearization with Jacobians independent of the linearization point. Non-biased IMU dynamics in navigation can be constructed into linear observed settings, leading to invariant filters with guaranteed behaviors such as local convergence and consistency. In this letter, we establish linear observed property for systems evolving on a smooth manifold through the connection structure endowed upon this space. Our key findings are the existence of linear observed systems on manifolds poses constraints on the curvature of the state space, beyond requiring the dynamics to be compatible with some connection-preserving transformations. Specifically, the flat connection case reproduces the characterization of linear observed systems on Lie groups, showing our theory is a true generalization.

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arXiv2023

InGVIO: A Consistent Invariant Filter for Fast and High-Accuracy GNSS-Visual-Inertial Odometry

Combining Global Navigation Satellite System (GNSS) with visual and inertial sensors can give smooth pose estimation without drifting. The fusion system gradually degrades to Visual-Inertial Odometry (VIO) with the number of satellites decreasing, which guarantees robust global navigation in GNSS unfriendly environments. In this letter, we propose an open-sourced invariant filter-based platform, InGVIO, to tightly fuse monocular/stereo visual-inertial measurements, along with raw data from GNSS. InGVIO gives highly competitive results in terms of computational load compared to current graph-based algorithms, meanwhile possessing the same or even better level of accuracy. Thanks to our proposed marginalization strategies, the baseline for triangulation is large although only a few cloned poses are kept. Moreover, we define the infinitesimal symmetries of the system and exploit the various structures of its symmetry group, being different from the total symmetries of the VIO case, which elegantly gives results for the pattern of degenerate motions and the structure of unobservable subspaces. We prove that the properly-chosen invariant error is still compatible with all possible symmetry group structures of InGVIO and has intrinsic consistency properties. Besides, InGVIO has strictly linear error propagation without linearization error. InGVIO is tested on both open datasets and our proposed fixed-wing datasets with variable levels of difficulty and various numbers of satellites. The latter datasets, to the best of our knowledge, are the first datasets open-sourced to the community on a fixed-wing aircraft with raw GNSS.

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