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giuliodelama May 13, 2026
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giuliodelama May 13, 2026
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Expand Up @@ -82,6 +82,10 @@ This page collects and categorizes key papers on invariant and equivariant filte
_Robert Mahony, Tarek Hamel, Jochen Trumpf_
Technical companion to the EqF papers that develops the underlying systems-theoretic foundation: equivariant lifts, the relationship between symmetry groups and homogeneous state spaces, and the structural properties that enable EqF and IEKF design.

- **[Equivariant Filter Design for Discrete-time systems](https://arxiv.org/abs/2209.04965)** (2022)
_Yixiao Ge, Pieter van Goor, Robert Mahony_
Presents the equivariant structure of a discrete-time system and proposes a discrete-time version of the EqF.

### 2.2 Advanced EqF Architectures

- **[Equivariant Filter Design for Inertial Navigation Systems with Input Measurement Biases](https://arxiv.org/pdf/2202.02058)** (2022)
Expand All @@ -108,6 +112,10 @@ This page collects and categorizes key papers on invariant and equivariant filte
_Alessandro Fornasier, Yonhon Ng, Christian Brommer, Christoph Böhm, Robert Mahony, Stephan Weiss_
Paper that introduces a new generic formulation for a gyroscope aided attitude estimator, taking advantage of states in a single equivariant geometric structure.

- **[Equivariant Filter for Radar-Inertial Odometry](https://arxiv.org/abs/2604.23033)** (2026)
_Giulio Delama, Jan Michalczyk, Morten Nissov, Martin Scheiber, Alessandro Fornasier, Kostas Alexis, Stephan Weiss_
Proposes a discrete-time EqF for RIO based on a state-of-the-art Lie group symmetry that geometrically couples navigation states and IMU biases, and incorporates radar-IMU extrinsic calibration and multi-state constraint updates.

## 3. Applications and Advanced Topics

### 3.1 Legged Robotics & Contact Estimation
Expand Down Expand Up @@ -148,6 +156,12 @@ This page collects and categorizes key papers on invariant and equivariant filte
_Anbo Tao, Yarong Luo, Chunxi Xia, Chi Guo, Xingxing Li_
An EqF-based tightly coupled LiDAR-inertial odometry system. Uses a semi-direct product symmetry group that jointly couples IMU bias, navigation state, and LiDAR extrinsic calibration into a single equivariant structure, suppressing linearization error and improving robustness.

### 3.4 IMU Preintegration

- **[Equivariant IMU Preintegration with Biases: a Galilean Group Approach](https://arxiv.org/abs/2411.05548)** (2024)
_Giulio Delama, Alessandro Fornasier, Robert Mahony, Stephan Weiss_
An equivariant formulation of discrete-time IMU preintegration on the left-trivialized tangent group of the Galilean group.

## 4. General Equivariance

**Disclaimer**: There are many more works in the field of general equivariance than we can list here. This part will not be exhaustive, but rather an interesting pointer into that literature!
Expand Down Expand Up @@ -186,4 +200,4 @@ This page collects and categorizes key papers on invariant and equivariant filte

---

For software and practical implementations, see the **[Examples and Implementations](notebooks.md)** section of this site and the GTSAM EKF variants documentation.
For software and practical implementations, see the **[Examples and Implementations](notebooks.md)** section of this site and the GTSAM EKF variants documentation.