Maintainer: Giulio Delama
This is a header-only C++ library for equivariant Inertial Measurement Unit (IMU) preintegration, a fundamental building block that can be leveraged in different optimization-based Inertial Navigation System (INS) localization solutions. By utilizing an equivariant symmetry, our method geometrically couples navigation states and biases, leading to reduced errors and improved consistency compared to existing state-of-the-art techniques (paper).
The library has the following dependencies which are automatically downloaded and linked against:
This is a header-only C++ library meant to be used within other projects. Either copy the content of include folder within the external project's include folder or use cmake's FetchContent_Declare as follows
FetchContent_Declare(
EquivariantPreintegration
GIT_REPOSITORY https://github.com/aau-cns/equivariant-preintegration
GIT_TAG main
GIT_SHALLOW TRUE
GIT_PROGRESS TRUE
)
list(APPEND external EquivariantPreintegration)
list(APPEND include_dirs ${EQUIVARIANTPREINTEGRATION_INCLUDE_DIR})
list(APPEND libs EquivariantPreintegration)Alternatively, if you want to clone the repository and do a local build, follow these steps:
git clone https://github.com/aau-cns/equivariant-preintegration.git
cd equivariant-preintegration
mkdir build && cd build
cmake ../ -DCMAKE_BUILD_TYPE=Release -DBUILD_TESTS=True
cmake --build .To use the Equivariant Preintegration library in your project, include the preintegration.hpp header from the include directory. Here is a sample usage in a test file:
#include <iostream>
#include "core/preintegration.hpp"
#include "utils/tools.hpp"
int main() {
using namespace preintegration;
// Define the parameters
std::shared_ptr<PreintegrationParams<double>> params = std::make_shared<PreintegrationParams<double>>();
params->setGravity(Eigen::Vector3d::UnitZ() * -9.81);
params->setGyroNoiseSigma(1e-4);
params->setAccNoiseSigma(1e-3);
params->setGyroBiasNoiseSigma(1e-6);
params->setAccBiasNoiseSigma(1e-5);
// Initialize the preintegration object
EquivariantPreintegration<double> pim(params);
// Example IMU measurements
size_t n = 1000;
double dt = 0.01;
std::vector<Eigen::Vector3d> accs = utils::randomAcc<double>(-10, 10, n);
std::vector<Eigen::Vector3d> gyros = utils::randomGyro<double>(-1, 1, n);
// Integrate IMU measurements
for (int j = 0; j < n; ++j) {
pim.integrateMeasurement(accs[j], gyros[j], dt);
}
// Display preintegrated measurements
std::cout << "Preintegration Matrix:\n"
<< pim.Upsilon().asMatrix() << std::endl;
std::cout << "Preintegrated Rotation:\n"
<< pim.deltaRij() << std::endl;
std::cout << "Preintegrated Velocity: " << pim.deltaVij().transpose() << std::endl;
std::cout << "Preintegrated Position: " << pim.deltaPij().transpose() << std::endl;
std::cout << "Preintegration Time: " << pim.deltaTij() << std::endl;
std::cout << "Preintegration Covariance:\n" << pim.Cov() << "\n\n" << std::endl;
return 0;
}This code was written within the Control of Networked System (CNS), University of Klagenfurt.
This software is made available to the public to use (source-available), licensed under the terms of the BSD-2-Clause-License with no commercial use allowed, the full terms of which are made available in the LICENSE file. No license in patents is granted.
If you use this software in an academic research setting, please cite the corresponding paper.
@ARTICLE{10777045,
author={Delama, Giulio and Fornasier, Alessandro and Mahony, Robert and Weiss, Stephan},
journal={IEEE Robotics and Automation Letters},
title={Equivariant IMU Preintegration With Biases: A Galilean Group Approach},
year={2025},
volume={10},
number={1},
pages={724-731},
keywords={Lie groups;Navigation;Manifolds;Filtering theory;Vectors;Location awareness;Algebra;Accuracy;Libraries;Kalman filters;Localization;sensor fusion;SLAM},
doi={10.1109/LRA.2024.3511424}}