author: [email protected] (Cedric)

Unified Gaussian Preintegrated Measurements (UGPMs)

and the Linear Preintegrated Measurements (LPMs)

THIS VERSION IS ASSOCIATED TO OUR IJRR'23 PAPER, if you are after the RSS'21 implementation, please check the rss branch

This repository provides the C++ implementation of the preintegration methods presented in our IJRR'23 paper titled Continuous Latent State Preintegration for Inertial-Aided Systems. If you are using that code for any purpose, please cite the corresponding work as explained at the end of this page.

In short preintegration is a way to combine IMU data into pseudo measurements called preintegrated measurements. This is especially useful in the context of optimisation-based state estimation.

This repository contains the implementation of the UGPMs and LPMs (extended from our RSS'21 paper).

Dependencies

This repository depends on cmake and g++ for the compilation.

Libraries needed (boost is only needed for the example code, not in the preintegration code):

sudo apt-get install libeigen3-dev
sudo apt-get install libboost-all-dev
sudo apt-get install libceres-dev

Compile

You will need to compile the code in a build directory.

cd <this-repo>
mkdir build
cd build
cmake ..
make

Run

This repository contains two executables:

• ./ugpm_demo
• ./ugpm_tests

ugpm_demo

This allows you to run the different preintegration methods (UGPM, LPM, GPM) with different parameters over simulated IMU data. It then compute the error with respect to the ground truth. The parameters are:

• -m, --method : choice of the preintegration method "ugpm", "lpm", or "gpm" (with "ugpm" being the default value)
• -l, --length : length of the integration window (1 seconds by default)
• -q, --quantum : controls the length of the chunks in the per-chunk mode of the preintegrated measurements. If the quantum is negative, the per-chunk mode is deactivated (-1 by default).
• -n, -nb_inference : number of inference to compute to test/show the small marginal computational cost of additional inferences in the same integration window (useful when dealing with high framerate sensor fusion, e.g., lidar-inertial)
• -j, -jacobian : displays the Jacobian matrices produced by the preintegration method for postintegration correction vs. the numerical differentiation (most used for debugging, there is a full performance analysis of the postintegration corrections in the paper)
• -c, -correlate : flag to activate the correlation of the covariance matrix
• -h, --help: produces a succinct help message

Here is a typical output of the proposed program (ran from the build repository):

./ugpm_demo

Preintegration demonstration with UGPM
Time elapsed: 48.836 ms
Preintegration errors over window of 2 seconds:
  Rotation [deg] = 0.00965282
  Velocity [m/s] = 0.00557632
  Position [m]   = 0.00952968

Covariance
 7.71467e-08  5.65872e-10  5.75752e-10  8.79113e-08  1.65319e-09  3.63768e-07 -3.53171e-07  9.62554e-07  7.69773e-07
 5.65872e-10  7.71667e-08  5.14963e-10  1.81363e-07 -3.13346e-07  6.90536e-07 -3.91895e-07 -1.17165e-06  1.76373e-06
 5.75752e-10  5.14963e-10  7.69021e-08 -1.64092e-08 -7.89181e-07 -2.69892e-07  4.24886e-07 -1.51773e-06 -7.40387e-07
 8.79113e-08  1.81363e-07 -1.64092e-08  1.12349e-05  -2.4541e-07  2.57008e-06  6.34687e-05  2.22228e-06  7.88625e-06
 1.65319e-09 -3.13346e-07 -7.89181e-07  -2.4541e-07  2.25064e-05 -1.66091e-07  1.20559e-06  0.000100579 -2.22998e-06
 3.63768e-07  6.90536e-07 -2.69892e-07  2.57008e-06 -1.66091e-07  2.14592e-05 -6.27162e-06 -4.01028e-06  9.68205e-05
-3.53171e-07 -3.91895e-07  4.24886e-07  6.34687e-05  1.20559e-06 -6.27162e-06  0.000488208   2.8271e-05 -4.11921e-06
 9.62554e-07 -1.17165e-06 -1.51773e-06  2.22228e-06  0.000100579 -4.01028e-06   2.8271e-05  0.000657667 -3.34832e-05
 7.69773e-07  1.76373e-06 -7.40387e-07  7.88625e-06 -2.22998e-06  9.68205e-05 -4.11921e-06 -3.34832e-05  0.000599425

ugpm_tests

This executable runs a few simple test to check different features of this implementation (it intentionally triggers some warnings). Refer to the source code in ugpm_random_tests.cpp for more information.

Ideas and stuff to have in mind if you want to use in your system:

Choice of preintegration method

If your main constraint is the computation time, I recommend the use of the LPMs. For slow/normal scenarios, LPMs and UGPMs perform relatively similarly. In more challenging setups, the UGPMs provide better accuracy, and the UGPMs (per chunk) is still quite fast regardless of the interval window.

Preintegration object

In short, the overall use of the ImuPreintegration object corresponds to the instantiation of the object with the constructor ugpm::ImuPreintegration(data, start_t, t, preint_opt, prior) with:

• data: an ImuData structure defined in preint/types.h (basically just two vectors of accelerometer and gyroscope data).
• start_t: a double that represents the timestamp of the beginning of the integration window
• t: a std::vector<std::vector<double> > that contains the timestamps at which you want to infer the preintegrated measurements. Each of the vectors in t needs to be of increasing order (the vector of vector thing allows for passing multiple series of timestamp to ease the data management in the case of multi-modal systems).
• preint_opt: a PreintOption structure that specifies the parameters of the preintegration method. Its definition can be found in preint/types.h
• prior: a PreintPrior structure that specifies the prior knowledge of the IMU biases. Its definition can be found in preint/types.h.

Then, you can retrieve the preintegrated measurements using ugpm::ImuPreintegration::get(index_1, index_2) with index_1 and index_2 corresponding to the indexes in the vector of vector t[index_1][index_2]. The output will be a PreintMeas structure as defined in preint/types.h

Note that this version provides overloads of the constructor and get methods to allow the user to provide only one timestamp or a vector of timestamps for t. I also included a way to account for the uncertainty of the biases in the covariance via optional arguments of the method get (can be useful for later use in optimisation).

Heads-up

The computation time is impacted in different ways. We invite the user to read the paper for better understanding of the different parameters/options. To perform optimally, the UGPMs need a bit of data overlap between integration windows (8*state period in the code, can probably be changed).

Not all the features implemented have been fully tested, bugs are still possible.

Citing

The UGPMs and LPMs have both been introduced in Continuous Latent State Preintegration for Inertial-Aided Systems

@article{LeGentil2023,
	title={{Continuous Latent State Preintegration for Inertial-Aided Systems}},
	author={{Le Gentil}, Cedric and {Vidal-Calleja}, Teresa},
	journal={The International Journal of Robotics Research},
	year={2023},
	doi={10.1177/02783649231199537},
	publisher={Sage Publications}
}