IMU as an Input vs. a Measurement of the State in Inertial-Aided State Estimation (2403.05968v2)

Abstract: Treating IMU measurements as inputs to a motion model and then preintegrating these measurements has almost become a de-facto standard in many robotics applications. However, this approach has a few shortcomings. First, it conflates the IMU measurement noise with the underlying process noise. Second, it is unclear how the state will be propagated in the case of IMU measurement dropout. Third, it does not lend itself well to dealing with multiple high-rate sensors such as a lidar and an IMU or multiple asynchronous IMUs. In this paper, we compare treating an IMU as an input to a motion model against treating it as a measurement of the state in a continuous-time state estimation framework. We methodically compare the performance of these two approaches on a 1D simulation and show that they perform identically, assuming that each method's hyperparameters have been tuned on a training set. We also provide results for our continuous-time lidar-inertial odometry in simulation and on the Newer College Dataset. In simulation, our approach exceeds the performance of an imu-as-input baseline during highly aggressive motion. On the Newer College Dataset, we demonstrate state of the art results. These results show that continuous-time techniques and the treatment of the IMU as a measurement of the state are promising areas of further research. Code for our lidar-inertial odometry can be found at: https://github.com/utiasASRL/steam_icp

• The paper introduces a continuous-time GP framework that treats IMU readings directly as state measurements, addressing noise and dropout issues.
• It demonstrates that both IMU input and measurement approaches achieve identical performance in 1D simulations under optimal hyperparameters.
• Application to lidar-inertial odometry reveals practical challenges and opportunities for integrating heterogeneous high-rate sensor data.

Continuous-Time State Estimation with IMU: Input vs. Measurement Approach

Introduction

Accurate state estimation is critical for robotic systems, and inertial measurement units (IMUs) serve a pivotal role in achieving this. Traditionally, IMUs have been treated as inputs to a motion model, a technique enhanced through preintegration to account for the high-rate output of these sensors. However, this standard practice confronts several challenges, notably the conflation of IMU measurement noise with process noise, ambiguity in state propagation during IMU dropout, and difficulties integrating multiple high-rate sensors. This paper introduces an alternative perspective by considering IMU measurements as direct measurements of the state within a continuous-time Gaussian process (GP) framework. We explore the implications of this shift in approach through a detailed comparison on a 1D simulation problem and extend our findings to lidar-inertial odometry.

IMU as an Input versus as a Measurement

The conventional method of preintegrating IMU inputs, while efficient, conflates measurement noise with process noise and lacks a clear strategy for handling IMU dropouts. In contrast, treating IMU readings as measurements of the state entails using a continuous-time state estimation framework, specifically employing GP interpolation for state propagation. This method opens the door to dealing with heterogeneous sensor inputs and multiple IMUs in a way that maintains computational efficiency comparable to the preintegration method. Key contributions include a systematic comparison of both approaches on a 1D simulation showing identical performance under optimal hyperparameters, the demonstration of preintegration within a continuous-time framework, and the application of these concepts to lidar-inertial odometry, demonstrating the practical value and potential of the measurement-centric approach.

Simulation Results and Discussion

Through a 1D simulation problem, we found that treating the IMU as an input versus as a state measurement yielded identical performance when hyperparameters were optimally tuned. The experiment underscored the flexibility and the potential of our proposed method in treating high-rate sensors within a unified framework without sacrificing computational efficiency. However, when applying our continuous-time lidar-inertial odometry to the Newer College Dataset, our approach did not demonstrate a consistent advantage over lidar odometry augmented with only gyroscope data. Several reasons, such as the fidelity of the ground truth and the limitations of our lidar-only odometry in highly dynamic environments, could account for this result, underscoring the necessity for further investigation.

Conclusion and Future Directions

This work challenges the conventional wisdom that treats IMU measurements as inputs within robotic state estimation problems. By proposing an alternative where these measurements are considered direct measurements of the state, we open new avenues for research, especially in handling heterogeneous and high-rate sensor data. Our simulation results affirm the viability of this approach, which performs on par with established methods under optimal conditions. However, the experimental evaluation on real-world datasets highlights the need for further refinement, particularly in enhancing the robustness of lidar odometry in dynamic scenarios. Future research will aim to address these challenges, explore the integration of multiple IMUs, and further exploit the advantages offered by the continuous-time framework for state estimation in robotics.