Closed-form Preintegration Methods for Graph-based Visual-Inertial Navigation (1805.02774v2)

Abstract: In this paper we propose a new analytical preintegration theory for graph-based sensor fusion with an inertial measurement unit (IMU) and a camera (or other aiding sensors).Rather than using discrete sampling of the measurement dynamics as in current methods,we derive the closed-form solutions to the preintegration equations, yielding improved accuracy in state estimation.We advocate two new different inertial models for preintegration: (i) the model that assumes piecewise constant measurements, and (ii) the model that assumes piecewise constant local true acceleration.We show through extensive Monte-Carlo simulations the effect that the choice of preintegration model has on estimation performance.To validate the proposed preintegration theory, we develop both direct and indirect visual-inertial navigation systems (VINS) that leverage our preintegration.In the first, within a tightly-coupled, sliding-window optimization framework, we jointly estimate the features in the window and the IMU states while performing marginalization to bound the computational cost.In the second, we loosely-couple the IMU preintegration with a direct image alignment that estimates relative camera motion by minimizing the photometric errors (i.e., image intensity difference), allowing for efficient and informative loop closures. Both systems are extensively validated in real-world experiments and are shown to offer competitive performance to state-of-the-art methods.

• The paper introduces closed-form preintegration methods that replace traditional discrete sampling to enhance state estimation in visual-inertial systems.
• It proposes two new inertial models—piecewise constant measurements and local true acceleration—that better capture motion dynamics.
• Monte-Carlo simulations and real-world trials validate these methods, demonstrating improved accuracy and efficiency over existing approaches.

An Analytical Approach to Preintegrating Visual-Inertial Navigation

The paper by Eckenhoff, Geneva, and Huang introduces an analytical preintegration theory aiming to enhance graph-based visual-inertial navigation systems (VINS) that integrate inertial measurement units (IMUs) with visual input from cameras. This research proposes a framework that deviates from traditional discrete sampling methods, presenting closed-form solutions to the preintegration equations. This advancement promises improved accuracy in state estimation within VINS while maintaining computational efficiency.

Key Contributions

A noteworthy contribution of this research is the advocacy for two novel inertial models for preintegration:

1. Piecewise Constant Measurements Model - Assumes that inertial measurements remain constant over time intervals.
2. Piecewise Constant Local True Acceleration Model - Assumes local acceleration is constant over these intervals, arguably capturing the motion dynamics more effectively compared to the piecewise constant global acceleration model typically employed.

The authors utilize Monte-Carlo simulations to illustrate the influence of these models on estimation performance, substantiating the theories' robustness. Consequently, two variants of VINS were developed to validate the proposed methodologies:

• Indirect, Tightly-Coupled VINS - Employing a sliding-window optimization structure to concurrently estimate features within the window, optimizing computation via marginalization.
• Direct, Loosely-Coupled VINS - Integrates the IMU preintegration with direct image alignment, minimizing photometric errors to estimate relative camera motion efficiently.

Both systems were subjected to comprehensive real-world trials demonstrating competitive performance when benchmarked against state-of-the-art approaches.

Implications and Future Directions

This paper's implications extend both practically and theoretically within the field of sensor fusion and autonomous navigation. Practically, this research offers robust real-time solutions suitable for scenarios where GPS or other global references are unavailable—such as planetary exploration or indoor localization. Theoretically, it provides critical insights into the continuous nature of preintegration, introducing models that accurately reflect real-world dynamics over globally constant simplifications.

Future directions might involve further refinement to accommodate increasingly dynamic environments or integrating this approach with additional sensory data like LiDAR. Moreover, investigating applications beyond traditional mobile robotics could be fruitful.

Numerical Results and Performance

In terms of numerical results, the paper highlights that both proposed preintegration models outperform existing discrete integration methods, particularly in scenarios with more limited IMU frequency—common in low-cost systems. The models were tested against multiple datasets, yielding lower Root Mean Square Error (RMSE) values in both position and orientation estimates. These results confirm the models' validity and effectiveness.

Overall, this paper provides substantial contributions within the VINS domain, enhancing both accuracy and computational efficiency. While comprehensive, it invites further exploration into new and dynamic application domains, potentially shaping the future of autonomous navigation systems.