Continuous-Time Visual-Inertial State Estimation Using Chebyshev Polynomial Optimization

核心概念

This paper proposes an innovative continuous-time visual-inertial state estimation method based on Chebyshev polynomial optimization, which transforms the pose estimation problem into an optimization of polynomial coefficients and achieves higher accuracy compared to traditional preintegration methods.

要約

The paper presents a continuous-time visual-inertial state estimation algorithm based on Chebyshev polynomial optimization. The key highlights are:

1. Pose is modeled as a Chebyshev polynomial, with velocity and position obtained through analytical integration and differentiation. This transforms the continuous-time state estimation problem into a constant parameter optimization problem.

2. The optimization objective function incorporates the original IMU measurements, visual reprojection errors, and initial state constraints, avoiding the linearization issues in filtering methods and preserving the quasi-Gaussian nature of the measurements.

3. The use of Chebyshev polynomials ensures high accuracy and efficiency in the functional approximation. Simulation and experimental results on public datasets demonstrate that the proposed method outperforms traditional preintegration methods in both accuracy and computational efficiency.

4. The paper discusses the limitations of the current method, such as the lack of adaptive polynomial order selection and the focus on batch optimization. Future work will address these limitations by developing adaptive and real-time implementations of the Chebyshev polynomial optimization for visual-inertial state estimation.

統計

The simulation results show that, compared to the preintegration method, the Chebyshev polynomial optimization achieves:

47% lower attitude accumulative RMSE, 58% lower velocity accumulative RMSE, and 65% lower position accumulative RMSE for the circular trajectory.
68% lower attitude accumulative RMSE, 49% lower velocity, and 59% lower position accumulative RMSE for the straight-line trajectory.
The experimental results on the EuRoC MAV dataset demonstrate that the Chebyshev polynomial optimization achieves:

30% improvement in velocity estimation accuracy and 50% improvement in position estimation accuracy on average.
50% improvement in computational efficiency on average.

引用

"The core of VINS is the visual-inertial fusion state estimation algorithm."
"Optimization-based algorithms have sought to mitigate the errors induced by linearization."
"Continuous-time poses do not require the estimation of poses at each sensor measurement point, and the state dimension depends on the polynomial order of the pose representation, facilitating the fusion of sensors with different sampling rates."

抽出されたキーインサイト

Visual-inertial state estimation based on Chebyshev polynomial optimization

by Hongyu Zhang... 場所 arxiv.org 04-02-2024

https://arxiv.org/pdf/2404.01150.pdf

深掘り質問

How can the proposed Chebyshev polynomial optimization framework be extended to handle more complex sensor configurations, such as multi-camera or multi-IMU setups

The proposed Chebyshev polynomial optimization framework can be extended to handle more complex sensor configurations, such as multi-camera or multi-IMU setups, by adapting the optimization problem to incorporate data from multiple sensors. For multi-camera setups, each camera's measurements can be integrated into the optimization process by including additional visual measurement models and constraints. This would involve extending the state vector to include parameters related to each camera's pose and intrinsic parameters. The Chebyshev polynomial representation of poses can be expanded to accommodate the increased complexity of multiple camera views.
Similarly, for multi-IMU setups, the optimization framework can be modified to incorporate measurements from multiple IMUs. This would involve integrating the IMU measurements from each sensor into the dynamic constraints and objective function of the optimization problem. By including data from multiple IMUs, the system can benefit from redundancy and improved accuracy in estimating the state of the system.
In summary, extending the Chebyshev polynomial optimization framework to handle more complex sensor configurations involves adapting the optimization problem to incorporate data from multiple sensors, expanding the state vector to include parameters from each sensor, and modifying the dynamic constraints and objective function accordingly.

What are the potential challenges and considerations in developing a real-time, sliding-window implementation of the Chebyshev polynomial optimization for visual-inertial state estimation

Developing a real-time, sliding-window implementation of the Chebyshev polynomial optimization for visual-inertial state estimation poses several challenges and considerations. One key challenge is the computational complexity of continuously updating the optimization problem as new sensor measurements arrive. Real-time implementation requires efficient algorithms for updating the state estimation in a sliding window fashion without sacrificing accuracy.
Some potential considerations for developing a real-time implementation include:

Algorithm Efficiency: Ensuring that the optimization algorithm can handle the computational load of continuously updating the state estimation in real-time.
Memory Management: Managing the memory requirements of storing historical data within the sliding window while maintaining efficient access for optimization.
Sensor Synchronization: Ensuring that data from multiple sensors are synchronized and integrated correctly within the sliding window framework.
Robustness: Implementing error-handling mechanisms to address outliers or sensor failures that may impact the state estimation.
Latency: Minimizing the latency in processing sensor data and updating the state estimation to meet real-time requirements.

Developing a real-time, sliding-window implementation of the Chebyshev polynomial optimization requires a balance between computational efficiency, accuracy, and robustness to handle the challenges of continuous state estimation.

Given the improved accuracy and efficiency of the Chebyshev polynomial optimization, how can it be leveraged to enable new applications or enhance the performance of existing visual-inertial navigation systems in domains like autonomous driving, robotics, or augmented reality

The improved accuracy and efficiency of the Chebyshev polynomial optimization can be leveraged to enable new applications and enhance the performance of existing visual-inertial navigation systems in various domains. Some potential applications and enhancements include:

Autonomous Driving: The accurate and efficient state estimation provided by Chebyshev polynomial optimization can enhance the localization and mapping capabilities of autonomous vehicles. This can lead to improved navigation in complex urban environments and challenging weather conditions.

Robotics: In robotics applications, the precise state estimation enabled by Chebyshev polynomial optimization can enhance robot localization, path planning, and obstacle avoidance. This can lead to more efficient and reliable robotic operations in dynamic environments.

Augmented Reality: Chebyshev polynomial optimization can improve the accuracy of pose estimation in augmented reality systems, leading to more seamless integration of virtual objects into the real world. This can enhance user experiences and enable new interactive AR applications.

By leveraging the accuracy and efficiency of Chebyshev polynomial optimization, visual-inertial navigation systems can achieve higher performance levels and enable new capabilities in autonomous driving, robotics, augmented reality, and other domains.