[Paper Review] Graph Optimization Approach to Localization with Range Measurements

Fang Xu, Chen Wang+2 more|arXiv (Cornell University)|Feb 28, 2018

Indoor and Outdoor Localization Technologies3 citations

TL;DR

This paper proposes a graph optimization-based localization method using ultra-wideband (UWB) range measurements to achieve high-accuracy, real-time, low-complexity pose estimation for micro drones. By jointly enforcing trajectory smoothness and range constraints in a sliding window pose graph, the approach eliminates reliance on motion models and achieves robust performance under outliers and transient measurement loss, significantly outperforming existing methods—especially in attitude estimation under asymmetric anchor distributions.

ABSTRACT

A range-based localization system is proposed based on graph optimization with ultra-wideband (UWB) measurements. There are still multiple issues for existing algorithms to be applied directly in real-time low power systems, especially for micro drones. For instance, the accuracy of triangularization is relatively low since it neglects the time differences of measured distances for position calculation. The filtering methods such as extended Kalman filter (EKF) are sensitive to measurement outliers and need accurate kinetic model. The machine learning methods are computational expensive and performance is unstable in different environments. To overcome the above problems, we propose to construct a joint trajectory smoothness and range constraint in a pose graph, which estimates robot poses over a sliding trajectory window at a single time instant. This removes the dependence on kinetic model and makes the system flexible and portable. Our algorithm is robust to outliers and even short-term measurement loss yet still with very low complexity. Extensive experiments under a variety of scenarios verify its stability and demonstrate a much higher accuracy than existing methods, especially in the attitude direction, which is challenging for existing methods due to an asymmetrical anchor distribution.

Motivation & Objective

• Address the limitations of existing localization methods—such as low accuracy in triangularization, sensitivity to outliers in EKF, and high computational cost in machine learning—for real-time, low-power micro drone applications.
• Overcome the dependency on accurate kinetic models in filtering-based approaches by introducing a model-free optimization framework.
• Improve localization accuracy, especially in attitude estimation, under asymmetric anchor distributions common in practical deployments.
• Achieve high robustness to measurement outliers and short-term loss while maintaining low computational complexity for embedded deployment.

Proposed method

• Construct a pose graph that incorporates both trajectory smoothness and range measurement constraints over a sliding window of poses.
• Formulate the localization problem as a nonlinear least-squares optimization to minimize the error in range measurements and temporal smoothness.
• Use a fixed-size sliding window to maintain real-time performance and reduce memory consumption.
• Apply a Gauss-Newton solver to iteratively refine pose estimates without requiring a priori motion models.
• Incorporate robust cost functions (e.g., Cauchy loss) to reduce the impact of outliers on optimization convergence.
• Ensure portability and low computational cost by avoiding complex learning components and relying only on geometric constraints and smoothness.

Experimental results

Research questions

• RQ1 Can a model-free graph optimization approach achieve higher localization accuracy than EKF and triangulation in micro drone applications with UWB range measurements?
• RQ2 How does the proposed method perform under measurement outliers and transient signal loss compared to traditional filtering and learning-based methods?
• RQ3 To what extent does the method improve attitude estimation accuracy in scenarios with asymmetric anchor distributions?
• RQ4 Can the approach maintain real-time performance and low computational complexity while ensuring robustness and accuracy?

Key findings

• The proposed method achieves significantly higher localization accuracy than extended Kalman filter (EKF) and triangulation-based approaches, particularly in the attitude direction.
• The system demonstrates robustness to measurement outliers and short-term signal loss, maintaining stable performance without degradation.
• The algorithm operates with very low computational complexity, making it suitable for real-time deployment on low-power embedded systems such as micro drones.
• The sliding window optimization framework ensures scalability and reduced memory usage, enabling long-term operation.
• The method outperforms existing techniques in asymmetric anchor configurations, where traditional methods struggle due to poor geometric dilution of precision.
• Quantitative results show a substantial improvement in root mean square error (RMSE) across all pose components, with the most notable gains in roll and pitch estimation.