Localization Optimization for UAVs Using Graph Algorithms

Overview

This project focuses on real-time localization optimization for unmanned aerial vehicles (UAVs) using graph-based optimization techniques. It integrates GPS and IMU data to enhance position accuracy, leveraging factor graph optimization to minimize localization errors.

Features

• Graph-Based Localization Optimization: GTSAM C++ factors graph library.
• Integration with ROS & PX4: Compatible with Robot Operating System (ROS) and PX4 autopilot for seamless UAV control.
• Simulation & Visualization: Supports Gazebo simulation and RVIZ visualization for real-time trajectory monitoring.
• Containerized Environment: Built using Docker for easy deployment and reproducibility.

Results

The statistical analysis involved examining plots and calculating error metrics such as RMSE (Root Mean Squared Error) and SD (Standard Deviation). A Python program was developed to compute trajectory errors and generate visualizations:

• 3D plots to track the trajectory.
• 2D plots displaying the distance between the optimized and true trajectories over time.

These visualizations were created using the Matplotlib library, while mathematical operations were performed with NumPy. The trajectory colors are consistent with RVIZ visualization:

• Blue - True trajectory.
• Red - Simulated GPS trajectory (noisy trajectory).
• Green - Optimized trajectory.

Additionally, error metrics for the simulated GPS trajectory were computed for comparison:

Metric	Value
SD	0.1464
RMSE	0.4860

The system was tested under three different scenarios:

1. Trajectory Results Using GPS Only

a) Real and optimized trajectories.	b) Noisy and optimized trajectories.
c) Point-wise trajectory of the optimized path, where point size represents the distance from the true position.	d) Plot of the distance between the optimized position and the true position over successive time intervals.

Metric	Value
SD	0.1466
RMSE	0.4917

2. Trajectory Results Using IMU Only

a) Real and optimized trajectories.	b) Noisy and optimized trajectories.
c) Point-wise trajectory of the optimized path, where point size represents the distance from the true position.	d) Plot of the distance between the optimized position and the true position over successive time intervals.

Metric	Value
SD	1.0279
RMSE	1.8808

3. Trajectory Results Using GPS + IMU (Optimized)

a) Real and optimized trajectories.	b) Noisy and optimized trajectories.
c) Point-wise trajectory of the optimized path, where point size represents the distance from the true position.	d) Plot of the distance between the optimized position and the true position over successive time intervals.

Metric	Value
SD	0.0511
RMSE	0.1374

Key Findings

• GPS alone provided unstable positioning due to lack of odometry constraints.
• IMU alone drifted significantly over time, causing large positioning errors.
• GPS + IMU fusion significantly improved localization.

Technologies

• Languages: C++ (for graph optimization), Python (for system integration)
• Frameworks: ROS Noetic, PX4 Autopilot
• Simulation & Visualization: Gazebo 11, RVIZ
• Containers: Docker

Future Work

• Extending support to UWB-based localization.
• Enhancing performance for real-world UAV missions.
• Expanding compatibility with additional sensors (a.g. camera, radio distance).