Universität Bonn

IGG | Geodesy

Trajectory Estimation and Evaluation

© IGG Geodesy

Trajectory evaluation using repeated railbound measurements

Accurately determining the position and the orientation of a moving platform, known as its trajectory is of great importance in various domains such as kinematic laser scanning. To get a better understanding of the quality of a trajectory and the products derived with it, trajectories can be evaluated using various techniques. A common method is to compare the test trajectory to the result of a more accurate sensor or trajectory estimation algorithm. At the University of Bonn this approach is taken one step further by using a rail-track based testing facility.

On this rail track, test systems can be moved repeatedly along the same trajectory while being tracked by a total station. Using this approach the system can be evaluated in two regards:

  • Repeatability of the trajectory: Knowing that the rail-bound trajectory should not change in shape, any differences between repeatedly recorded trajectories are most likely due to sensor deviations.
  • Accuracy of the trajectory: Achieved by comparing the mean test trajectory of multiple traversed laps to the higher-order reference trajectory of the total station. 



  • Tombrink, G., Dreier, A., Klingbeil, L. & Kuhlmann, H. (2023). Trajectory evaluation using repeated rail-bound measurements. Journal of Applied Geodesy, 17(3), 205-216. https://doi.org/10.1515/jag-2022-0027
© IGG Geodesy

High Accurate Vehicle Trajectory Estimation

The accurate estimation trajectory (position and orientation) of vehicles is of crucial importance in research areas like navigation, and mapping of urban or agricultural field environments. One popular technique for pose estimation is the use of GNSS (Global Navigation Satellite System) and IMU (Inertial Measurement Unit) sensors. The focus of the research is on the development of filter techniques combining the sensor data of multiple sensors. These include classical Kalman Filter and Kalman smoother methods, but also more recent techniques such as factor graph optimizations. The algorithms are implemented in a number of the systems that are used in our research.

The fusion of GNSS and IMU data for accurate pose estimation can be visualized illustrative by graph structure as shown in the top figure left. The goal estimates are the vehicle’s trajectory composed of the position and orientation, highlighted in orange dots. The position measurement coming from GNSS is marked in green. The IMU measures the vehicle's acceleration [𝑚∕𝑠^2 ] and angular velocity [𝑟𝑎𝑑∕𝑠]. These measurements are integrated over time to determine the vehicle's change in position and orientation. This Integration is highlighted as blue dots. Within a least-squares adjustment, the poses are estimated at a position accuracy of just a few centimeters. Current research focuses on the extension of the pose estimation by including precise prism measurements coming from a total station or including angle information of dual antenna GNSS receivers.

One application is the trajectory estimation of the PhenoRob agricultural field robot for the generation of high-resolution plant scans in the field, see image left, middle. The centimeter-accurate trajectory estimation enables multi-temporal registration of the robot’s laser data and 3D crop models and high potential crop health monitoring and understanding plant growth processes.



  • Esser, F., Rosu, R. A., Cornelißen, A., Klingbeil, L., Kuhlmann, H., & Behnke, S. (2023). Field Robot for High-Throughput and High-Resolution 3D Plant Phenotyping: Towards Efficient and Sustainable Crop Production. IEEE Robotics & Automation Magazine. https://doi.org/10.1109/MRA.2023.3321402
  • Esser, F.; Klingbeil, L.; Zabawa, L.; Kuhlmann, H. (2023) Quality Analysis of a High-Precision Kinematic Laser Scanning System for the Use of Spatio-Temporal Plant and Organ-Level Phenotyping in the Field. Remote Sens.  15, 1117. https://doi.org/10.3390/rs15041117
  • Esser, F., Moraga, J. A., Klingbeil, L., & Kuhlmann, H. (2023). Accuracy improvement of mobile laser scanning point clouds using graph-based trajectory optimization. Presentation at the 5th Joint International Symposium on Deformation Monitoring (JISDM), Valencia, Spain, 2022, http://doi.org/10.4995/JISDM2022.2022.13728

© IGG Geodesy

LiDAR-Inertial Fusion-based State Estimation

State estimation is crucial for mobile robot navigation. To this end, LiDAR-inertial fusion is often used to take the complementary advantages of the two sensors, so as to reduce the long-term error drift. Although LiDAR-inertial odometry (LIO) has been a hot research topic in last decades, existing methods usually require proper parameter tuning to be applied to different datasets.

We propose a simple yet accurate, generic and efficient LIO system based on point-to-point registration and extended Kalman filter, named LIO-EKF. We further propose a novel adaptive model to automatically compute the point-to-point matching threshold for the data association by accounting for the pose uncertainty, map discretization error and sensor noise. LIO-EKF can be employed in different environments with different vehicle motion profiles at a very high frequency.



  • Y. Wu, T. Guadagnino, L. Wiesmann, L. Klingbeil, C. Stachniss, and H. Kuhlmann (2023) “LIO-EKF: High frequency LiDAR-inertial odometry using extended Kalman filters,” arXiv, (preprint)
© IGG Geodesy

State Estimation using Wheel-mounted IMUs

Improving the state estimation accuracy while reducing the cost is crucial for real-world mobile robot applications. To this end, we proposed Wheel-INS, a dead reckoning solution for wheeled vehicles using only one low-cost wheel-mounted IMU. There are two major advantages of mounting IMU to the wheel: 1) the vehicle velocity can be directly obtained by the Wheel-IMU without wheel encoder; 2) the rotation modulation can be leveraged to mitigate the error accumulation of the inertial navigation system.

Wheel-INS has been further extended to a multiple IMUs-based localization system with different configurations (Wheel-INS2), and a SLAM solution (Wheel-SLAM) that uses the terrain features (road bank angles) estimated by Wheel-INS for loop closure detection.



  • Y. Wu, J. Kuang, X. Niu, J. Behley, L. Klingbeil and H. Kuhlmann, "Wheel-SLAM: Simultaneous Localization and Terrain Mapping Using One Wheel-Mounted IMU," in IEEE Robotics and Automation Letters, vol. 8, no. 1, pp. 280-287, 2022.
  • X. Niu, Y. Wu, and J. Kuang, “Wheel-INS: A wheel-mounted MEMS IMU-based dead reckoning system,” IEEE Transactions on Vehicular Technology, vol. 70, no. 10, pp. 9814–9825, 2021.
  • Y. Wu, X. Niu, and J. Kuang, “A comparison of three measurement models for the wheel-mounted MEMS IMU-based dead reckoning system,” IEEE Transactions on Vehicular Technology, vol. 70, no. 11, pp. 11 193–11 203, 2021.
  • Y. Wu, J. Kuang and X. Niu, "Wheel-INS2: Multiple MEMS IMU-Based Dead Reckoning System With Different Configurations for Wheeled Robots," in IEEE Transactions on Intelligent Transportation Systems, vol. 24, no. 3, pp. 3064-3077, 2022.


Avatar Kuhlmann

Prof. Dr.-Ing. Heiner Kuhlmann

Head of working group


Nußallee 17

53115 Bonn

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