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Comparison of different pseudo-linear estimators for vision-based target motion estimation

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Abstract

Vision-based target motion estimation based Kalman filtering or least-squares estimators is an important problem in many tasks such as vision-based swarming or vision-based target pursuit. In this paper, we focus on a problem that is very specific yet we believe important. That is, from the vision measurements, we can formulate various measurements. Which and how the measurements should be used? These problems are very fundamental, but we notice that practitioners usually do not pay special attention to them and often make mistakes. Motivated by this, we formulate three pseudo-linear measurements based on the bearing and angle measurements, which are standard vision measurements that can be obtained. Different estimators based on Kalman filtering and least-squares estimation are established and compared based on numerical experiments. It is revealed that correctly analyzing the covariance noises is critical for the Kalman filtering-based estimators. When the variance of the original measurement noise is unknown, the pseudo-linear least-squares estimator that has the smallest magnitude of the transformed noise can be a good choice.

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Data Availability

The data used in this study are available from the corresponding author upon request.

References

  1. Vrba, M., & Saska, M. (2020). Marker-less micro aerial vehicle detection and localization using convolutional neural networks. IEEE Robotics and Automation Letters, 5(2), 2459–2466. https://doi.org/10.1109/lra.2020.2972819

    Article  Google Scholar 

  2. Li, J., Ning, Z., He, S., Lee, C.-H., & Zhao, S. (2022). Three-dimensional bearing-only target following via observability-enhanced helical guidance. IEEE Transactions on Robotics, 39(2), 1509–1526. https://doi.org/10.1109/tro.2022.3218268

  3. Kang, H., Joung, J., Kim, J., Kang, J., & Cho, Y. S. (2020). Protect your sky: A survey of counter unmanned aerial vehicle systems. IEEE Access, 8, 168671–168710. https://doi.org/10.1109/access.2020.3023473

    Article  Google Scholar 

  4. Dressel, L., & Kochenderfer, M.J.: (2019). Hunting drones with other drones: Tracking a moving radio target. In: 2019 International Conference on Robotics and Automation (ICRA). Montreal, QC, Canada. https://doi.org/10.1109/icra.2019.8794243

  5. Fogel, E., & Gavish, M. (1988). Nth-order dynamics target observability from angle measurements. IEEE Transactions on Aerospace and Electronic Systems, 24(3), 305–308. https://doi.org/10.1109/7.192098

    Article  MathSciNet  Google Scholar 

  6. He, S., Shin, H.-S., & Tsourdos, A. (2019). Trajectory optimization for target localization with bearing-only measurement. IEEE Transactions on Robotics, 35(3), 653–668. https://doi.org/10.1109/tro.2019.2896436

    Article  Google Scholar 

  7. Griffin, B.A., & Corso, J.J. (2021). Depth from camera motion and object detection. In: 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Nashville, TN, USA. https://doi.org/10.1109/cvpr46437.2021.00145

  8. Ma, Y., Soatto, S., & Kosecká, J., & Sastry, S.S. (2012). An Invitation to 3-D Vision, Interdisciplinary Applied Mathematics (1st ed., Vol. 26). New York: Springer. https://doi.org/10.1007/978-0-387-21779-6

  9. Walter, V., Staub, N., Franchi, A., & Saska, M. (2019). UVDAR system for visual relative localization with application to leader/follower formations of multirotor UAVs. IEEE Robotics and Automation Letters, 4(3), 2637–2644. https://doi.org/10.1109/lra.2019.2901683

    Article  Google Scholar 

  10. Schilling, F., Schiano, F., & Floreano, D. (2021). Vision-based drone flocking in outdoor environments. IEEE Robotics and Automation Letters, 6(2), 2954–2961. https://doi.org/10.1109/lra.2021.3062298

    Article  Google Scholar 

  11. Lin, X., Kirubarajan, T., Bar-Shalom, Y., Maskell, S. (2002). Comparison of EKF, pseudomeasurement, and particle filters for a bearing-only target tracking problem. In: O.E. Drummond (Ed.), SPIE Proceedings. Orlando, FL, USA. https://doi.org/10.1117/12.478508

  12. Lingren, A., & Gong, K. (1978). Position and velocity estimation via bearing observations. IEEE Transactions on Aerospace and Electronic Systems, AES–14(4), 564–577. https://doi.org/10.1109/taes.1978.308681

    Article  Google Scholar 

  13. Aidala, V., & Nardone, S. (1982). Biased estimation properties of the pseudolinear tracking filter. IEEE Transactions on Aerospace and Electronic Systems, AES–18(4), 432–441. https://doi.org/10.1109/taes.1982.309250

    Article  Google Scholar 

  14. Boie, R. A., & Cox, I. J. (1992). An analysis of camera noise. IEEE Transactions on Pattern Analysis & Machine Intelligence, 14(6), 671–674. https://doi.org/10.1109/34.141557

  15. Zhao, S., Chen, B. M., & Lee, T. H. (2013). Optimal sensor placement for target localisation and tracking in 2D and 3D. International Journal of Control, 86(10), 1687–1704. https://doi.org/10.1080/00207179.2013.792606

    Article  MathSciNet  MATH  Google Scholar 

  16. Bishop, A. N., Fidan, B., Anderson, B. D. O., Doğançay, K., & Pathirana, P. N. (2010). Optimality analysis of sensor-target localization geometries. Automatica, 46(3), 479–492. https://doi.org/10.1016/j.automatica.2009.12.003

    Article  MathSciNet  MATH  Google Scholar 

  17. Zhao, S., & Zelazo, D. (2019). Bearing rigidity theory and its applications for control and estimation of network systems: Life beyond distance rigidity. IEEE Control Systems Magazine, 39(2), 66–83. https://doi.org/10.1109/mcs.2018.2888681

    Article  MathSciNet  MATH  Google Scholar 

  18. Dogancay, K. (2015). 3D pseudolinear target motion analysis from angle measurements. IEEE Transactions on Signal Processing, 63(6), 1570–1580. https://doi.org/10.1109/tsp.2015.2399869

    Article  MathSciNet  MATH  Google Scholar 

  19. He, S., Wang, J., & Lin, D. (2018). Three-dimensional bias-compensation pseudomeasurement kalman filter for bearing-only measurement. Journal of Guidance, Control, and Dynamics, 41(12), 2678–2686. https://doi.org/10.2514/1.g003785

    Article  Google Scholar 

  20. Islam, S. A. U., & Bernstein, D. S. (2019). Recursive least squares for real-time implementation [lecture notes]. IEEE Control Systems, 39(3), 82–85. https://doi.org/10.1109/mcs.2019.2900788

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science and Technology, Zhejiang University, Hangzhou, 310058, Zhejiang, China

    Zian Ning

  2. School of Engineering, Westlake University, Hangzhou, 310024, Zhejiang, China

    Zian Ning, Yin Zhang & Shiyu Zhao

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  1. Zian Ning
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  2. Yin Zhang
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  3. Shiyu Zhao
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Correspondence to Shiyu Zhao.

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Ning, Z., Zhang, Y. & Zhao, S. Comparison of different pseudo-linear estimators for vision-based target motion estimation. Control Theory Technol. 21, 448–457 (2023). https://doi.org/10.1007/s11768-023-00161-y

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