Journal of Industrial Technology (산업기술연구)

Kangwon National University, Institute of Industrial Technology (강원대학교 산업기술연구소)
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A Study on the Point-Mass Filter for Nonlinear State-Space Models

비선형 상태공간 모델을 위한 Point-Mass Filter 연구

  • Yeongkwon Choe (Department of Smart Health Science and Technology, Graduate School, Kangwon National University)
  • Received : 2023.12.18
  • Accepted : 2023.12.26
  • Published : 2023.12.31
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Abstract

In this review, we introduce the non-parametric Bayesian filtering algorithm known as the point-mass filter (PMF) and discuss recent studies related to it. PMF realizes Bayesian filtering by placing a deterministic grid on the state space and calculating the probability density at each grid point. PMF is known for its robustness and high accuracy compared to other nonparametric Bayesian filtering algorithms due to its uniform sampling. However, a drawback of PMF is its inherently high computational complexity in the prediction phase. In this review, we aim to understand the principles of the PMF algorithm and the reasons for the high computational complexity, and summarize recent research efforts to overcome this challenge. We hope that this review contributes to encouraging the consideration of PMF applications for various systems.

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References

  1. Tuncer, B., Orguner, U., Ozkan, E., 2022, Multi-Ellipsoidal Extended Target Tracking With Variational Bayes Inference, IEEE Transactions on Signal Processing 70 3921-3934. https://doi.org/10.1109/TSP.2022.3192617
  2. Kuutti, S., Fallah, S., Katsaros, K., Dianati, M., Mccullough, F., Mouzakitis, A., 2018, A Survey of the State-of-the-Art Localization Techniques and Their Potentials for Autonomous Vehicle Applications, IEEE Internet of Things Journal 5:2 829-846. https://doi.org/10.1109/JIOT.2018.2812300
  3. Gallego, G., Lund, J. E.A., Mueggler, E., Rebecq, H., Delbruck, T., Scaramuzza, D., 2018, Event-Based, 6-DOF Camera Tracking from Photometric Depth Maps, IEEE Transactions on Pattern Analysis and Machine Intelligence 20:10 2402-2412. https://doi.org/10.1109/TPAMI.2017.2769655
  4. Daum, F., 2005, Nonlinear filters: beyond the Kalman filter, IEEE Aerospace and Electronic Systems Magazine 20:8 57-69. https://doi.org/10.1109/MAES.2005.1499276
  5. Li, T., Sun, S., Sattar, T. P., Corchado, J. M., 2014, Fight sample degeneracy and impoverishment in particle filters: A review of intelligent approaches, Expert Systems with Applications 41:8 3944-3954. https://doi.org/10.1016/j.eswa.2013.12.031
  6. Dunik, J., Sotak, M., Vesely, M., Straka, O., Hawkinson, W., 2019, Design of Rao-Blackwellized Point-Mass Filter With Application in Terrain Aided Navigation, IEEE Transactions on Aerospace and Electronic Systems 55:1 251-272. https://doi.org/10.1109/TAES.2018.2850210
  7. Park, J., Park, Y.-g., Park, C. G., 2020, Parameter Estimation of Radar Noise Model for Terrain Referenced Navigation Using a New EM Initialization Method, IEEE Transactions on Aerospace and Electronic Systems 56:1 107-112. https://doi.org/10.1109/TAES.2019.2911766
  8. Anonsen, K.B., Hallingstad, O., 2006, Terrain Aided Underwater Navigation Using Point Mass and Particle Filters, 2006 IEEE/ION Position, Location, And Navigation Symposium 1027-1035.
  9. Jeon, H. C., Park, W. J., Park, C. G., 2018, Grid Design for Efficient and Accurate Point Mass Filter-Based Terrain Referenced Navigation, IEEE Sensors Journal 18:4 1731-1738. https://doi.org/10.1109/JSEN.2017.2779463
  10. Vaman, D., 2012, TRN history, trends and the unused potential, 2012 IEEE/AIAA 31st Digital Avionics Systems Conference (DASC) 1A3-1-1A3-16.
  11. Yoo, Y. M., Park, C. G., 2015, Improvement of terrain referenced navigation using a Point Mass Filter with grid adaptation, International Journal of Control, Automation and Systems 13:5 1173-1181. https://doi.org/10.1007/s12555-013-0410-4
  12. Choe, Y., 2022, Numerical Methods for the Nonlinear Bayesian Filtering Problem of Terrain Referenced Navigation: Efficiency and Robustness Perspectives, Doctorate Thesis, Seoul National University, Republic of Korea.
  13. Choe, Y., Park, C. G. 2021, Point-Mass Filtering With Boundary Flow and Its Application to Terrain Referenced Navigation, IEEE Transactions on Aerospace and Electronic Systems 57:6 3600-3613. https://doi.org/10.1109/TAES.2021.3079585
  14. Bergman, N., 1999, Recursive Bayesian Estimation - Navigation and Tracking Applications, Doctorate Thesis, Linkoping University, Sweden.
  15. Park, Y.-G., Park, C. G., 2018, Grid Support Adaptation for Point Mass Filter Based Terrain Referenced Navigation Using Mutual Information, IEEE Sensors Journal 18:18 7603-7610. https://doi.org/10.1109/JSEN.2018.2862941
  16. Matousek, J., Dunik, J., Straka, O., 2020, Density Difference Grid Design in a Point-Mass Filter, Energies 13:16 4080.
  17. Simandl, M., Kralovec, J., Soderstrom, T., 2006, Advanced point-mass method for nonlinear state estimation, Automatica 42:7 1133-1145. https://doi.org/10.1016/j.automatica.2006.03.010
  18. Simandl, M., Kralovec, J., Soderstrom, T., 2002, Anticipative grid design in point-mass approach to nonlinear state estimation, IEEE Transactions on Automatic Control 47:4 699-702. https://doi.org/10.1109/9.995053
  19. Dunik, J., Straka, O., Matousek, J., 2020, Conditional Density Driven Grid Design in Point-Mass Filter, ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 9180-9184.
  20. Dunik, J., Straka, O.. Matousek, J.. Blasch, E., 2020, Copula-based convolution for fast point-mass prediction, Signal Processing 192 108367.
  21. Tichavsky, P., Straka, O., Dunik, J., 2020, Grid-Based Bayesian Filters With Functional Decomposition of Transient Density, IEEE Transactions on Signal Processing 71 92-104. https://doi.org/10.1109/TSP.2023.3240359
  22. Dunik, J., Straka, O., Matousek, J., Brandner, M., 2021, Accurate Density-Weighted Convolution for Point-Mass Filter and Predictor, IEEE Transactions on Aerospace and Electronic Systems 57:6 3574-3584. https://doi.org/10.1109/TAES.2021.3079568