|Table of Contents|

Citation:
 Yanqi Niu,Dandan Zhu,Yaan Li.An Improved High-Degree Cubature Particle Filter and its Application in Bearing-only Tracking[J].Journal of Marine Science and Application,2026,(1):300-311.[doi:10.1007/s11804-025-00619-2]
Click and Copy

An Improved High-Degree Cubature Particle Filter and its Application in Bearing-only Tracking

Info

Title:
An Improved High-Degree Cubature Particle Filter and its Application in Bearing-only Tracking
Author(s):
Yanqi Niu Dandan Zhu Yaan Li
Affilations:
Author(s):
Yanqi Niu Dandan Zhu Yaan Li
School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China
Keywords:
Nonlinear filteringFifth-degree cubature particle filterEKF-5CPFBearings-only target motion analysis
分类号:
-
DOI:
10.1007/s11804-025-00619-2
Abstract:
In this study, a fifth-degree cubature particle filter (5CPF) is proposed to address the limited estimation accuracy in traditional particle filter algorithms for bearings-only tracking (BOT). This algorithm calculates the recommended density function by introducing a fifth-degree cubature Kalman filter algorithm to guide particle sampling, which effectively alleviates the problem of particle degradation and significantly improves the estimation accuracy of the filter. However, the 5CPF algorithm exhibits high computational complexity, particularly in scenarios with a large number of particles. Therefore, we propose the extended Kalman filter (EKF)-5CPF algorithm, which employs an EKF to replace the time update step for each particle in the 5CPF. This enhances the algorithm’s real-time capability while maintaining the high precision advantage of the 5CPF algorithm. In addition, we construct bearing-only dual-station and single-motion station target tracking systems, and the filtering performances of 5CPF and EKF-5CPF algorithms under different conditions are analyzed. The results show that both the 5CPF algorithm and EKF-5CPF have strong robustness and can adapt to different noise environments. Furthermore, both algorithms significantly outperform traditional nonlinear filtering algorithms in terms of convergence speed, tracking accuracy, and overall stability.

References:

[1] Arasaratnam I, Haykin SS (2009) Cubature Kalman filters. IEEE Transactions on Automatic Control 54(6):1254-1269. https://doi.org/10.1109/TAC.2009.2019800
[2] Arulampalam MS, Maskell S, Gordon N, Clapp T (2002) A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Transactions on Signal Processing 50(2): 174-188. https://doi.org/10.1109/78.978374
[3] Arulampalam S, Ristic B (2000) Comparison of the particle filter with range-parameterized and modified polar EKFs for angle-only tracking. Signal and Data Processing of Small Targets Bellingham: SPIM 4048: 288-299. https://doi.org/10.1117/12.391985
[4] Badriasl L, Arulampalam S, Nguyen NH, Finn A (2020) An algebraic closed-Form solution for bearings-only maneuvering target motion analysis from a nonmaneuvering platform. IEEE Transactions on Signal Processing 68: 4672-4687. https://doi.org/10.1109/TSP.2020.3012004
[5] Boli? M, Djuri? PM, Hong S (2004) Resampling algorithms for particle filters: A computational complexity perspective. EURASIP Journal on Advances in Signal Processing Article number: 403686. https://doi.org/10.1155/S1110865704405149
[6] Divya KS, Ramesh KS, Rao SK, Naga Divya G (2021) Underwater object tracking using unscented Kalman filter. 2021 3rd International Conference on Advances in Computing, Communication Control and Networking (ICAC3N). Piscataway: IEEE 1729-1733. https://doi.org/10.1109/ICAC3N53548.2021.9725674
[7] Farina A (1999) Target tracking with bearings-Only measurements. Signal Processing 78(1): 61-78. https://doi.org/10.1016/S0165-1684(99)00047-X
[8] Gao B, Xu D, Yan W (2010) Framed-quadtree path planning for an underwater vehicle with the task of tracking a moving target. Journal of Marine Science and Application 9: 27-33. https://doi.org/10.1007/s11804-010-8011-6
[9] Hammersley JM, Morton KW (1954) Poor man’s Monte Carlo. Journal of the Royal Statistical Society Series B(Methodological) 16: 23-38. https://doi.org/10.1111/j.2517-6161.1954.tb00145.x
[10] Havangi R (2018) Target tracking with unknown noise statistics based on intelligent H infty particle filter. International Journal of Adaptive Control and Signal Processing 32: 858-874. https://doi.org/10.1002/acs.2872
[11] Jia B, Xin M, Cheng Y (2013) High-degree cubature Kalman filter. Automatica 49(2): 510-518. https://doi.org/10.1016/j.automatica.2012.11.014
[12] Jia B, Xin M, Cheng Y (2012) The high-degree cubature Kalman filter. 2012 IEEE 51st IEEE Conference on Decision and Control (CDC). Piscataway: IEEE 4095-4100. https://doi.org/10.1109/CDC.2012.6426413
[13] Kotecha JH, Djuric PM (2003) Gaussian particle filtering. IEEE Transactions on Signal Processing 51(10): 2592-2601. https://doi.org/10.1109/TSP.2003.816758
[14] Kulikova MV, Kulikov GY (2021) MATLAB-based general approach for square-root extended-unscented and fifth-degree cubature Kalman filtering methods. European Journal of Control 59: 1-12. https://doi.org/10.1016/j.ejcon.2021.01.003
[15] Kumar DVANR, Rao SK, Raju KP (2016) Integrated unscented Kalman filter for underwater passive target tracking with towed array measurements. Optik 127(5): 2840-2847. https://doi.org/10.1016/j.ijleo.2015.11.217
[16] Kuptametee C, Aunsri N (2022) A review of resampling techniques in particle filtering framework. Measurement 193:110836. https://doi.org/10.1016/j.measurement.2022.110836
[17] Li T, Villarrubia G, Sun S, Corchado JM, Bajo J (2015) Resampling methods for particle filtering: Identical distribution, a new method, and comparable study. Frontiers of Information Technology & Electronic Engineering 16: 969-984. https://doi.org/10.1631/FITEE.1500199
[18] Li Y, Zhao Z (2019) Passive tracking of underwater targets using dual observation stations. 2019 16th International Bhurban Conference on Applied Sciences and Technology (IBCAST). Piscataway: IEEE 867-872. https://doi.org/10.1109/IBCAST.2019.8667211
[19] Lu X, Li F, Tang J, Chai Z, Hu M (2022) A new performance index for measuring the effect of single target tracking with Kalman particle filter. International Journal of Modern Physics C 33(9): 2250116. https://doi.org/10.1142/S0129183122501169
[20] Mu J, Tian F, Cheng J (2024) Adaptive and robust fractional gain based interpolatory cubature Kalman filter. Measurement and Control 57(4): 428-442. https://doi.org/10.1177/00202940231200954
[21] Nardone S, Lindgren A, Gong K (1984) Fundamental properties and performance of conventional bearings-only target motion analysis. IEEE Transactions on Automatic Control 29(9): 775-787. https://doi.org/10.1109/TAC.1984.1103664
[22] Pillon D, Perez-Pignol AC, Jauffret C (2016) Observability: Range-only vs. bearings-only target motion analysis for a leg-by-leg observer’s trajectory. IEEE Transactions on Aerospace and Electronic Systems 52(4): 1667-1678. https://doi.org/10.1109/TAES.2016.150016
[23] Shen Y, Li Y, Li W, Gao H, Wu C (2024a) A novel underwater weak target detection method based on 3D chaotic system and maximal overlap discrete wavelet transform. The European Physical Journal Plus 139: 325. https://doi.org/10.1140/epjp/s13360-024-05135-w
[24] Shen Y, Li Y, Li W, Gao H, Wu C (2024b) A novel underwater weak signal detection method based on parameter optimized VMD and 3D chaotic system. Digital Signal Processing 151: 104571. https://doi.org/10.1016/j.dsp.2024.104571
[25] Shen Y, Li Y, Li W, Yao Q (2024c) Generalized fined-grained multiscale information entropy with multi-feature extraction and its application in phase space reconstruction. Chaos, Solitons & Fractals 189(part 2): 115710. https://doi.org/10.1016/j.chaos.2024.115710
[26] Shen Y, Li Y, Li W, Yao Q, Gao H (2025) Extremely multi-stable grid-scroll memristive chaotic system with omni-directional extended attractors and application of weak signal detection. Chaos, Solitons & Fractals 190: 115791. https://doi.org/10.1016/j.chaos.2024.115791
[27] Singh AK, Bhaumik S (2015) Higher degree cubature quadrature kalman filter. International Journal of Control, Automation and Systems 13: 1097-1105. https://doi.org/10.1007/s12555-014-0228-8
[28] van der Merwe R, Doucet A, de Freitas N, Wan E (2000) The unscented particle filter. Advances in Neural Information Processing Systems 13 (NIPS 2000). Cambridge: Cambridge University Technical Report CUED/F-INFENG/TR 380
[29] Wang S, Feng J, Tse CK (2014) Spherical simplex-radial cubature Kalman filter. IEEE Signal Processing Letters 21: 43-46. https://doi.org/10.1109/LSP.2013.2290381
[30] Weiss H, Moore J (1980) Improved extended Kalman filter design for passive tracking. IEEE Transactions on Automatic Control 25(4): 807-811. https://doi.org/10.1109/TAC.1980.1102436
[31] Xu B, Wang Z (2006) A new algorithm of bearings-only multi-target tracking of bistatic system. Journal of Control Theory and Applications 4: 331-337. https://doi.org/10.1007/s11768-006-5320-z
[32] Zhang X, Liu D, Yang Y, Liang J (2021) An intelligent particle filter with adaptive M-H resampling for liquid-level estimation during silicon crystal growth. IEEE Transactions on Instrumentation and Measurement 70: 1-12. https://doi.org/10.1109/TIM.2020.3026760
[33] Zhu J, Liu B, Wang H, Li Z, Zhang Z (2020) State estimation based on improved cubature Kalman filter algorithm. IET Science, Measurement & Technology 14: 536-542. https://doi.org/10.1049/iet-smt.2019.0363

Memo

Memo:
Received date:2024-10-21;Accepted date:2025-4-17。<br>Foundation item:Supported by the Guangxi Special Program for Technological Innovation Guidance (No. GuiKeAC25069006).<br>Corresponding author:Yaan Li,Email:E-mail:liyaan@nwpu.edu.cn
Last Update: 2026-03-10