SpringerLink
Log in

On distributed Kalman filter based state estimation algorithm over a bearings-only sensor network

  • Article
  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

This paper studies the distributed state estimation problem for a class of discrete-time linear time-varying systems over a bearings-only sensor network. A novel fusion estimation algorithm of the distance between the target and each sensor is constructed with the mean square error matrix of corresponding estimation being timely provided. Then, the refined estimation of distance is presented by minimizing the mean square error matrix. Furthermore, the distributed Kalman filter based state estimation algorithm is proposed based on the refined distance estimation. It is rigorously proven that the proposed method has the consistency and stability. Finally, numerical simulation results show the effectiveness of our methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Zhang Y, Tian Y P. Consensus tracking in sensor networks with periodic sensing and switching connected topologies. Syst Control Lett, 2015, 84: 44–51

    Article  MathSciNet  MATH  Google Scholar 

  2. He Q B, Chen F Y, Cai S M, et al. An efficient range-free localization algorithm for wireless sensor networks. Sci China Tech Sci, 2011, 54: 1053–1060

    Article  MATH  Google Scholar 

  3. Li C H, Zou H G, Shi D W, et al. Dual-quaternion-based satellite pose estimation and control with event-triggered data transmission. Sci China Tech Sci, 2023, 66: 1214–1224

    Article  Google Scholar 

  4. Yick J, Mukherjee B, Ghosal D. Wireless sensor network survey. Comput Networks, 2008, 52: 2292–2330

    Article  Google Scholar 

  5. Ren X, Wu J, Johansson K H, et al. Infinite horizon optimal transmission power control for remote state estimation over fading channels. IEEE Trans Automat Contr, 2017, 63: 85–100

    Article  MathSciNet  MATH  Google Scholar 

  6. Pei Y Q, Gu H B, Liu K X, et al. An overview on the designs of distributed observers in LTI multi-agent systems. Sci China Tech Sci, 2021, 64: 2337–2346

    Article  Google Scholar 

  7. Li W, Wang Z, Wei G, et al. A survey on multisensor fusion and consensus filtering for sensor networks. Discrete Dyn Nat Soc, 2015, 1–12

  8. Huang Z, Chen S, Hao C, et al. Bearings-only target tracking with an unbiased pseudo-linear Kalman filter. Remote Sens, 2021, 13: 2915

    Article  Google Scholar 

  9. Li J R, Li H Y, Tang G J, et al. Research on the strategy of angles-only relative navigation for autonomous rendezvous. Sci China Tech Sci, 2011, 54: 1865–1872

    Article  MATH  Google Scholar 

  10. Arun A, Ayyalasomayajula R, Hunter W, et al. P2SLAM: Bearing based WiFi SLAM for indoor robots. IEEE Robot Autom Lett, 2022, 7: 3326–3333

    Article  Google Scholar 

  11. Gong Z Y, Qiu C R, Tao B, et al. Tracking and gras** of moving target based on accelerated geometric particle filter on colored image. Sci China Tech Sci, 2021, 64: 755–766

    Article  Google Scholar 

  12. Woffinden D C, Geller D K. Observability criteria for angles-only navigation. IEEE Trans Aerosp Electron Syst, 2009, 45: 1194–1208

    Article  Google Scholar 

  13. Martinelli A, Siegwart R. Observability analysis for mobile robot localization. In: Proceedings of the 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems. Edmonton: IEEE, 2005. 1471–1476

    Google Scholar 

  14. Han X, Liu M, Zhang S, et al. A multi-node cooperative bearing-only target passive tracking algorithm via UWSNs. IEEE Sens J, 2019, 19: 10609–10623

    Article  Google Scholar 

  15. Nguyen N H, Dogancay K. Improved pseudolinear Kalman filter algorithms for bearings-only target tracking. IEEE Trans Signal Process, 2017, 65: 6119–6134

    Article  MathSciNet  MATH  Google Scholar 

  16. Asfia U, Radhakrishnan R, Sharma S N. Three-dimensional bearings-only target tracking: Comparison of few sigma point Kalman filters. In: Communication and Control for Robotic Systems. Singapore: Springer, 2022. 273–289

    Chapter  Google Scholar 

  17. Badriasl L, Dogancay K. Three-dimensional target motion analysis using azimuth/elevation angles. IEEE Trans Aerosp Electron Syst, 2014, 50: 3178–3194

    Article  Google Scholar 

  18. Nardone S C, Aidala V J. Observability criteria for bearings-only target motion analysis. IEEE Trans Aerospace Electro Syst, 1981, 17: 162–166

    Article  MathSciNet  Google Scholar 

  19. Bicchi A, Prattichizzo D, Marigo A, et al. On the observability of mobile vehicle localization. In: Theory and Practice of Control and Systems. Singapore: World Scientific, 1998. 142–147

    Google Scholar 

  20. Ma L, Hovakimyan N. Vision-based cyclic pursuit for cooperative target tracking. J Guid Control Dyn, 2013, 36: 617–622

    Article  Google Scholar 

  21. Xu S, Doğançay K, Hmam H. Distributed pseudolinear estimation and UAV path optimization for 3D AOA target tracking. Signal Process, 2017, 133: 64–78

    Article  Google Scholar 

  22. Zhang Q, **e Y, Song T L. Distributed multi-target tracking in clutter for passive linear array sonar systems. In: Proceedings of the 2017 20th International Conference on Information Fusion (Fusion). **’an: IEEE, 2017. 1–8

    Google Scholar 

  23. Zhong W, Luo X, Li X, et al. Lower bound accuracy of bearing-based localization for wireless sensor networks. IEEE Trans Signal Inf Process over Networks, 2020, 6: 556–569

    Article  MathSciNet  Google Scholar 

  24. Luo X, Zhong W, Li X, et al. Bearing rigidity-based localizability analysis for wireless sensor networks. IEEE Trans Signal Inf Process over Networks, 2020, 6: 526–539

    Article  MathSciNet  Google Scholar 

  25. Diao J, Guo J, Sun C. Vision-based target localization: A distributed convex optimization approach. In: Proceedings of the 2017 36th Chinese Control Conference (CCC). Dalian: IEEE, 2017. 8999–9004

    Chapter  Google Scholar 

  26. Mohammadi A, Asif A. Distributed consensus + innovation particle filtering for bearing/range tracking with communication constraints. IEEE Trans Signal Process, 2014, 63: 620–635

    Article  MathSciNet  MATH  Google Scholar 

  27. Huang S, Dissanayake G. Convergence and consistency analysis for extended Kalman filter based SLAM. IEEE Trans Robot, 2007, 23: 1036–1049

    Article  Google Scholar 

  28. Wang S, Ren W. On the convergence conditions of distributed dynamic state estimation using sensor networks: A unified framework. IEEE Trans Contr Syst Technol, 2017, 26: 1300–1316

    Article  Google Scholar 

  29. Hu J, **e L, Zhang C. Diffusion Kalman filtering based on covariance intersection. IEEE Trans Signal Process, 2011, 60: 891–902

    Article  MathSciNet  MATH  Google Scholar 

  30. Battistelli G, Chisci L. Kullback-Leibler average, consensus on probability densities, and distributed state estimation with guaranteed stability. Automatica, 2014, 50: 707–718

    Article  MathSciNet  MATH  Google Scholar 

  31. Reif K, Gunther S, Yaz E, et al. Stochastic stability of the discrete-time extended Kalman filter. IEEE Trans Automat Contr, 1999, 44: 714–728

    Article  MathSciNet  MATH  Google Scholar 

  32. Cai B, Yang J, Yuan S, et al. Estimation for fuzzy semi-Markov jump systems with indirectly accessible mode information and nonideal data transmission. IEEE Trans Syst Man Cyber Syst, 2019, 51: 4016–4027

    Article  Google Scholar 

  33. Cai B, Zhang L, Shi Y. Observed-mode-dependent state estimation of hidden semi-Markov jump linear systems. IEEE Trans Automat Contr, 2019, 65: 442–449

    Article  MathSciNet  MATH  Google Scholar 

  34. Jiang Y, Huang Y, Xue W, et al. On designing consistent extended Kalman filter. J Syst Sci Complex, 2017, 30: 751–764

    Article  MathSciNet  MATH  Google Scholar 

  35. Bai W, Xue W, Huang Y, et al. On extended state based Kalman filter design for a class of nonlinear time-varying uncertain systems. Sci China Inf Sci, 2018, 61: 042201

    Article  MathSciNet  Google Scholar 

  36. Liang C, Xue W, Fang H, et al. On distributed state estimation with bearing measurements. In: Proceedings of the 2022 International Conference on Guidance, Navigation and Control (ICGNC). Singapore: Springer, 2022

    Google Scholar 

  37. Hu J, Wang Z, Liu G P, et al. A prediction-based approach to distributed filtering with missing measurements and communication delays through sensor networks. IEEE Trans Syst Man Cyber Syst, 2020, 51: 7063–7074

    Article  Google Scholar 

  38. Horn R A, Johnson C R. Matrix Analysis. Cambridge: Cambridge University Press, 2012

    Book  Google Scholar 

  39. He X, Xue W, Fang H. Consistent distributed state estimation with global observability over sensor network. Automatica, 2018, 92: 162–172

    Article  MathSciNet  MATH  Google Scholar 

  40. Rockafellar R T. Convex Analysis. Princeton: Princeton University Press, 1997

    MATH  Google Scholar 

  41. Boyd S, Boyd S P, Vandenberghe L. Convex Optimization. Cambridge: Cambridge University Press, 2004

    Book  MATH  Google Scholar 

  42. Liang C, Xue W, Fang H. Observability analysis for target tracking systems with bearing measurements. In: Proceedings of the 2020 39th Chinese Control Conference (CCC). Shenyang: IEEE, 2020. 224–229

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Key Laboratory of Systems and Control, National Center for Mathematics and Interdisciplinary Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Bei**g, 100190, China

    ChenXu Liang, WenChao Xue & HaiTao Fang

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Bei**g, 100049, China

    ChenXu Liang, WenChao Xue & HaiTao Fang

  3. School of Astronautics, Beihang University, Bei**g, 100083, China

    Ran Zhang

Authors
  1. ChenXu Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. WenChao Xue
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. HaiTao Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ran Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to WenChao Xue.

Additional information

This work was supported by the National Key Research and Development Program of China (Grant No. 2022YFA1004703), the National Natural Science Foundation of China (Grant Nos. 62122083 and 62103014), and the Chinese Academy of Sciences Youth Innovation Promotion Association (Grant No. 2021003).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liang, C., Xue, W., Fang, H. et al. On distributed Kalman filter based state estimation algorithm over a bearings-only sensor network. Sci. China Technol. Sci. 66, 3174–3185 (2023). https://doi.org/10.1007/s11431-023-2433-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-023-2433-6

Search

Navigation