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Fully distributed variational Bayesian non-linear filter with unknown measurement noise in sensor networks

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  • Special Focus on Multi-source Information Fusion
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Abstract

In practical applications, the measurement noise statistics is usually unknown or may change over time. However, most existing distributed filtering algorithms for sensor networks are constructed based on exact knowledge of measurement noise statistics. Therefore, under situations with measurement uncertainty, the existing algorithms may result in deteriorated performance. To solve such problems, a distributed adaptive cubature information filter based on variational Bayesian (VB-DACIF) is proposed here. Firstly, the predicted estimates of interest from inclusive neighbours are fused by minimizing the weighted Kullback-Leibler average, in which the cubature rule is utilized to tackle system nonlinearity. Then, the free form variational Bayesian approximation is applied to recursively update both the local estimate and the precision matrices of sensing nodes. Finally, the posterior Cramér-Rao lower bound is exploited to evaluate performance of the proposed VB-DACIF. Simulation results with a maneuvering target tracking scenario validates the feasibility and superiority of the proposed VB-DACIF.

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References

  1. Olfati-Saber R, Fax J A, Murray R M. Consensus and cooperation in networked multi-agent systems. Proc IEEE, 2007, 95: 215–233

    MATH  Google Scholar 

  2. Kamal A T, Farrell J A, Roy-Chowdhury A K. Information weighted consensus filters and their application in distributed camera networks. IEEE Trans Autom Control, 2013, 58: 3112–3125

    MathSciNet  MATH  Google Scholar 

  3. Battistelli G, Chisci L, Mugnai G, et al. Consensus-based linear and nonlinear filtering. IEEE Trans Autom Control, 2015, 60: 1410–1415

    MathSciNet  MATH  Google Scholar 

  4. Wang S C, Ren W. On the convergence conditions of distributed dynamic state estimation using sensor networks: a unified framework. IEEE Trans Control Syst Technol, 2018, 26: 1300–1316

    Google Scholar 

  5. Chandra K P B, Gu D W, Postlethwaite I. Square root cubature information filter. IEEE Sens J, 2013, 13: 750–758

    Google Scholar 

  6. Lee D J. Nonlinear estimation and multiple sensor fusion using unscented information filtering. IEEE Signal Process Lett, 2008, 15: 861–864

    Google Scholar 

  7. Olfati-Saber R, Murray R M. Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Autom Control, 2004, 49: 1520–1533

    MathSciNet  MATH  Google Scholar 

  8. Talebi S P, Werner S. Distributed Kaiman filtering and control through embedded average consensus information fusion. IEEE Trans Autom Control, 2019, 64: 4396–4403

    MATH  Google Scholar 

  9. Song B, Kamal A T, Soto C, et al. Tracking and activity recognition through consensus in distributed camera networks. IEEE Trans Image Process, 2010, 19: 2564–2579

    MathSciNet  MATH  Google Scholar 

  10. Kwon C, Hwang I. Sensing-based distributed state estimation for cooperative multiagent systems. IEEE Trans Autom Control, 2019, 64: 2368–2382

    MathSciNet  MATH  Google Scholar 

  11. Olfati-Saber R. Kalman-consensus filter: optimality, stability, and performance. In: Proceedings of the 48th IEEE Conference on Decision and Control (CDC), Shanghai, 2009. 7036–7042

    Google Scholar 

  12. Li W L, Jia Y M. Distributed consensus filtering for discrete-time nonlinear systems with non-Gaussian noise. Signal Process, 2012, 92: 2464–2470

    Google Scholar 

  13. Hu C, Lin H S, Li Z H, et al. Kullback-Leibler divergence based distributed cubature Kaiman Alter and its application in cooperative space object tracking. Entropy, 2018, 20: 116

    Google Scholar 

  14. Cattivelli F S, Lopes C G, Sayed A H. Diffusion strategies for distributed Kaiman filtering: formulation and performance analysis. In: Proceedings of the 1st IAPR Workshop on Cognitive Information Processing, 2008. 36–41

    Google Scholar 

  15. Hu J W, Xie L H, Zhang C S. Diffusion Kaiman filtering based on covariance intersection. IEEE Trans Signal Process, 2012, 60: 891–902

    MathSciNet  MATH  Google Scholar 

  16. Kamal A T, Bappy J H, Farrell J A, et al. Distributed multi-target tracking and data association in vision networks. IEEE Trans Pattern Anal Mach Intell, 2016, 38: 1397–1410

    Google Scholar 

  17. Jia B, Pham K D, Blasch E, et al. Cooperative space object tracking using space-based optical sensors via consensus-based filters. IEEE Trans Aerosp Electron Syst, 2016, 52: 1908–1936

    Google Scholar 

  18. Wang S C, Lyu Y, Ren W. Unscented-transformation-based distributed nonlinear state estimation: algorithm, analysis, and experiments. IEEE Trans Control Syst Technol, 2019, 27: 2016–2029

    Google Scholar 

  19. Battistelli G, Chisci L, Fantacci C. Parallel consensus on likelihoods and priors for networked nonlinear filtering. IEEE Signal Process Lett, 2014, 21: 787–791

    Google Scholar 

  20. Mohammadi A, Asif A. Distributed consensus + innovation particle filtering for bearing/range tracking with communication constraints. IEEE Trans Signal Process, 2015, 63: 620–635

    MathSciNet  MATH  Google Scholar 

  21. Hlinka O, Hlawatsch F, Djuric P M. Consensus-based distributed particle filtering with distributed proposal adaptation. IEEE Trans Signal Process, 2014, 62: 3029–3041

    MathSciNet  MATH  Google Scholar 

  22. Arasaratnam I, Haykin S. Cubature Kaiman filters. IEEE Trans Autom Control, 2009, 54: 1254–1269

    MATH  Google Scholar 

  23. He S M, Shin H, Xu S Y, et al. Distributed estimation over a low-cost sensor network: a review of state-of-the-art. Inf Fusion, 2020, 54: 21–43

    Google Scholar 

  24. Chen Q, Yin C, Zhou J, et al. Hybrid consensus-based cubature Kaiman filtering for distributed state estimation in sensor networks. IEEE Sens J, 2018, 18: 4561–4569

    Google Scholar 

  25. Chen Q, Wang W C, Yin C, et al. Distributed cubature information filtering based on weighted average consensus. Neurocomputing, 2017, 243: 115–124

    Google Scholar 

  26. Mehra R. Approaches to adaptive filtering. IEEE Trans Autom Control, 1972, 17: 693–698

    MathSciNet  MATH  Google Scholar 

  27. Maybeck P S. Stochastic Models, Estimation, and Control. Orlando: Academic Press, 1982

    MATH  Google Scholar 

  28. Li X R, Bar-Shalom Y. Recursive multiple model approach to noise identification. IEEE Trans Aerosp Electron Syst, 1994, 30: 671–684

    Google Scholar 

  29. Storvik G. Particle filters for state-space models with the presence of unknown static parameters. IEEE Trans Signal Process, 2002, 50: 281–289

    MathSciNet  Google Scholar 

  30. Sarkka S, Nummenmaa A. Recursive noise adaptive kalman filtering by variational Bayesian approximations. IEEE Trans Autom Control, 2009, 54: 596–600

    MathSciNet  MATH  Google Scholar 

  31. Sarkka S, Hartikainen J. Non-linear noise adaptive Kalman filtering via variational Bayes. In: Proceedings of IEEE International Workshop on Machine Learning for Signal Processing (MLSP), 2013

    Google Scholar 

  32. Dong P, Jing Z L, Leung H, et al. Variational Bayesian adaptive cubature information filter based on wishart distribution. IEEE Trans Autom Control, 2017, 62: 6051–6057

    MathSciNet  MATH  Google Scholar 

  33. Shen K, Jing Z L, Dong P. A consensus nonlinear filter with measurement uncertainty in distributed sensor networks. IEEE Signal Process Lett, 2017, 24: 1631–1635

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  35. Bishop C M. Pattern Recognition and Machine Learning. Berlin: Springer, 2006

    MATH  Google Scholar 

  36. Akaike H. Information theory and an extension of the maximum likelihood principle. Berlin: Springer, 1998

    MATH  Google Scholar 

  37. Hurley M B. An information theoretic justification for covariance intersection and its generalization. In: Proceedings of the 5th International Conference on Information Fusion, 2002. 505–511

    Google Scholar 

  38. Julier S, Uhlmann J K. General decentralized data fusion with covariance intersection. In: Handbook of Multisensor Data Fusion. Boca Raton: CRC Press, 2017. 339–364

    Google Scholar 

  39. Wang B L, Yi W, Hoseinnezhad R, et al. Distributed fusion with multi-bernoulli filter based on generalized covariance intersection. IEEE Trans Signal Process, 2017, 65: 242–255

    MathSciNet  MATH  Google Scholar 

  40. Julier S J, Uhlmann J K. A non-divergent estimation algorithm in the presence of unknown correlations. In: Proceedings of American Control Conference, 1997, 4: 2369–2373

    Google Scholar 

  41. Jia B, Xin M, Cheng Y. High-degree cubature Kalman filter. Automatica, 2013, 49: 510–518

    MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  43. Niehsen W. Information fusion based on fast covariance intersection filtering. In: Proceedings of the 5th International Conference on Information Fusion, 2002, 2: 901–904

    Google Scholar 

  44. Liu G L, Worgotter F, Markelic I. Square-root sigma-point information filtering. IEEE Trans Autom Control, 2012, 57: 2945–2950

    MathSciNet  MATH  Google Scholar 

  45. Leong P H, Arulampalam S, Lamahewa T A, et al. A Gaussian-sum based cubature Kalman filter for bearings-only tracking. IEEE Trans Aerosp Electron Syst, 2013, 49: 1161–1176

    Google Scholar 

  46. Tichavsky P, Muravchik C H, Nehorai A. Posterior Cramer-Rao bounds for discrete-time nonlinear filtering. IEEE Trans Signal Process, 1998, 46: 1386–1396

    Google Scholar 

  47. Golub G H, van Loan C F. Matrix Computations. 4th ed. Baltimore: Johns Hopkins University Press, 2012

    MATH  Google Scholar 

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61790550, 91538201, 61531020, 61671463). The authors give their sincere thanks to the anonymous reviewers for their constructive comments of the manuscripts.

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Authors and Affiliations

  1. Research Institute of Information Fusion, Naval Aviation University, Yantai, 264001, China

    Yu Liu, Jun Liu, Congan Xu & You He

  2. Department of Electronic Engineering, Tsinghua University, Beijing, 100084, China

    Yu Liu & Gang Li

Authors
  1. Yu Liu
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  2. Jun Liu
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  3. Congan Xu
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  4. Gang Li
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  5. You He
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Correspondence to Jun Liu.

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Liu, Y., Liu, J., Xu, C. et al. Fully distributed variational Bayesian non-linear filter with unknown measurement noise in sensor networks. Sci. China Inf. Sci. 63, 210202 (2020). https://doi.org/10.1007/s11432-020-3000-1

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  • DOI: https://doi.org/10.1007/s11432-020-3000-1

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