Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

State Estimation in Linear Dynamical Systems By Partial Update Kalman Filtering

  • Short Paper
  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

In this letter, we develop a partial update Kalman filtering (PUKF) algorithm to solve the state of a discrete-time linear stochastic dynamical system. In the proposed algorithm, only a subset of the state vector is updated at every iteration, which reduces its computational complexity, compared to the original KF algorithm. The required conditions for the stability of the algorithm are discussed. A closed-form expression for steady-state mean-square deviation is also derived. Numerical examples are used to validate the correctness of the provided analysis. They also reveal the PUKF algorithm exhibits a trade-off between the estimation accuracy and the computational load which is extremely profitable in practical applications.

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
$34.99 /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 excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Data Availability

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

References

  1. R. Arablouei, S. Werner, K. Dogancay, Partial-diffusion recursive least-squares estimation over adaptive networks. In Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)

  2. R. Arablouei, S. Werner, Y.-F. Huang, K. Dogancay, Distributed least mean-square estimation with partial diffusion. IEEE Trans. Signal Process. 62(2), 472–484 (2014)

    Article  MathSciNet  Google Scholar 

  3. R. Claser, V.H. Nascimento, Low-complexity approximation to the kalman filter using convex combinations of adaptive filters from different families (2017), pp. 2630–2633

  4. F.S.C. Dobarro, Distributed collaborative processing over adaptive networks (University of California, Los Angeles, 2010)

    Google Scholar 

  5. S.C. Douglas, Adaptive filters employing partial updates. IEEE Trans. Circuits Syst. II Analog Digit. Signal Process. 44(3), 209–216 (1997)

    Article  Google Scholar 

  6. H. Fang, G. Zhu, V. Stojanovic, R. Nie, S. He, X. Luan, F. Liu, Adaptive optimization algorithm for nonlinear markov jump systems with partial unknown dynamics. Int. J. Robust Nonlinear Control 31(6), 2126–2140 (2021)

    Article  MathSciNet  Google Scholar 

  7. M. Godavarti, A.O. Hero, Partial update lms algorithms. IEEE Trans. Signal Process. 53(7), 2382–2399 (2005)

    Article  MathSciNet  Google Scholar 

  8. J.B. Jorgensen, P.G. Thomsen, H. Madsen, M.R. Kristensen, A computationally efficient and robust implementation of the continuous-discrete extended Kalman filter (2007), pp. 3706–3712

  9. T. Kailath, A.H. Sayed, B. Hassibi, Linear estimation (Prentice Hall, Number BOOK, 2000)

    MATH  Google Scholar 

  10. M. Katzfuss, J.R. Stroud, C.K. Wikle, Ensemble kalman methods for high-dimensional hierarchical dynamic space-time models. J. Am. Stat. Assoc. 115(530), 866–885 (2020)

    Article  MathSciNet  Google Scholar 

  11. A. Khalili, V. Vahidpour, A. Rastegarnia, W.M. Bazzi, S. Sanei, Partial diffusion kalman filter with adaptive combiners. IEEE Trans. Aerosp. Electron. Syst. 57, 1972 (2020)

    Article  Google Scholar 

  12. C. Li, S. Chu, S. Tsai, Improved variable step-size partial update lms algorithm (2016), pp. 17–19

  13. K. Mayyas, L. Afeef, A variable step-size partial-update normalized least mean square algorithm for second-order adaptive volterra filters. Circuits Syst. Signal Process. 39, 6073–6097 (2020)

    Article  Google Scholar 

  14. J. Minglu, Partial updating rls algorithm. In Proceedings 7th International Conference on Signal Processing, 2004. Proceedings. ICSP ’04. 2004. 1, 392–395 (2004)

  15. M. Raitoharju, R. Piché, On computational complexity reduction methods for Kalman filter extensions. IEEE Aerosp. Electron. Syst. Mag. 34(10), 2–19 (2019)

    Article  Google Scholar 

  16. M. Roth, G. Hendeby, C. Fritsche, F. Gustafsson, The ensemble Kalman filter: a signal processing perspective. EURASIP J. Adv. Signal Process (2017). https://doi.org/10.1186/s13634-017-0492-x

    Article  Google Scholar 

  17. V. Stojanovic, D. Prsic, Robust identification for fault detection in the presence of non-gaussian noises: application to hydraulic servo drives. Nonlinear Dyn. 100, 2299–2313 (2020)

    Article  Google Scholar 

  18. V. Stojanovic, S. He, B. Zhang, State and parameter joint estimation of linear stochastic systems in presence of faults and non-gaussian noises. Int. J. Robust Nonlinear Control 30(16), 6683–6700 (2020)

    Article  MathSciNet  Google Scholar 

  19. X. Sun, M. Medvedovic, Model reduction and parameter estimation of non-linear dynamical biochemical reaction networks. IET Syst. Biol. 10(1), 10–16 (2016)

    Article  Google Scholar 

  20. V. Vahidpour, A. Rastegarnia, A. Khalili, S. Sanei, Partial diffusion Kalman filtering for distributed state estimation in multiagent networks (2019a)

  21. V. Vahidpour, A. Rastegarnia, A. Khalili, W.M. Bazzi, S. Sanei, Analysis of partial diffusion lms for adaptive estimation over networks with noisy links. IEEE Trans. Network Sci. Eng. 5(2), 101–112 (2017a)

    Article  MathSciNet  Google Scholar 

  22. V. Vahidpour, A. Rastegarnia, A. Khalili, S. Sanei, Analysis of partial diffusion recursive least squares adaptation over noisy links. IET Signal Proc. 11(6), 749–757 (2017b)

    Article  Google Scholar 

  23. V. Vahidpour, A. Rastegarnia, M. Latifi, A. Khalili, S. Sanei, Performance analysis of distributed Kalman filtering with partial diffusion over noisy network. IEEE Trans. Aerosp. Electron. Syst. 56, 1767 (2019b)

    Article  Google Scholar 

  24. V. Vahidpour, A. Rastegarnia, A. Khalili, W.M. Bazzi, S. Sanei, Variants of partial update augmented clms algorithm and their performance analysis. IEEE Trans. Signal Process. 68, 3146–3157 (2020)

    MathSciNet  Google Scholar 

  25. S. Werner, M.L. De Campos, P.S. Diniz, Partial-update NLMS algorithms with data-selective updating. IEEE Trans. Signal Process. 52(4), 938–949 (2004)

    Article  MathSciNet  Google Scholar 

  26. B. Xie, T. Bose, Partial update least-square adaptive filtering. Synth. Lect. Commun. 7(1), 1–115 (2014)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Electrical Engineering Department, Urmia University of Technology, Band Road, P.O. Box 57155-419, Urmia, Iran

    Yaghoub Pourasad

  2. Department of Electrical Engineering, Malayer University, Malayer, 65719-95863, Iran

    Vahid Vahidpour & Amir Rastegarnia

  3. Computer Engineering Department, Urmia University of Technology, Urmia, Iran

    Parviz Ghorbanzadeh

  4. School of Science and Technology, Nottingham Trent University, Nottingham, NG11 8NS, UK

    Saeid Sanei

Authors
  1. Yaghoub Pourasad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vahid Vahidpour
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Amir Rastegarnia
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Parviz Ghorbanzadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Saeid Sanei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yaghoub Pourasad.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pourasad, Y., Vahidpour, V., Rastegarnia, A. et al. State Estimation in Linear Dynamical Systems By Partial Update Kalman Filtering. Circuits Syst Signal Process 41, 1188–1200 (2022). https://doi.org/10.1007/s00034-021-01815-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-021-01815-5

Keywords

Search

Navigation