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On Event Based State Estimation

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Hybrid Systems: Computation and Control (HSCC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5469))

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Abstract

To reduce the amount of data transfer in networked control systems and wireless sensor networks, measurements are usually taken only when an event occurs, rather than at each synchronous sampling instant. However, this complicates estimation and control problems considerably. The goal of this paper is to develop a state estimation algorithm that can successfully cope with event based measurements. Firstly, we propose a general methodology for defining event based sampling. Secondly, we develop a state estimator with a hybrid update, i.e. when an event occurs the estimated state is updated using measurements; otherwise the update makes use of the knowledge that the monitored variable is within a bounded set that defines the event. A sum of Gaussians approach is employed to obtain a computationally tractable algorithm.

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References

  1. Akyildiz, I.F., Su, W., Sankarasubramaniam, Y., Cayirci, E.: Wireless Sensor Networks: a survey. Computer Networks 38, 393–422 (2002)

    Article  Google Scholar 

  2. Tabuada, P.: Event-Triggered Real-Time Scheduling for Stabilizing Control Tasks. IEEE Transactions on Automatic Control 52, 1680–1685 (2007)

    Article  MathSciNet  Google Scholar 

  3. Velasco, M., Marti, P., Lozoya, C.: On the Timing of Discrete Events in Event-Driven Control Systems. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 670–673. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  4. Wang, X., Lemmon, M.: State based self-triggered feedback control systems with \(\mathcal{L}_2\) stability. In: 17th IFAC World Congres, Seoul, South Korea (2008) (accepted in IEEE Transactions on Automatic Control)

    Google Scholar 

  5. Heemels, W.P.M.H., Sandee, J.H., van den Bosch, P.P.J.: Analysis of event-driven controllers for linear systems. International Journal of Control 81(4) (2008)

    Google Scholar 

  6. Henningsson, T., Johannesson, E., Cervin, A.: Sporadic event-based control of first-order linear stochastic systems. Automatica 44(11), 2890–2895 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Sorenson, H.W., Alspach, D.L.: Recursive Bayesian estimation using Gaussian sums. Automatica 7, 465–479 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kotecha, J.H., Djurić, P.M.: Gaussian sum particle filtering. IEEE Transaction Signal Processing 51(10), 2602–2612 (2003)

    Article  MathSciNet  Google Scholar 

  9. Johnson, N.L., Kotz, S., Kemp, A.W.: Univariate discrete distributions. John Wiley and Sons, Chichester (1992)

    MATH  Google Scholar 

  10. Aggoun, L., Elliot, R.: Measure Theory and Filtering. Cambridge University Press, Cambridge (2004)

    Book  Google Scholar 

  11. Lebesque, H.L.: Integrale, longueur, aire. PhD thesis, University of Nancy (1902)

    Google Scholar 

  12. Åström, K.J., Bernhardsson, B.M.: Comparison of Riemann and Lebesque sampling for first order stochastic systems. In: 41st IEEE Conf. on Dec. and Contr., Las Vegas, USA (2002)

    Google Scholar 

  13. Miskowicz, M.: Send-on-delta concept: an event-based data-reporting strategy. Sensors 6, 49–63 (2006)

    Article  Google Scholar 

  14. Miskowicz, M.: Asymptotic Effectiveness of the Event-Based Sampling according to the Integral Criterion. Sensors 7, 16–37 (2007)

    Article  Google Scholar 

  15. Kalman, R.E.: A new approach to linear filtering and prediction problems. Transaction of the ASME Journal of Basic Engineering 82(D), 35–42 (1960)

    Article  Google Scholar 

  16. Mallick, M., Coraluppi, S., Carthel, C.: Advances in Asynchronous and Decentralized Estimation. In: Proceeding of the 2001 Aerospace Conference, Big Sky, MT, USA (2001)

    Google Scholar 

  17. Ristic, B., Arulampalam, S., Gordon, N.: Beyond the Kalman filter: Particle filter for tracking applications. Artech House, Boston (2004)

    MATH  Google Scholar 

  18. Nguyen, V.H., Suh, Y.S.: Improving estimation performance in Networked Control Systems applying the Send-on-delta transmission method. Sensors 7, 2128–2138 (2007)

    Article  Google Scholar 

  19. Mardia, K.V., Kent, J.T., Bibby, J.M.: Mutlivariate analysis. Academic Press, London (1979)

    MATH  Google Scholar 

  20. Montgomery, D.C., Runger, G.C.: Applied Statistics and Probability for Engineers. John Wiley and Sons, Chichester (2007)

    MATH  Google Scholar 

  21. Hautus, M.L.J.: Controllability and observability conditions of linear autonomous systems. In: Indagationes Mathemathicae, vol. 32, pp. 448–455 (1972)

    Google Scholar 

  22. Balakrishnan, A.V.: Kalman Filtering Theory. Optimization Software, Inc., New York (1987)

    MATH  Google Scholar 

  23. Sinopoli, B., Schenato, L., Franceschetti, M., Poolla, K., Jordan, M., Sastry, S.: Kalman Filter with Intermittent Observations. IEEE Transactions on Automatic Control 49, 1453–1464 (2004)

    Article  MathSciNet  Google Scholar 

  24. Mo, Y., Sinopoli, B.: A characterization of the critical value for Kalman filtering with intermittent observations. In: 47th IEEE Conference on Decision and Control, Cancun, Mexico, pp. 2692–2697 (2008)

    Google Scholar 

  25. Bernstein, D.S.: Matrix Mathematics. Princeton University Press, Princeton (2005)

    Google Scholar 

  26. Curry, R.E.: Estimation and control with quantized measurements. MIT Press, Boston (1970)

    MATH  Google Scholar 

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Sijs, J., Lazar, M. (2009). On Event Based State Estimation. In: Majumdar, R., Tabuada, P. (eds) Hybrid Systems: Computation and Control. HSCC 2009. Lecture Notes in Computer Science, vol 5469. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00602-9_24

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  • DOI: https://doi.org/10.1007/978-3-642-00602-9_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00601-2

  • Online ISBN: 978-3-642-00602-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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