BAYESIAN ESTIMATION OF DISTRIBUTED PHENOMENA USING DISCRETIZED REPRESENTATIONS OF PARTIAL DIFFERENTIAL EQUATIONS

Felix Sawo, Kathrin Roberts, Uwe D. Hanebeck

2006

Abstract

This paper addresses a systematic method for the reconstruction and the prediction of a distributed phenomenon characterized by partial differential equations, which is monitored by a sensor network. In the first step, the infinite-dimensional partial differential equation, i.e. distributed-parameter system, is spatially and temporally decomposed leading to a finite-dimensional state space form. In the next step, the state of the resulting lumped-parameter system, which provides an approximation of the solution of the underlying partial differential equations, is dynamically estimated under consideration of uncertainties both occurring in the system and arising from noisy measurements. By using the estimation results, several additional tasks can be achieved by the sensor network, e.g. optimal sensor placement, optimal scheduling, and model improvement. The performance of the proposed model-based reconstruction method is demonstrated by means of simulations.

References

  1. Anderson, B. D. O. and Moore, J. B. (1979). Optimal Filtering. Prentice-Hall.
  2. Baker, A. J. (1983). Finite Element Computational Fluid Mechanics. Taylor and Francis.
  3. Culler, D. E. and Mulder, H. (2004). Smart sensors to network the world. In Scientific American.
  4. Faulds, A. L. and King, B. B. (2000). Sensor location in feedback control of partial differential equation systems. In CCA'00, Proceedings of the 2000 IEEE International Conference on Control Applications.
  5. Fournier, A., Bunge, H.-P., Hollerbach, R., and Vilotte, J.-P. (2004). Application of the spectral-element method to the axisymmetric navier-stokes equation. In Geophysical Journal International.
  6. Hanebeck, U. D., Briechle, K., and Rauh, A. (2003). Progressive bayes: A new framework for nonlinear state estimation. In Proceedings of SPIE, AeroSense Symposium.
  7. Karniadakis, G. E. and Sherwin, S. (2005). Spectral/hp Element Methods for Computational Fluid Dynamics. Oxford University Press.
  8. Kumar, T., Zhao, F., and Shepherd, D. (2002). Collaborative signal and information processing in microsensor networks. In IEEE Signal Processing Magazine.
  9. Levin, J. G., Iskandarani, M., and Haidvogel, D. B. (2000). A nonconforming spectral element ocean model. In International Journal for Numerical Methods in Fluids.
  10. Ortmaier, T., Groeger, M., Boehm, D. H., Falk, V., and Hirzinger, G. (2005). Motion estimation in beating heart surgery. In IEEE Transactions on Biomedical Engineering.
  11. Rao, B., Durrant-Whyte, H., and Sheen, J. (1993). A fully decentralized multisensor system for tracking and surveillance. In International Journal of Robotics Research.
  12. Roberts, K. and Hanebeck, U. D. (2005). Prediction and reconstruction of distributed dynamic phenomena characterized by linear partial differential equations. In Fusion'05, The Eight International Conference on Information Fusion.
  13. Thuraisingham, B. (2004). Secure sensor information management and mining. In IEEE Signal Processing Magazine.
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Paper Citation


in Harvard Style

Sawo F., Roberts K. and D. Hanebeck U. (2006). BAYESIAN ESTIMATION OF DISTRIBUTED PHENOMENA USING DISCRETIZED REPRESENTATIONS OF PARTIAL DIFFERENTIAL EQUATIONS . In Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO, ISBN 978-972-8865-61-0, pages 16-23. DOI: 10.5220/0001203800160023


in Bibtex Style

@conference{icinco06,
author={Felix Sawo and Kathrin Roberts and Uwe D. Hanebeck},
title={BAYESIAN ESTIMATION OF DISTRIBUTED PHENOMENA USING DISCRETIZED REPRESENTATIONS OF PARTIAL DIFFERENTIAL EQUATIONS},
booktitle={Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,},
year={2006},
pages={16-23},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001203800160023},
isbn={978-972-8865-61-0},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,
TI - BAYESIAN ESTIMATION OF DISTRIBUTED PHENOMENA USING DISCRETIZED REPRESENTATIONS OF PARTIAL DIFFERENTIAL EQUATIONS
SN - 978-972-8865-61-0
AU - Sawo F.
AU - Roberts K.
AU - D. Hanebeck U.
PY - 2006
SP - 16
EP - 23
DO - 10.5220/0001203800160023