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

### Felix Sawo, Kathrin Roberts, Uwe D. Hanebeck

#### 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.

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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