Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
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Tawsif Khan, MMath Candidate
Department of Applied Mathematics, University of Waterloo
Optimal Sensor Location for the Estimation of a Linear Dispersive Wave Equation
The problem of optimal sensor location for the estimation of a linear dispersive wave equation is considered in this work. A steady-state Kalman filter was used as an optimal state observer with localized velocity information as the measurement. Since the main model is a partial differential equation, the states evolve in infinite-dimensional spaces, and hence an approximation (finite representation) was required to design the observer. Three different approximation methods were compared - eigenfunctions and finite element methods using a linear and a high-order polynomial basis. The latter two methods are the more common choice of approximation schemes for systems with a complex geometry. It was found that the eigenfunctions perform much better as expected. The finite element methods require larger matrices to approximate the system with reasonable accuracy and hence calls for numerical methods to solve the Algebraic Riccati Equation efficiently. The optimal sensor location was considered for three different noise models - a localized noise, a more distributed nature of noise and finally an one-dimensional turbulence model. It was seen that the optimal location tend to be closer to the point where the physical shape of the noise reaches its maximum. Placing the sensor in the optimal location showed significant improvement in the estimation process.
Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
PDF files require Adobe Acrobat Reader
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within the Office of Indigenous Relations.