Computation of the optimal sensor location for the estimation of an 1-D linear dispersive wave equation

The problem of finding the optimal sensor location is considered for a Kalman filter used to estimate the state of an one-dimensional linear dispersive wave equation. Various bases for a Galerkin approximation were studied: sine functions, linear finite elements and a sixth order polynomial finite element basis. The calculated estimator and the optimal sensor location converge for all the bases. For this problem, the sine basis was the most efficient method. Calculations with the noise concentrated in different locations suggest that the sensor should be placed near the noise. However, for measurements with a large noise variance, the sensor location has a smaller effect on estimator performance.