Sensor distribution partitioning and filter design for parabolic PDEs using modified Centroidal Voronoi Tessellations

This paper utilizes computational geometry methods to partition the sensor spatial distribution in order to arrive at realistic sensor distributions. An ideal sensor representing a sensor distribution with enhanced observability and filter performance properties is approximated by a network of sensor distributions that describe available sensing devices. Such approximate sensor distributions take the form of spatial delta functions representing realistic sensing devices. The approximation is made feasible via computational geometry methods using a modification of the Centroidal Voronoi Tessellations (CVT). This modified version of CVT ensures that the ideal sensor distribution is partitioned into cells of equal areas and a single pointwise sensor is placed in each cell. Once the ideal sensor distribution is approximated, an optimal filter is subsequently designed for the original process resulting in a state estimator using realistic sensing devices. Extensive numerical studies on a parabolic PDE examine the various aspects of the decomposition using a single and multiple pointwise sensors.