Kalman Filter Based Sensor Placement For Burgers Equation

Abstract

The algorithm used for determining sensor placement in this thesis will be based on the Kalman filter. This filter is very famous and its application are numerous - some examples include aircraft navigation, finance and weather forecasting. It is used to extract an estimate of the true state of a system based on noisy measurements. For linear systems, where the noise satisfies certain assumptions, the Kalman filter minimizes the expected squared error between the filter's estimate and the true state of the system. By varying the sensor location, and therefore the observation matrix, one can further minimize the expected squared error to determine an optimal sensor placement. For linear systems, a regular as well as steady state Kalman filter are used for the sensor placement algorithm. This thesis examines this concept further, for nonlinear systems by using the Extended Kalman filter.