Optimization of measurements for state estimation in parabolic distributed systems

The aim of this paper is to consider the optimal, from the viewpoint of a state estimation accuracy, measurement location problem in linear distributed-parameter systems with white Gaussian noises. In contrary to earlier works the proposed approach consists of two steps. Namely, to find closed form solution for the optimal measurement weighting function (MWF), assuming measurements continuous in space, and then to approximate this solution using point sensors. At the first step it was also shown that the Green function of the system can be used as a suboptimal MWF. State estimation in one-dimensional heat transfer problem illustrates the results.