An Eigenfunction Approach to State Estimation of Distributed Parameter Systems

The spectral decomposition of the process model has been exploited to develop low order state estimation algorithms for linear distributed parameter systems. The use of a measurement function obtained by representing the measurements in an eigenfunction expansion allowed for late discretization and resulted in computationally simple algorithms. It has been demonstrated with the help of experiments and simulations that the algorithm performs well, converges rapidly, requires a relatively small number of measurements and is computationally efficient. Estimates of the state of a very general class of linear distributed parameter systems can be obtained provided the eigenfunctions of the process model are known. Results indicate that the effort required to obtain the spectral properties is justified as good estimates of the state result from using a 3-4 term expansion. The computational effort required is small for the complex multidimensional models studied and the states can be estimated in a fraction of real time on a microcomputer.