Computationally efficient steady-state multiscale estimation for 1-D diffusion processes (Q5930057)

A new methodology of dynamic estimation for distributed parameter systems governed by PDE's is presented. The approach is based on implicit calculations and propagations of statistics for the estimation error as a sequence of multiscale models. The multiscale stochastic modelling and estimation methodology has been developed in: \textit{M. Basseville}, IEEE Trans. Inf. Theory 38, 766-784 (1992) and \textit{K. Chou, A. Willsky} and \textit{A. Benveniste}, IEEE Trans. Autom. Control 39, No. 3, 464-478 (1994; Zbl 0828.93062). Computational complexity of the proposed method is significantly lower compared to that of the standard Kalman filter. The method is especially suitable for large scale systems. An example concerning a 1D diffusion is discussed.