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

Conventional optimal estimation algorithms for distributed parameter system s have been limited due to their computational complexity. In this paper, w e consider an alternative modeling framework recently developed for large-s cale static estimation problems and extend this methodology to dynamic esti mation. Rather than propagate estimation error statistics in conventional r ecursive estimation algorithms, we propagate a more compact multiscale mode l for the errors. In the context of 1-D diffusion which we use to illustrat e the development of our algorithm, for a discrete-space process of N point s the resulting multiscale estimator achieves O(N log N) computational comp lexity (per time step) with near-optimal performance as compared to the O(N -3) complexity of the standard Kalman filter. (C) 2001 Elsevier Science Ltd . All rights reserved.