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

Conventional optimal estimation algorithms for distributed parameter systems have been limited due to their computational complexity. In this paper, we consider an alternative modeling framework recently developed for large-scale static estimation problems and extend this methodology to dynamic estimation. Rather than propagate estimation error statistics in conventional recursive estimation algorithms, we propagate a more compact multiscale model for the errors. In the context of 1-D diffusion which we use to illustrate the development of our algorithm, for a discretespace process of N points the resulting multiscale estimator achieves O(N log N) computational complexity (per time step) with near-optimal performance as compared to the O(N) complexity of the standard Kalman filter.