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 discrete-space 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-3) complexity of the standard Kalman filter.