|Title||Computationally efficient steady-state multiscale estimation for 1-D diffusion processes|
|Publication Type||Journal Article|
|Year of Publication||2001|
|Authors||Ho, T. T., P. Fieguth, and A. S. Willsky|
|Pagination||325 - 340|
|Keywords||diffusion, distributed parameter systems, dynamic estimation, multiscale realization|
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.