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

Authors:
Terrence T. Ho;Paul W. Fieguth;Alan S. Willsky
Affiliations:
Booz Allen & Hamilton, New York, USA;Systems Design Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1;Massachusetts Institute of Technology, Cambridge, MA, USA
Venue:
Automatica (Journal of IFAC)
Year:
2001

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Abstract

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(NlogN) computational complexity (per time step) with near-optimal performance as compared to the O(N^3) complexity of the standard Kalman filter.