Kalman filtering and smoothing for linear wave equations with model error

Details Kalman filtering and smoothing for linear wave equations with model error Kalman filtering and smoothing for linear wave equations with model error

2011-01-26

arxiv.org/abs/1101.5096v2

Mathematics

Probability

Scientific paper

Filtering is a widely used methodology for the incorporation of observed data into time-evolving systems. It provides an online approach to state estimation inverse problems when data is acquired sequentially. The Kalman filter plays a central role in many applications because it is exact for linear systems subject to Gaussian noise, and because it forms the basis for many approximate filters which are used in high dimensional systems. The aim of this paper is to study the effect of model error on the Kalman filter, in the context of linear wave propagation problems. A consistency result is proved when no model error is present, showing recovery of the true signal in the large data limit. This result, however, is not robust: it is also proved that arbitrarily small model error can lead to inconsistent recovery of the signal in the large data limit. If the model error is in the form of a constant shift to the velocity, the filtering and smoothing distributions only recover a partial Fourier expansion, a phenomenon related to aliasing. On the other hand, for a class of wave velocity model errors which are time-dependent, it is possible to recover the filtering distribution exactly, but not the smoothing distribution. Numerical results are presented which corroborate the theory, and also to propose a computational approach which overcomes the inconsistency in the presence of model error, by relaxing the model.

Affiliated with

Also associated with

No associations

Rating

Kalman filtering and smoothing for linear wave equations with model error does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Kalman filtering and smoothing for linear wave equations with model error, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Kalman filtering and smoothing for linear wave equations with model error will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-419493