Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kalman filtering and smoothing for linear wave equations with model
  error   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.

34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
19
The categories of this paper are: eess