Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Explicit Probabilistic Derivation of Inflation in a Scalar Ensemble
  Kalman Filter for Finite Step, Finite Ensemble Convergence   This paper uses a probabilistic approach to analyze the converge of an
ensemble Kalman filter solution to an exact Kalman filter solution in the
simplest possible setting, the scalar case, as it allows us to build upon a
rich literature of scalar probability distributions and non-elementary
functions. To this end we introduce the bare-bones Scalar Pedagogical Ensemble
Kalman Filter (SPEnKF). We show that in the asymptotic case of ensemble size,
the expected value of both the analysis mean and variance estimate of the
SPEnKF converges to that of the true Kalman filter, and that the variances of
both tend towards zero, at each time moment. We also show that the ensemble
converges in probability in the complementary case, when the ensemble is
finite, and time is taken to infinity. Moreover, we show that in the
finite-ensemble, finite-time case, variance inflation and mean correction can
be leveraged to coerce the SPEnKF converge to its scalar Kalman filter
counterpart. We then apply this framework to analyze perturbed observations and
explain why perturbed observations ensemble Kalman filters underperform their
deterministic counterparts.

27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org