Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Forward-backward kernel-based state and parameter estimation for linear
  systems of arbitrary order   Previous results pertaining to algebraic state and parameter estimation of
linear systems based on a special construction of a forward-backward kernel
representation of linear differential invariants are extended to handle large
noise in output measurement. Explicit expressions for the kernel functions for
single-input, single-output (SISO) linear time-invariant (LTI) systems of
arbitrary order are first stated and proved. A two-stage solution of the
estimation problem is proposed next. The parameter estimation sub-problem,
which is the task of the first stage, is solved by way of stochastic
regression. The parameter estimation method presented in earlier publications
is enhanced using multiple regression. The regression model does not satisfy
the assumptions of the Gauss-Markov theorem in that the random regressor is
heteroskedastic. This does not impede achieving high accuracy of estimation. A
recursive version of a feasible generalized least squares with covariance
weighting is employed to attenuate adverse effects due to heteroskedasticity.
The output of the system and its time derivatives are reconstructed smoothly in
the second stage of the approach by way of projection, while minimizing a mean
square criterion.

27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex