  The covariance matrix of measurements of Markov random fields (processes) has
useful properties that allow to develop effective computational algorithms for
many problems in the study of Markov fields on the basis of field observations
(parametric identification problems, filtering problems, interpolation problems
and others). Therefore, approximation of arbitrary random fields by Markov
fields is of great interest, as it gives an opportunity to use computationally
efficient algorithms of Markov fields analysis to study them. The paper deals
with approximation of the covariance matrix of the field being observed with
the help of covariance matrix of a multiply connected (m-connected) Markov
field. Using computer simulation, the accuracy of such replacements at
different values of the connectivity coefficient m for the problem of
parametric identification of deterministic component of the field has been
studied. Various models of deterministic polynomial component of the field and
a number of covariance functions that are often used as a mathematical model of
real random noise and measurements noise have been reviewed. It has been shown
that for many problems such approximation, even at small connectivity m values
of approximating Markov field, provides necessary accuracy. This allows to
achieve good compromise between accuracy of the estimates and complexity of
calculating them.
