  In this paper we consider the behavior of Kalman Filter state estimates in
the case of distribution with heavy tails .The simulated linear state space
models with Gaussian measurement noises were used. Gaussian noises in state
equation are replaced by components with alpha-stable distribution with di
erent parameters alpha and beta. We consider the case when "all parameters are
known" and two methods of parameters estimation are compared: the maximum
likelihood estimator (MLE) and the expectation- maximization algorithm (EM). It
was shown that in cases of large deviation from Gaussian distribution the total
error of states estimation rises dramatically. We conjecture that it can be
explained by underestimation of the state equation noises covariance matrix
that can be taken into account through the EM parameters estimation and ignored
in the case of ML estimation.
