  In a strongly nonlinear system the particle distribution in the phase space
may develop long tails which contribution to the covariance (sigma) matrix
should be suppressed for a correct estimate of the beam emittance. A method is
offered based on Gaussian approximation of the original particle distribution
in the phase space (Klimontovich distribution) which leads to an equation for
the sigma matrix which provides efficient suppression of the tails and cannot
be obtained by introducing weights. This equation is easily solved by
iterations in the multi-dimensional case. It is also shown how the
eigen-emittances and coupled optics functions can be retrieved from the sigma
matrix in a strongly coupled system. Finally, the developed algorithm is
applied to 6D ionization cooling of muons in HFOFO channel.
