  The Gaussian mixture distribution is important in various statistical
problems. In particular it is used in the Gaussian-sum filter and smoother for
linear state-space model with non-Gaussian noise inputs. However, for this
method to be practical, an efficient method of reducing the number of Gaussian
components is necessary. In this paper, we show that a closed form expression
of Pearson chi^2-divergence can be obtained and it can apply to the
determination of the pair of two Gaussian components in sequential reduction of
Gaussian components. By numerical examples for one dimensional and two
dimensional distribution models, it will be shown that in most cases the
proposed criterion performed almost equally as the Kullback-Libler divergence,
for which computationally costly numerical integration is necessary.
Application to Gaussian-sum filtering and smoothing is also shown.
