This paper examines the effect of the moment-matched single Gaussian approximation, which is made in various multiple-model filtering applications to approximate a Gaussian mixture, on the Bayesian filter performance. The estimation error caused by the approximation is analysed for both the prediction and the measurement updates of a Bayesian filter. An approximate formula is found for the covariance of the error caused by the approximation for a general Gaussian mixture with arbitrary components. The calculated error covariance is used for obtaining a mixed multiple-model estimation algorithm which has a performance near that of GPB2 with less computations.