This paper introduces an approximate approach for filtering,smoothing and estimation of mixture state space models with the observation error being a Gaussian mixture through a degree parameter k governing the maximum number of components in the approximate filter,AMF(k).The proposed approach can be used to estimate time-varying volatilities in the stochastic volatility model by transforming it into the mixture state space form.Simulation results show that the approximate approach performs remarkably well according to both accuracy and relative performance compared to the Kalman filter.