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This paper describes a robust glottal source estimation method based on a joint source-filter separation technique. In this method, the glottal flow derivative is modelled as the Liljencrants-Fant (LF) model and the vocal tract is described as a time-varying ARX model. Since the joint estimation problem is a multi-parameter nonlinear optimization procedure, we separate the optimization procedure into two passes. The first pass initializes the glottal source and vocal tract models providing robust initial parameters to the following joint optimization procedure. The joint estimation determines the accuracy of model estimation, which is implemented with a trust-region descent optimization algorithm. Experiments with synthetic and real voices show the proposed method is a robust glottal source parameter estimation method with a considerable degree of accuracy.