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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 Liljencrants-Fant (LF) model, which models the glottal flow derivative, is integrated into a time-varying ARX speech production model. These two models are estimated in a joint optimization procedure, in which a Kalman filtering process is embedded for adaptively identifying the vocal tract parameters. Since the formulated joint estimation problem is a multiparameter nonlinear optimization procedure, we separate the optimization procedure into two passes. The first pass initializes the glottal source and vocal tract models by solving a quasi-convex approximate optimization problem. Having robust initial values, the joint estimation procedure determines the accuracy of model estimation implemented with a trust-region descent optimization algorithm. Experiments with synthetic and real voice signals show that the proposed method is a robust glottal source parameter estimation method with a high degree of accuracy.