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With the development of Global Navigation Satellite System (GNSS) and the opening of Application Programming Interface (API) of Android terminals, the positioning research of Android terminals has attracted the attention of GNSS community. In this paper, three static experiments were conducted to analyze the raw GNSS observations quality and positioning performances of the smartphones. For the two experimental smartphones, the numbers of visible satellites with dual-frequency signals are unstable and not enough for dual-frequency Precise Point Positioning (PPP) processing all through the day. Therefore, the ionosphere-constrained single-frequency PPP model was employed to improve the positioning with the smartphones, and its performance was evaluated and compared with those of the Single Point Positioning (SPP) and the traditional PPP models. The results show that horizontal positioning accuracies of the smartphones with the improved PPP model are better than 1 m, while those with the SPP and the traditional PPP models are about 2 m. [ABSTRACT FROM AUTHOR]