This paper proposes a pedestrian dead reckoning (PDR) algorithm based on the strap-down inertial navigation system (SINS) using the gyros, accelerometers, and magnetometers on smartphones. In addition to using a gravity vector, magnetic field vector, and quasi-static attitude, this algorithm employs a gait model and motion constraint to provide pseudo-measurements (i.e., three-dimensional ... [Show full abstract] velocity and two-dimensional position increment) instead of using only pseudo-velocity measurement for a more robust PDR algorithm. Several walking tests show that the advanced algorithm can maintain good position estimation compare to the existing SINS-based PDR method in the four basic smartphone positions, i.e., handheld, calling near the ear, swaying in the hand, and in a pants pocket. In addition, we analyze the navigation performance difference between the advanced algorithm and the existing gait-model-based PDR algorithm from three aspects, i.e., heading estimation, position estimation, and step detection failure, in the four basic phone positions. Test results show that the proposed algorithm achieves better position estimation when a pedestrian holds a smartphone in a swaying hand and step detection is unsuccessful.