In recent years, the integration of Wi-Fi, pedestrian dead reckoning (PDR), and indoor map for smartphone-based indoor positioning has gained significant attention due to its low cost, easy implementation, and adequate accuracy. However, consumer microelectromechanical system (MEMS) in smartphones is subject to large deviations in heading estimation. Meanwhile, Wi-Fi signal fluctuations can result in selecting unsuitable reference points, significantly degrading Wi-Fi positioning performance. To deal with these issues and improve positioning accuracy, we first utilize the typical indoor structure (i.e., corners) as constraints to improve heading estimation. Second, we optimize the traditional weighted K-nearest neighbor (WKNN) algorithm, to weaken the effects of Wi-Fi signal fluctuation. Third, we develop an improved integrated positioning algorithm that uses particle filter (PF) to integrate PDR, Wi-Fi, and indoor map including wall lines and corners information. Finally, a backpropagation (BP) neural network-based position mapping model is proposed, which aims to further reduce the errors of the integrated positioning method. The experimental results show that the root-mean-square error (RMSE) of our proposed integrated positioning algorithm using the position mapping model is only 1.12 and 1.23 m at two experimental fields, which is considerably better than the other three existing integrated algorithms.