Positioning accuracy and efficiency are two important features for embedded positioning devices of Internet of Things (IoT) in smart cities. In modern urban canyon environments, Non Line-of-Sight (NLoS) satellite signals may degrade positioning accuracy. The mirror ray tracing algorithm can be used to reconstruct NLoS propagation path and enhance positioning accuracy. However, for the embedded positioning devices of IoT, real-time reconstruction of NLoS propagation path is difficult. In this article, an inherited sampling algorithm ensuring positioning accuracy and efficiency is proposed. Experimental results show that the proposed inherited sampling algorithm saves computation time by 69.8% compared to the double sampling algorithm. Furthermore, a mirror ray tracing accelerator is designed and built in FPGA, which greatly reduces the NLoS path reconstruction time. Finally, a real-time positioning system with a CPU and FPGA heterogeneous architecture is built. For a single trajectory point, test results show that the correction time of the proposed inherited sampling algorithm with an FPGA accelerator takes only 0.45 s, which is 80 times faster than that with CPU calculation alone.