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The positioning accuracy of the conventional GNSS can be degraded severely in dense urban areas due to the blockage and the reflection of satellite signals, resulting in measurement errors varying from tens to hundreds of meters. To improve the GNSS performance, receiver autonomous integrity monitoring (RAIM) approaches have been widely adopted. However, these methods are insufficient to obtain high-precision solutions in deep urban canyons. Three-dimension (3D) city models can be used to predict the satellite visibility and calculate the path delays of satellite signals, which have been involved in 3D-mapping-aided (3DMA) approaches to improve the GNSS performance. However, the heavy computational burden and poor availability of 3D models in most cities have restricted the deployment of this method. Therefore, an efficient approach without using 3D models is desperately needed to improve the positioning accuracy in urban canyons. In this paper, we propose a novel approach, named multi-epoch offset searching (MEOS), to improve the positioning performance of GNSS technology under GNSS-challenged environments. It utilizes raw GNSS measurements to mitigate multipath effects in the measurement domain. The MEOS approach is innovative in using the short-term GNSS measurement residuals with the PDR technology to identify LOS and NLOS signals, and further to achieve high-precision positioning in urban canyons. Theory of the proposed method is introduced, and experiments are conducted to verify the theory and validate the performance of the proposed algorithm. The results show that the proposed method is effective to obtain positioning solution with higher accuracy using minimal satellites. Under the situation that several satellites were contaminated by multipath effects, the proposed method could remove the contaminated satellites, and obtain the positioning solution with high accuracy. It shows the potential to achieve realtime and high-precision GNSS positioning in urban canyons.