Low-cost GNSS receivers, such as U-Blox, have become a mass-market device used by millions of people every day. Current positioning accuracy of few meters with these devices is not precise enough for applications such as intelligent transportation systems, precise agriculture and unmanned aerial vehicle (UAV) guidance, which requiring sub-meter to centimeter level accuracy. Real-Time Kinematics (RTK) is a differential method that can steady offer centimeter level solutions in real time if a dual-frequency geodetic GNSS receiver and a physical or virtual base station are available. However, such geodetic-grade receivers are currently too expensive to gain popularity in the mass market. In this paper, we proposed a single-frequency GPS/BDS RTK algorithm using raw carrier phase, pseudorange and Doppler observations from a low-cost GNSS receiver. As we all know, this kind of receiver is usually designed for mass-market applications, so constraints in power consumption and costs are very stringent and then result in lower-quality measurements compared to high-precision receiver. There are two main challenges that code measurements suffer from serious multipath error and carrier phase measurements frequently loss of lock. To cope with these problems, a new outlier and cycle slip detection strategy is developed and a new robust Kalman filter is implemented. The RTK implementation presented in this paper utilizes the Hi-Target Continuously Operating Reference Stations Network (HT-CORS) as the base station, both in single-base and network RTK mode. For comparison purpose, a geodetic-grade dual-frequency receiver is also used to provide a reference position solution in different testing scenarios. The test results show that a horizontal position accuracy of better than 0.5 meters can be achieved for more than 99% of the time using a U-Blox M8T receiver with a small helix antenna in kinematic mode. Both single-baseline and network RTK experiment show comparable positioning performance. Obtaining sub-meter accuracy with such a low-cost device expected to be useful in various precise applications, such as intelligent transportation systems and geographic information system. Furthermore, we investigated the possibility of ambiguity resolution (AR) with this low-cost receiver in a post-processing test. Instead of a helix antenna, we use an external high precise antenna (~150$) to guarantee that code measurements are good enough to provide carrier phase ambiguity datum. A Trimble BD970 dual-frequency GNSS receiver, which is one of the stations of HT-CORS, is selected as the single-base station. Both static and kinematic observations are collected within a short-baseline (<10km) with time span of 4 hours and half an hour, respectively. A new partial ambiguity resolution (PAR) algorithm is adopted, which is of great benefit when full ambiguity resolution fails under challenging conditions. The results are encouraging that a positioning accuracy of 1.2cm (2D RMS) is achievable in static mode, with an ambiguity fixing rate greater than 98%. For kinematic test, the ambiguity fixing rate is about 90% and a positioning accuracy of 2.4cm (2D RMS) is also achievable. The results indicate that using a consumer-grade receiver can obtain comparable accuracy instead of using an expensive geodetic-grade receiver, making it a promising technique in various high precise applications, especially in the field of UAV guidance.